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Kathleen Schueller Richardson 



ORGANIC CHEMxo x xv x 


Smith College 


The Ohio State University 

Harper & Row, Publishers 

New York, Hagerstown, San Francisco, London 

To Nancy and Frank 

Sponsoring Editor : John A. Woods 
Special Projects Editor : Carol J. Dempster 
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Mechanism and Theory in Organic Chemistry 

Copyright © 1 976 by Thomas H. Lowry and Kathleen Schueller Richardson 

All rights reserved. Printed in the United States of America. No part of this book may be used or 
reproduced in any manner whatsoever without written permission except in the case of brief quotations 
embodied in critical articles and reviews. For information address Harper & Row, Publishers, Inc., 
10 East 53rd Street, New York, N. Y. 10022. 

Library of Congress Cataloging in Publication Data 

Lowry, Thomas H. 

Mechanism and theory in organic chemistry. 

Includes bibliographical references and index. 

1. Chemistry, Physical organic. I. Richardson, 
Kathleen Schueller, joint author. II. Title. 
QD476.L68 547'. 1'3 75-43926 

ISBN 0-06-044082-1 


Preface ix 


1.1 Models of Chemical Bonding 1 

1 .2 Molecular Orbitals 9 

1.3 Hybrid Orbitals 20 

1.4 Delocalized it Bonding 27 

1 .5 Aromaticity 28 
Problems 40 

Appendix 1 : Hybrid Orbitals 43 
Appendix 2 : Molecular Orbital Theory 50 


2.1 Stereochemistry 57 

2.2 Linear Free-Energy Relationships 60 

2.3 Thermochemistry 71 

2.4 Solutions 84 

2.5 Kinetics 90 

2.6 Interpretation of Rate Constants 94 

2.7 Isotope Effects 105 
Problems 1 1 1 


vi Contents 

Appendix 1 : Derivation of the Transition State Theory Expression for a 

Rate Constant 113 
Appendix 2: The Transition State Theory of Isotope Effects 120 


3.1 Br0nsted Acids and Bases 124 

3.2 Strengths of Weak Br0nsted Bases 129 

3.3 Strengths of Weak Br0nsted Acids 138 

3.4 substituent effects on strengths of br0nsted acids and 
Bases 150 

3.5 Lewis Acids and Bases 163 
Problems 168 


4.1 Sjyl and S w 2 Substitution Mechanisms 171 

4.2 Stereochemistry of the S^2 Reaction 174 

4.3 The Solvent, Substrate, Nucleophile, and Leaving Group 
^ 177 


BON 203 

Problems 210 


5.1 Limiting Unimolecular Nucleophilic Reactions — Kinetics 
and Stereochemistry 213 

5.2 Limiting Unimolecular Nucleophilic Reactions — Effects of 
Structure and Solvent 222 

5.3 Carbocations 233 

'57? s Mechanisms Intermediate Between S^l and S n 2 237 
bj* Unimolecular Electrophilic Substitutions — Carbanions 250 

5.6 Carbenes 256 
Problems 265 


6.1 1,2-Shifts in Carbenium Ions 268 
^P Carbonium Ions 288 
6.3 Migrations to Carbonyl Carbon 316 

6\4) Rearrangement to Electron-Deficient Nitrogen and Oxy- 
"^ gen 318 

Problems 332 


7.1 Electrophilic Addition to Double and Triple Bonds 337 

7.2 1,2-Elimination Reactions 355 

7.3 Nucleophilic Addition to Multiple Bonds 377 

Contents vii 

7.4 Elegtrophilic Aromatic Substitution 379 

7.5 Nucleophilic Aromatic Substitution 395 
Problems 399 


8. 1 Hydration and Acid-Base Catalysis 403 

8.2 Other Simple Additions 416 

8.3 Addition Followed by Elimination 424 

8.4 Addition of Nitrogen Nucleophiles 432 

8.5 Carboxylic Acid Derivatives 439 

8.6 Enols, Enolates, and Addition of Carbon Nucleophiles to 
C=0 449 

Problems 459 


9. 1 Characteristics of Organic Free Radicals 462 

9.2 Radical Reactions 475 

9.3 Free-Radical Substitutions 497 

9.4 Radical Additions and Eliminations 506 

9.5 Rearrangements of Radicals 517 
Problems 524 

Appendix 1 : Chemically Induced Dynamic Nuclear Polarization 
(CIDNP) 527 


10.1 Perturbation Theory 538 

10.2 Symmetry 541 

10.3 Interactions Between Molecules 552 

10.4 Application of Perturbation Theory and Symmetry to it 
Systems 559 

Problems 566 


11.1 Definitions 569 

11.2 Perturbation Theory in Pericyclic Reactions 579 

11.3 Correlation Diagrams and Pericyclic Selection Rules 581 

11.4 Interaction Diagrams and the Generalized Woodward- 
Hoffmann Pericyclic Selection Rules 596 

11.5 Aromatic and Antiaromatic Transition States 602 

11.6 Comparison of the Woodward-Hoffmann and Dewar- 
Zimmerman Pericyclic Selection Rules 611 

11.7 Correlation of Electronic States 617 
Problems 623 

RULES 626 

12.1 Cycloadditions 626 

12.2 Electrocyclic Reactions 645 

viii Contents 

12.3 Sigmatropic Reactions 657 
Problems 677 


13.1 Light Absorption 681 

13.2 Unimolecular Photophysical Processes 687 

13.3 Bimolecular Photophysical Processes 693 

13.4 Photochemical Reactions 706 
Problems 729 

Index 731 


This book is intended as a text for undergraduate and first-year graduate 
students who have completed a one-year course in organic chemistry. Its aim 
is to provide a structure that will help the student to organize and interrelate ,- 
the factual information obtained in the earlier course and serve as a basis for '"V 
study in greater depth of individual organic reactions and of methods by which 
chemists obtain information about chemical processes. 

The primary focus of the book is on reaction mechanisms, not only because 
knowledge of mechanism is essential to understanding chemical processes but 
also because theories about reaction mechanisms can explain diverse chemical 
phenomena in terms of a relatively small number of general principles. It is 
this latter capability of mechanistic theory which makes it important as an 
organizing device for the subject of organic chemistry as a whole. 

In treating mechanisms of the important classes of organic reactions, we 
have tried to emphasize the experimental evidence upon which mechanistic 
ideas are built and to point out areas of uncertainty and controversy where 
more work still needs to be done. In this way we hope to avoid giving the 
impression that all organic mechanisms are well understood and completely 
agreed upon but instead to convey the idea that the field is a dynamic one, still 
very much alive and filled with surprises, excitement, and knotty problems. 

The organization of the book is traditional. We have, however, been\ 
selective in our choice of topics in order to be able to devote a significant portion I 
of the book to the pericyclic reaction theory and its applications and to include 
a chapter on photochemistry. 

The pericyclic theory is certainly the most important development in 
mechanistic organic chemistry in the past ten years. Because it is our belief that 


x Preface 

the ideas and method of thinking associated with the pericyclic theory will have 
an increasing impact in both organic and inorganic chemistry in the future, we 
have given a more detailed discussion of its purely theoretical aspects than has 
heretofore been customary in books of this kind. This discussion includes both 
the Woodward-Hoffmann approach and the Dewar-Zimmerman aromaticity 
approach and makes the connection between them. Our treatment requires as 
background a more sophisticated understanding of covalent bonding than is 
ordinarily given in introductory courses ; we have therefore included an exten- 
sive presentation of bonding theory. It begins at a basic level with a review of 
familiar concepts in Chapter 1 and introduces in Chapter 10 the terminology 
and ideas needed to understand the pericyclic theory and its ramifications. The 
treatment is qualitative throughout. Although quantitative molecular orbital 
calculations are not needed for our purposes, Appendix 2 to Chapter 1 sum- 
marizes the molecular orbital calculation methods in general use. The Hiickel 
MO method is covered in sufficient detail to allow the reader to apply it to 
simple systems. 

Another innovation in this text is the use of three-dimensional reaction 
coordinate diagrams, pioneered by Thornton, More O'Ferrall, and Jencks, in 
the discussions of nucleophilic substitutions, eliminations, and acid catalysis of 
carbonyl additions. We hope that the examples may lead to more widespread 
use of these highly informative diagrams. 

A chapter on photochemistry provides a discussion of photophysical 
processes needed as background for this increasingly important area of chemistry 
and treats the main categories of light-induced reactions. 

The text assumes elementary knowledge of the common organic spectro- 
scopic techniques. Nevertheless, we have included a description of the recently 
developed method of chemically induced dynamic nuclear polarization 
(CIDNP) , which has already proved to be of great importance in the study of 
radical reactions and which has not yet found its way into books covering 
spectroscopy of organic compounds. 

Problems of varying difficulty have been included at the ends of the 
chapters. Some problems illustrate points discussed in the text, but others are 
meant to extend the text by leading the student to investigate reactions, or 
even whole categories of reactions, which we have had to omit because of 
limitations of space. References to review articles and to original literature are 
given for all problems except those restricted to illustration of points that the 
text discusses in detail. Problems that represent significant extensions of the 
text are included in the index. 

The book is extensively footnoted. It is neither possible nor desirable in 
a book of this kind to present exhaustive reviews of the topics taken up, and we 
have made no effort to give complete references. We have tried to include 
references to review articles and monographs wherever recent ones are avail- 
able, to provide key references to the original literature for the ideas discussed, 
and to give sources for all factual information presented. The text also contains 
numerous cross references. 

The amount of material included is sufficient for a full-year course. For 
a one-semester course, after review of the first two chapters, material may be 
chosen to emphasize heterolytic reactions (Chapters 3-8), to cover a broader 

Preface xi 

range including radicals and photochemistry (selections from Chapters 3-8 
plus 9 and 13), or to focus primarily on pericyclic reactions (Chapters 10-12). 
In selecting material for a one-semester course, the following sections should be 
considered for possible omission: 3.5, 4.4, 4.5, 5.6, 6.3, 7.3, 7.5, 8.3, 9.5, 10.4, 
11.6, 11.7. 

We would like to thank the following people for reviewing parts of the 
manuscript and for providing helpful comments: Professors D. E. Applequist, 
C. W. Beck, J. C. Gilbert, R. W. Holder, W. P. Jencks, J. R. Keeffe, C. Levin, 
F. B. Mallory, D. R. McKelvey, N. A. Porter, P. v. R. Schleyer, J. Swenton, 
and T. T. Tidwell. We are particularly grateful to Professor N. A. Porter, who 
reviewed and commented on the entire manuscript. We owe special thanks to 
Professor Charles Levin for many enlightening discussions and to Carol Demp- 
ster for essential help and encouragement. 

Thomas H. Lowry 
Kathleen Schueller Richardson 


Chapter 1 



Because the covalent bond is of central importance to organic chemistry, we 
begin with a review of bonding theory. Later, in Chapter 10, we shall return to 
develop certain aspects of the theory further in preparation for the discussion of 
pericyclic reactions. 


Understanding and progress in natural science rest largely on models. A little 
reflection will make it clear that much of chemical thinking is in terms of models, 
and that the models useful in chemistry are of many kinds. Although we cannot 
see atoms, we have many excellent reasons for believing in them, and when we 
think about them we think in terms of models. For some purposes a very simple 
model suffices. Understanding stoichiometry, for example, requires only the idea 
of atoms as small lumps of matter that combine with each other in definite pro- 
portions and that have definite weights. The mechanism by which the atoms are 
held together in compounds is not of central importance for this purpose. When 
thinking about stereochemistry, we are likely to use an actual physical model con- 
sisting of small balls of wood or plastic held together by springs or sticks. Now the 
relative weights of atoms are immaterial, and we do not bother to reproduce 
them in the model ; instead we try to have the holes drilled carefully so that the 
model will show the geometrical properties of the molecules. Still other models 
are entirely mathematical. We think of chemical rate processes in terms of sets of 
differential equations, and the details of chemical bonding require still more ab- 
stract mathematical manipulations. The point to understand is that there may be 
many ways of building a model for a given phenomenon, none of which is com- 

2 The Covalent Bond 

plete but each of which serves its special purpose in helping us understand some 
aspect of the physical reality. 

The Electron Pair Bond — Lewis Structures 

The familiar Lewis structure is the simplest bonding model in common use in 
organic chemistry. It is based on the idea that, at the simplest level, the ionic 
bonding force arises from the electrostatic attraction between ions of opposite 
charge, and the covalent bonding force arises from sharing of electron pairs be- 
tween atoms. 

The starting point for the Lewis structure is a notation for an atom and its 
valence electrons. The element symbol represents the core, that is, the nucleus and 
all the inner-shell electrons. T he core carr ies anumb er of positive charges equal 
to the numb er of val ence electrons. This po sitiyfTc Tiarge is railed, .the core, charge. 
Valpnre elec trons are shown explicitly . For elements in the third and later rows 
of the periodic table, the d electrons in atoms of Main Groups III, IV, V, VI, and 
VII are counted as part of the core. Thus: 

:Br: :Se: :I: 

Ions are obtained by adding or removing electrons. The charge on an ion is 
given by 

charge = core charge — numbe r_o f electrons shown exp licitly 

An ionic compound is indicated by writing the Lewis structures for the two ions. 
A covalent bond model is constructed by allowing atoms to share pairs of 
electrons. Ordinarily, a shared pair is designated by a line: 

H— H 

All valence electrons of all atoms in the structure must be shown explicitly. Those 
electrons not in shared covalent bonds are indicated as dots, for example: 

H— 6— H 

If an ion contains two or more atoms covalently bonded to each other, the 
total charge on the ion must equal the total core charge less the total number of 
electrons, shared and unshared: 

(H— O:)- 

H core = + 1 
O core = +6 

total core = + 7 
number of electrons = — 8 

total charge = — 1 

In order to write~correct Lewis structures, two more concepts are needed. 
First, consider the total number of electrons in the immediate neighborhood of 
each atom. This number is called the valence-shell occupancy of the atom, and to 
find it, all unshared electrons around the atom and all electrons in bonds leading 

Models of Chemical Bonding 3 

to the atom must be counted. The valence-shell occupancy must not exceed 2 for 
hydrogen and must not exceed 8 for atoms of the first row of the periodic table. 
For elements of the second and later rows, the valence-shell occupancy may 
exceed 8. The structures 

:F: p. :0: 

: F — S — F : H— 6— S— 6— H 

. .. .. (| .. 

•f. :F: :0: 

are acceptable. 

The second idea is that of formal charge. For purposes of determining 
formal charge, partition all the electrons into groups as follows: Assign to each 
atom all of its unshared pair electrons and half of all electrons in bonds leading to 
ij^Cgl l the number of electrons a ssignejjg jhe a tom by this proce ss its electron 
ownership. The formaL char gc of e ach atom is thc n-given-by 

f ormal charge = core' chargp — fl prt r o n own ership 

To illustrate formal charge, consider the hydroxide ion, OH~. The electron 
ownership of H is 1, its core charge is + 1, and its formal charge is therefore zero. 
The electron ownership of oxygen is 7, and the core charge is + 6 ; therefore the 
formal charge is — 1 . All nonzero formal charges must be shown explicitly in the 
structure. The reader should verify the formal charges shown in the following 
examples : 

H H 

I + I .. ♦ .. 

H— N— B— H H— N=N=N:- N 

i J, *f v.- 

The algebraic sum of all formal charges in a structure is equal to the total charge. 

Formal charge is primarily useful as a bookkeeping device for electrons, but 
it also gives a rough guide to the charge distribution within a molecule. 

In writing Lewis structures, the following procedure is to be followed: 

1. Count the total number of valence electrons contributed by the electri- 
cally neutral atoms. If the species being considered is an ion, add one electron to 
the total for each negative charge ; subtract one for each positive charge. 

2. Write the core symbols for the atoms and fill in the number of electrons 
determined in Step 1 . The electrons should be added so as to make the valence- 
shell occupancy of hydrogen 2 and the valence-shell occupancy of other atoms 
not less than 8 wherever possible. 

3. Valence-shell occupancy must not exceed 2 for hydrogen and 8 for a 
first-row atom; for a second-row atom it may be 10 or 12. 

4. Maximize the number of bonds, and minimize the number of unpaired 
electrons, always taking care not to violate Rule 3. 

5. Find the formal charge on each atom. 

We shall illustrate the procedure with two examples. 

4 The Covalent Bond 

Example 1. N0 2 

Step 1 1 7 valence electrons, charge = 1 7 electrons 

Step 2 6=N— 6: 

(Formation of another bond, 0=N=6, would give nitrogen valence- 
shell occupancy 9.) 

Step 3 Formal charge : 

Left O Ownership 6 charge 
Right O Ownership 7 — 1 charge 
N Ownership 4 + 1 charge 

Correct Lewis Structure: 

6=N— 6:~ 

Example 2. C0 3 2 ~ Ion 

Step 1 22 valence electrons, + 2 electrons for charge, = 24 electrons. 

Step 2 .. I .. 

:0— 0=O 

(More bonds to C would exceed its valence-shell limit.) 
Step 3 Formal charge: 

: O — Ownership 7 — 1 charge 
: O — Ownership 7 — 1 charge 

=0 Ownership 6 charge 
C Ownership 4 charge 

Correct Lewis Structure: 


.. I .. 
":0— C^O 


The Lewis structure notation is useful because it conveys the essential qualitative 
information about properties of chemical compounds. The main features of the 
chemical properties of the groups that make up organic molecules, 

I I \ .. I .. 

H— C— H — C— H C=0 — C— O— H 

I I / - | " 


and so forth, are to a iirst approximation constant from molecule to molecule, 
and one can therefore tell immediately from the Lewis structure of a substance 
that one has never encountered before roughly what the chemical properties will 

Models of Chemical Bonding 5 

There is a class of structures, however, for which the properties are not those 
expected from the Lewis structure. A familiar example is benzene, for which the 
heat of hydrogenation (Equation 1.1) is less exothermic by about 37 kcal mole -1 
than one would have expected from Lewis structure 1 on the basis of the measured 

+ 3H 2 ► (1.1) 

heat of hydrogenation of ethylene. The thermochemical properties of various 
types of bonds are in most instances transferable with good accuracy from molecule 
to molecule ; a discrepancy of this magnitude therefore requires a fundamental 
modification of the bonding model. 

The difficulty with model 1 for benzene is that there is another Lewis 
structure, 2, which is identical to 1 except for the placement of the double bonds. 

Whenever there_arejtwo _aher native .Xewis jrtructurejj one alone will be an 
inaccuraje_r^r^sentat|on_ij£lhx_rnciecular ^ructure. _A more accurate pictu re 
will be obtained by 'thejsujDej^Dojitfon jjf J^ 

whicTTTorbenzene is_ indicated by 3. The superposition of Jwo or more Lewis 
structures into a composite picture is called resonance. 

This terminology is well established, but unfortunate, because the term 
resonance when applied to a pair of pictures tends to convey the idea of a chang- 
ing back and forth with time. It is therefore difficult to avoid the pitfall of think- 
ing of the benzene molecule as a structure with three conventional double bonds, 
of the ethylene type, jumping rapidly back and forth from one location to 
another. This idea is incorrect. The ele ctrons in the mol ecule move in a field of 
force created by the six carbon and six hydrogen nuclei arranged around a regju- 
lar hexagon (4) . Each of the six sides of the hexagon is entirely equivalent to each 


*vV H 


other side; there is no reason why electrons should, even momentarily, seek out 

6 The Covalent Bond 

three sides and make them different from the other three, as the two alternative 
pictures 3 seem to imply that they do. 

The symmetry of the ring of nuclei (4) is called a sixfold symmetry because 
rotating the picture by one-sixth of a circle will give the identical picture again. 
This sixfold symmetry must be reflected in the electron distribution. A less mis- 
leading picture would be 5, in which the circle in the middle of the ring implies a 


distribution of the six double bond electrons of the same symmetry as the arrange- 
ment of nuclei. We shall nevertheless usually continue to use the notation 3, as it 
has certain advantages for thinking about reactions. 

The most jmrjort ant features of sjructures^br_whj^j^sojaanoe^s_needed 
are, first, that the molecule is more stabl e (of lower energy) th an one would 
eyrierlJWjTTTjnnkJTi igat on p nf the i ndividual stnictu rej^ancl j^cond^that the actual 
distributi on of electr x)ns_iiijhe molec ule is di fferent from what_one,WQuld. expect 
on the basis of one of the structure s^SJnce the composite pic ture shows that c er- 
tai n electro ns are free to move oyer a larger area of the molecule, than a single one 
of thj^!tmctures_ implies, resonance is often referred to as delocalization. We shall 
have more to say about delocalization later in connection with molecular orbitals. 

While the benzene ring is the most familiar example of the necessity for 
modifying the Lewis structure language by the addition of the resonance concept, 
there are many others. The carboxylic acids, for e x ample, are much stronger 
acidsjhan the alcoh^lsjjhls^iiference rrmsiJae^dueJarg^ly-Ja-greata^stability of 
the_c^b^yl^eJOTiJ^6J_ove^_the alkoxideJon_(7)j : it is the p ossibility nf writing 
twojgqu ivalent Lewis structures for t h^_caxbxtx.ylate-4on that alerts, us. to—this 

/?■ />•■ A-~ 

R— C x + H z O ^=^ H 3 + + R— C < y R— C . (1.2) 

6— H N 6:- % 6 


R— CH 2 — OH + H 2 :^^ H 3 + + R— CH 2 — 0:~ (1.3) 


Another example is the allylic system. The allyl cation (8), anion (9), and 

H H H 

H^ X +H H X ." H H X . H 

H H H H H H 

8 9 10 

radical (10), are all more stable than their saturated counterparts. Again, there is 
for each an alternative-structure: 

^^i " ► jX^s ^\C- ► >^ ^^< « > x^ 

8 9 10 

Models of Chemical Bonding 7 

In all the examples we have considered so far, the alternative structures 
have been equivalent. This will not always be the case, as the following examples 
illustrate : 


H— N— N=N: < ► H— N=N=N:" 

Whenever there are ^jionequiva lent structu r e s , each will ^ nn tr ibute to the^ 
posite picture to a different extejiL Th£.jStmcture_t^^ t he mo st 

stable ^lowest-energy) molecjJe J _w£r£.suah_j^.naQlecule. actually to exist, contri- 
butes the most to the composite, and others successively less as they represent 
higher-energy molecules . 

It is because the lowest-energy structures are most important that we speci- 
fied in the rules for writing Lewis structures that the number of bonds should be 
maximum and the valence-shell occupancy not less than 8 whenever possible. 
Structures that violate these stipulations, such as 11 and 12, represent high-energy 
forms and hence do not contribute significantly to the structural pictures, which 

H H 






• / 


1 1 

























11 12 

are quite adequately represented by 13 and 14: 

c=c— c=c 

H H 

13 14 

T he following rul es are useful in using resonance notation: 

1. All nuclei must be in the same location in every structure. Structures with 
nuclei in different locations, for example 15 and 16, are chemically distinct sub- 

.O: :6— H 

G . C N 

H C— H H C— H 

H H 

15 16 

stances, and interconversions between them are actual chemical changes, always 
designated by ^. 

2. Structures jvithjewer ;_bonds Lor ^with greater separatipii of fontiaLcliarge 
are les s sta ble_thanthose wjthjnore bonds or less charge separation. Thus 11 and 
12 are higher-energy, respectively, than 13 and 14. 

8 The Covalent Bond 

3. Where t^n^nTir^rp^jAfiH^frirrnal char ge ha ve the sa, raejTnrnhjgjTfjjonrte 
and approximatel y the same cha rge sep aration, t he_s_tmctu re w i th charge on th e 
more elec tr onegativ e^torn_wjll_usu ally be somewha t lower in enej gy^bulJiiC- 
differen ce w iH og linarilyjjesmal l en o ugh that both str uctu res mu st__bejnclud£d 
in_the coinposite picture. Thus in 17a <-> 17b, 17a should be more stable, but the 

= 6^ :0: 


/°\ < * / C V-- 

H C— H H C— H 

I I 

H H 

17a 17b 

chemistry of the ion can be understood only if it is described by the superposition 
of both structures. 

4. All_f^iporrrmp<i artarhed tn jjjTah^ nf_ atoms joined by a Hnnhle. bond in 
any_structu re must lie in th e sa me plane. For example, the structure 18b cannot 

contribute, because the bridged ring prevents carbons 6 and 7 from lying in the 
same plane as carbon 3 and the hydrogen on carbon 2. TjKMrnppjisibihYy-Qf^trji£- 
tures \tfith_Hnnhlp. han ds at hridg -eheads of small hrjdgfd r 1TlgS is kn""" 1 ag JBredtls. 
rule. 1 Double bonds can occur at a bridgehead if the rings are sufficiently large. 

Molecular Geometry 

Lewis structures provide a simple method of estimating molecular shapes. The 
geometry about any atom covalently bonded to two or more other atoms is found 
by counting the number of electron groups around the atom. Each unshar ed pair 
cou nts as one group, and each bond, whethe r single or multiple^ jcounts as one 
group. The number of electro n_grou ps ar ound an atom is t herefore p _qiial to thp 
surnof the number of electron j)ah^_on_the_atojD_and_ihe number of other atoms 
bonded toj tJ The geometry is linear if the number of electron groups is two, tri- 
gnjTajjfjj]ejTnrriher jsJJTree^a.nrl tetrah edral if the number is, fr»nr 

The rule is based on the electron-pair repulsion model, wh ich postulatesjhat 
because el ectron pairs repel each ot her, they will try to stay as far apart as p ossible. 
In trigonal and tetrahedral geometries, the shape will be exactly trigonal (120° 
bond angles), or exactly tetrahedral (109.5° bond angles) if the electron groups 
are all equivalent, as for example in BH 3 or CH 3 + (trigonal), or in CH 4 or NH 4 + 
(tetrahedral) . 

1 (a) F. S. Fawcett, Chem. Rev., 47, 219 ( 1950) ; (b) J. R. Wiseman and W. A. Fletcher, J. Amer. Chem. 
Soc, 92, 956 (1970); (c) C. B. Quinn and J. R. Wiseman, J. Amer. Chem. Soc, 95, 6120 (1973); 
(d) C. B. Quinn, J. R. Wiseman, and J. C. Calabrese, J. Amer. Chem. Soc, 95, 6121 (1973). 

Molecular Orbitals 9 

If the groups are not all equivalent, the angles will deviate from the ideal 
values. Thus in NH 3 (four electron groups, three in N — H bonds, one an unshared 
pair), the unshared pair, being attracted only by the nitrogen nucleus, will be 
closer to the nitrogen on the average than will the bonding pairs, which are also 
attracted by a hydrogen nucleus. Therefore the repulsion between the unshared 
pair and a bonding pair is greater than between two bonding pairs, and the 
bonding pairs will be pushed closer to each other. The H — N — H angle should 
therefore be less than 109.5°. It is found experimentally to be 107°. Similarly, in 
H a O (four electron groups, two unshared pairs, and two O — H bonds), the angle 
is 104.5°. 

Ambiguity may arise when more than one structure contributes. Then un- 
shared pairs in one structure may become multiple bonds in another, so that the 
number of electron groups around a given atom is not the same in both structures. 
An example is methyl azide (19). The central nitrogen is clearly linear (two 
electron groups), but the nitrogen bonded to CH 3 has three electron groups in 

H 3 C— N=N=N: .< »• H 3 C— N— N=N: 

19a 19b 

19a and four in 19b. In such a situation, the number of electron groups is deter- 
mined from the structure with the larger number of bonds. Thus the nitrogen in 
question in 19 is trigonal, not tetrahedral. 

Conventions for Structural Formulas 

This book contains large numbers of Lewis structural formulas. Frequently we 
shall not write out the full Lewis structure ; unshared pairs of electrons not shown 
explicitly are implied. When there are two or more contributing structures, we 
shall show them all only if that is essential to the point being illustrated ; again, it 
will be assumed that the reader will understand that the missing structures are 


Lewis structures serve admirably for many aspects of mechanistic organic 
chemistry. Frequently, however, we need a more accurate bonding model. 

Models Based on the Quantum Theory 

The description of chemical bonding must ultimately be based on an understand- 
ing of the motions of electrons. In order to improve our model, we need to appeal 
to the quantum theory, which summarizes the current understanding of the be- 
havior of particles of atomic and subatomic size. 

The quantum theory provides the mathematical framework for describing 
the motions of electrons in molecules. When several electrons are present, all 
interacting strongly with each other through their mutual electrostatic repulsion, 
the complexity is so great that exact solutions cannot be found. Therefore 
approximate methods must be used even for simple molecules. These methods 

10 The Govalent Bond 

take various forms, ranging from complex ab initio calculations, which begin from 
first principles and have no parameters adjusted to fit experimental data, to 
highly approximate methods such as the Huckel theory, which is discussed further 
in Appendix 2. The more sophisticated of these methods now can give results 
of quite good accuracy for small molecules, but they require extensive use 
of computing equipment. 2 Such methods are hardly suited to day-to-day qualita- 
tive chemical thinking. Furthermore, the most generally applicable and therefore 
most powerful methods are frequently simple and qualitative. 

Our ambitions in looking at bonding from the point of view of the quantum 
theory are therefore modest. We want to make simple qualitative arguments that 
will provide a practical bonding model. 

Atomic Orbitals 

The quantum theory specifies the mathematical machinery required to obtain a 
complete description of the hydrogen atom. There are a large number of func- 
tions that are solutions to the appropriate equation; they are functions of the x, 
y, and z coordinates of a coordinate system centered at the nucleus. 3 Each of these 
functions describes a possible condition, or state, of the electron in the atom, and 
each has associated with it an energy, which is the total energy (kinetic plus 
potential) of the electron when it is in the state described by the function in 

The functions we are talking about are the familiar Is, 2s, 2p, 3s, . . . 
atomic orbitals, which are illustrated in textbooks by diagrams like those in 
Figure 1.1. Each orbital function (or wave function) is a solution to the quantum 
mechanical equation for the hydrogen atom called the Schrodinger equation. 
The functions are ordinarily designated by a symbol such as <p, x, </<> and so on. 
We shall call atomic orbitals <p or x, and designate by a subscript the orbital 
meant, as for example <p ls , <p 2s , and so on. Later, we may abbreviate the notation 
by simply using the symbols Is, 2s, . . . , to indicate the corresponding orbital 
functions. Each function has a certain numerical value at every point in space ; 
the value at any point can be calculated once the orbital function is known. We 
shall never need to know these values, and shall therefore not give the formulas; 
they can be found in other sources. 4 The import ant thing ^Jorjour^airp-Qses^are, 
fir st, that the num erical valu es are positive in c erta in regions of .sfjaceartd nega : 
tiyejno ther regions, andjecond. that the value of each fu nction approaches zero 

2 A number of texts cover methods for obtaining complete orbital descriptions of molecules. Ex- 
amples, in approximate order of increasing coverage, are (a) A. Liberies, Introduction to Molecular- 
Orbital Theory, Holt, Rinehart, and Winston, New York, 1966; (b) J. D. Roberts, Notes on Molecular 
Orbital Theory, W. A. Benjamin, Menlo Park, Calif., 1962; (c) K. B. Wiberg, Physical Organic 
Chemistry, Wiley, New York, 1964; (d) A. Streitwieser, Jr., Molecular Orbital Theory for Organic 
Chemists, Wiley, New York, 1961; (e) M. J. S. Dewar, The Molecular Orbital Theory of Organic 
Chemistry, McGraw-Hill, New York, 1969; (f) P. O'D. Offenhartz, Atomic and Molecular Orbital 
Theory, McGraw-Hill, New York, 1970; (g) S. P. McGlynn, L. G. Vanquickenborne, M. Kinoshita, 
and D. G. Carroll, Introduction to Applied Quantum Chemistry, Holt, Rinehart. and Winston, New York, 

3 Actually, the origin is at the center of mass, which, because the nucleus is much more massive than 
the electron, is very close to the nucleus. 

4 See, for example, Wiberg, Physical Organic Chemistry, pp. 17, 19, and 25. 

Molecular Orbitals 11 


Figure 1.1 Hydrogen atomic orbital functions, (a) Is; (b) 2p; (c) 3d. The edges drawn are 
artificial, because orbitals have no edges but merely decrease in magnitude as 
distance from the nucleus increases. The important features of the orbitals are 
the nodal planes indicated, and the algebraic signs of the orbital functions, posi- 
tive in the shaded regions and negative in the unshaded regions. 

as one moves farther from the nucleus. In Figure 1.1, and in other orbital dia- 
grams used throughout this book, positive regions are shaded and negative regions 
are unshaded. 

Imagine walking around inside an orbital, and suppose that there is some 
way of sensing the value — positive, negative, or zero — of the orbital function as 
you walk from point to point. On moving from a positive region to a negative 
region, you must pass through some point where the value is zero. Thexollesitions 

12 The Covalent Bond 

of a ll adja cent ]Tnints_at w hich a functtf>w4s-7.f:rn are cgjjed nodes; they are surfaces 
in three-dimensional space, and most of the important ones for our purposes are 
planes, like those shown in Figure 1.1 for the p and d orbitals illustrated. (Nodes 
can also be spherical, and of other shapes, but these are of less concern to us.) 

The Physical Significance of Atomic Orbital Functions 

The fact that an orbital function 9 is of different algebraic sign in different regions 
has no particular physical significance for the behavior of an electron that finds 
itself in the state defined by the orbital. (We shall sec shortly that the significance 
of the signs comes from the way in which orbitals can be combined with each 
other.) The quantity that has physical meaning is the value at each point of the 
function <p 2 , which is positive everywhere, since the square of a negative number 
is positive. The squared. function, <g 2 , gives the probability of findingjhe electron 
at various points in space. Diagrams like that in Figure 1.2, with shading of 
varying density showing the relative probability of finding the electron in various 
regions or, more succinctly, t he electron di strib uti on o r electron density^ are_ac.tu.aJly 
pictures of g? 2 , not of 9 it^lf._JZ]ie_g.en.eraJjliapejo£9f_will be similar _the_shape 
qfjg. The orbitals and their squares have no edges, even though definite outlines 
are usually drawn in diagrams; the values merely approach closer and closer to 
zero as one goes farther and farther from the nucleus. 

Extension to Other Atoms 

The hydrogen atomic orbitals would not do us a great deal of good if orbitals of 
other atoms were radically different, since in that case different pictures would 
be required for each atom. But the feature of the hydrogen atom problem that 
determines the most important characteristics of the hydrogen atom orbitals is 
the spherical symmetry. Since all the atoms are spherically symmetric, the atomic 
orbitals of all atoms are similar, the main difference being in their radial depen- 
dence, that is, in how rapidly they approach zero as one moves away from the 
nucleus. Because the radial dependence is of minimal importance in qualitative 



Figure 1.2 Electron density, <p 2 , for Is and 2p atomic orbitals. The density of shading is 
roughly proportional to cp 2 . 

Molecular Orbitals 13 

applications, one may simply use orbitals of the shapes found for hydrogen to 
describe behavior of electrons in all the atoms. 

Ground and Excited States 

We know that an electron in a hydrogen atom in a stationary state will be described 
by one of the atomic orbital functions <p ls , (p 2s , <p 2v , and so forth. 5 We can make 
this statement in a more abbreviated form by saying that the electron is in one of 
the orbitals <p u , <p 2s , y>2v x -> ■ ■ ■> an d we shall use this more economical kind of 
statement henceforth. 

The orbital that has associated with it the lowest energy is <p ls ; if the electron 
is in this orbital, it has the lowest total energy possible, and we say the atom is in its 
electronic ground state. If we were to give the electron more energy, say enough to 
put it in the <p 2Px orbital, the atom would be in an electronic excited state. In general, 
for any atom or molecule, the state in which all electrons are in the lowest pos- 
sible energy orbitals (remembering always that the Pauli exclusion principle 
prevents more than two electrons from occupying the same orbital) is the elec- 
tronic ground state. Any higher-energy state is an electronic excited state. 

An Orbital Model for the Covalent Bond 

Suppose that we bring together two ground-state hydrogen atoms. Initially, the 
two electrons are in <p ls orbitals centered on their respective nuclei. We shall call 
one atom A and the other B, so that the orbitals arc cp lsA and <p lsB . When the 
atoms are very close, say within 1 A ( = 10~ 8 cm) of each other, each electron 
will feel strongly the attractive force of the other nucleus as well as of its own. 
Clearly, then, the spherical <p ls orbitals will no longer be appropriate to the 
description of the electron motions. We need to find new orbital functions appro- 
priate to the new situation, but we would prefer to do so in the simplest way 
possible, since going back to first principles and calculating the correct new orbi- 
tal functions is likely to prove an arduous task. 

We therefore make a guess that a possible description for a new orbital 
function will be obtained by finding at each point in space the value of <p lsA and 
of <p lsB and adding the two numbers together. This process will give us a new 
orbital function, which, since <p lsA and <p lsB are both positive everywhere, will 
also be positive everywhere. Figure 1.3 illustrates the procedure. Mathematically, 
the statement of what we have done is Equation 1.4: 

</>mo = Visa + <Pisb (1.4) 

The symbol MO means that the new function is a molecular orbital; a molecular 
orbital is any orbital function that extends over more than one atom. Sjnce-thfi 
technical term for a sum of functions of the type 1.4 is a linear combinatim y th£.-pzo- 
cedure of adding ujd atomic orbital functions is called Jinear combination .of. atomic 

This simple procedure turns out to fit quite naturally into the framework of 
the quantum theory, which with little effort provides a method for finding the 

5 We assume from here on that the reader is familiar with the number and shape of each type of 
atomic orbital function. This information may be found in standard introductory college chemistry 


14 The Covalent Bond 

^M0 - *>UA + ^liB 

Figure 1.3 The linear combination of \s orbital functions on hydrogen atoms A and B to 
yield a new orbital function, ip MO = <p lsA 4- q>iss- 

energy associated with the new orbital i// M0 . This energy is lower than the energy 
of either of the original orbitals (p lsAl <Pi s b- 

Instead of adding 9 lsA and <p lsB , we might have subtracted them. We would 
then have obtained Equation 1.5: 

'AmO — flsA ~ <PlsB 


Figure 1.4 illustrates the formation of this combination. Note that there is ajoode 
in this molecular orbital, because at any joint equidistant from the two nuclei 
the value of <g lsA is numerically equal to the value of <p UB , so that <p lsA — y> lsB is 

The procedures of the quantum theory require that the negative combina- 
tion be made as well as the positive, and they show also that the ene rg y associated 
with $mq will be: higher^than_that of g^i and 2i SB . 

Energies of Molecular Orbitals 

We can summarize the process of constructing our bonding model in an energy- 
level diagram. Figure 1.5 introduces the conventions we shall use for showing the 
formation of new orbitals by combining others. On either side we place the 
starting orbitals, and ^.t the center the orbitals resulting from the combination 
process. In Figure 1.5 we have also shown orbital occupancies: Before the inter- 
action, we have one electron in <p lsA and one in 9? lsB ; afterward we can place both 
electrons in </i M0 to obtain the ground state of the H 2 molecule, which will be of 

Molecular Orbitals 15 

Figure 1.4 The linear combination of Is orbital functions on hydrogen atoms A and B to 
yield orbital function ipfiio = fisA ~ fisB- 

lower energy than the separated atoms by an amount 2 AE (two electrons each 
decrease in energy by AE). 6 

The process of forming ground-state H 2 would be described in our LCAO 
model by saying that H A , with its electron in <pi sA , and H B , with its electron in 
<p lsB , will come together to give H 2 with a pair of electrons in ip M0 , and will in the 
process give off energy 2 AE to the surroundings. We can also obtain models for a 
singly excited state and for a doubly excited state of H 2 by adding energy 2 AE or 
4 AE to the ground-state molecule and placing either one or both electrons in 


Electr ons in M O _are_ stabilizing for the molecule, and electrons in i/^j^re 
destabilizing. Therefore we call </i MO a bonding orbital and i/i^o an antibonding 
orbital. In antibonding orbitals there is always a node between the nuclei, so that 

6 The energy change on formation of the molecule, known from experiment to be 104 kcal mole -1 , 
will not actually be equal to 2 AE, because the quantum mechanical procedures count the mutual 
repulsion of the electrons twice and neglect the mutual repulsion of the nuclei. The two corrections 
to 2 AE are opposite in sign and roughly cancel, but they are both large numbers (on the order of 
400—450 kcal mole -1 for H 2 ), and their difference (about 35 kcal mole -1 ) is significant. The actual 
energy lowering is less than 2 AE by this amount; in other words, for hydrogen the actual experi- 
mental dissociation energy is 104 kcal mole -1 , but 2 AE calculated from theory is about 139 kcal 
mole -1 and AE is about 69 kcal mole -1 . See C. A. Coulson, Valence, 2nd ed., Oxford University 
Press, London, 1963, p. 90. 

16 The Covalent Bond 

M . 



/"" " "\ 

• \ 



+ *, 

/ • 


Figure 1.5 The energy-level diagram for the interaction o(<p lsA with cp lsB . On either side are 
the atomic orbitals before interaction; at the center are the two molecular 
orbitals. Orbital occupancies are indicated for the two separate hydrogen atoms 
and for the molecule. 

electrons are excluded from that region^ whereas bonding orb ita ls have no _such 
node and concentrate electrons betvve£xi_tliejiuclei. 

Interaction of Orbitals 

There is an alternative way of looking at the process described in Figure 1.5 
which we shall find useful in subsequent discussions. We can think of the two orbitals 
<p lsA and <p lsB as interacting with each other to produce the two new orbitals 
i/i mo and >piw T ne interaction_ has associated with Jt^_an energy change _A£; 
mea suring from the en er gy of the o rbiuIs_y_ : ^_ai]Ld y 1 , P before the interaction 
occurs^, j/f M0 moves down by interactio n ener g:y_AiLand ^ moves up by inter- 
action energy AE. 7 

7 A somewhat more careful treatment shows that </iJ,o will actually have moved up above the <p lsA 
level by somewhat more than </i M0 moved down. This fact will be important in certain applications 
later, but need not concern us now. 

Molecular Orbitals 17 


Figure 1.6 The three-dimensional shapes of ^o an d "Amo- Each has infinite-fold rotational 
symmetry, because one can rotate each picture around the internuclear axis in 
an infinite number of steps and have at every step an identical picture. 

As we have noted above, AE can be calculated, but for our purposes we 
need only to know what quantities affect its magnitude. Theinlerac tion energy is 
greater the m orgjrtron gly the two in teracJmg_orbitals L overlap j_oyerlapJs_ large 
when both orhita.ls_ h.ave large v alues i n the same region of space. The overlap of 
two orbital functions-^-and-^^is-obtained by-multiplying the values of the two 
functionsjit^ each poinLand summing thf_produ cts over all points, in other words 
by integrjjtirig "w qU_j_he spatial coor dinates the quantity rp ir p z . 

The second factor affecting ihe magn itu de of AE is whether or not the two 
i nteracting orbitals a r e of the mmf rw different pnergy, Thp irit erafjjgri js maxi- 
mum _when the energie s of t he int erac ting pa ir ar e the s^f, aid^hgn"!"*^ 

smane_r__h_E^ar^crapjart injene rgy they are. W e shall return to consider the over- 
lap and the energy differences between the initial orbitals in more detail in 
Chapter 10. 

Basis Functions 

The initial functions taken for the starting point in the model-building process are 
called basis functions. We shall use this terminology henceforth. The reason for 
introducing a new term instead of just continuing to call the starting functions 
atomic orbitals is that molecular orbitals can themselves serve as starting func- 
tions in an interaction model. 

The H 2 model has illustrated an important point about orbital interactions 
which must be remembered: Whmeuei-Jmsis-JttkitoLJumiigru>_^^ new 

orbital Jwwtions_ L Jke^numbe7^o[_neu i functions obt ained^ is equal to the number of basis 
func tions use d. 

a Bonds and n Bonds 

In Figure 1.6 are shown the three-dimensional shapes of the electron distributions 
& an d i/'mo corresponding to the H 2 molecular orbitals. Suppose that we were 

18 The Covalent Bond 




'M0 2 ,„ - V>2p z A + ^2 Pz B 


V>2p 2 A 

f2p z B 


= *>, 

p 2 A 

^2p 2 B 


Figure 1.7 Combination of two p orbitals to give a molecular orbitals. (a) Bonding com- 
bination, (b) Antibonding combination. 

to rotate one of these pictures around an axis coinciding with the line joining the 
nuclei. We can rotate around this axis by any angle at all, and we shall get an 
identical picture. If you were to close your eyes while the rotation was done and 
then to open them, you would have no way of telling that any change had been 
made. To state this idea another way, we can say that we could divide one full 
rotation around the axis into an infinite number of steps, and have after each step 
an indentical picture. 

This property of the diagrams in Figure 1.6 is called a symmetry property. The 
axis of rotation is called a symmetry element. There are various kinds of symmetry 
elements; an axis is designated by the letter C. Since this particular axis is an 
infinite-fold rotation axis, in the sense specified above, it is called a C x axis. The 

Molecular Orbitals 19 


^2 P ,B 

2p x k 

Ko 2px flp x A + f 2px K 


2p x B 

l> M02p x *2p x A ^2p x B 


Figure 1.8 Combination of p orbitals to give tt molecular orbitals. (a) Bonding combina- 
tion, (b) Antibonding combination. 

process ofcarryi ng nut a c hange onjmjThjer^J-hat leaAzes-tbe-ab}ex,t4oa]<-ing exactly 
as be fore, in this cas e rotation by ^jq_axhkrary-angle, is called a symmetry operation... 

Any molecular orbitaJ_LhalJias_the symmetry property shown_i n Fig ure 1.6 
is called a a orbital . Both <{i M0 and </<m of our hydrogen molecule model are a 

Suppose that we make a molecular orbital by combining p orbitals on two 
atoms. We can do this in one of two ways. If we choose the p orbitals that are 
oriented toward each other (Figure 1.7), we get MO's with the same C x 
symmetry we had before. But if the p orbitals are oriented as shown in Figure 1.8, 
we get a new type of molecular orbital. 

Figure 1.9 shows the three-dimensional shape of the electron distributions 


and >p\ 

Now the symmetry is different: On^fuLLxc4atiefl-afeewt-the 

internuclear line m ust be djvi AexL intp_two ecjualjiteps if an identical pir.tu re_js__tQ 
be_ obtained after each step ^ This s ymmetry is a twofol d_JPJLaJjum,_ajQcLj:he _sy_m- 
metry ele ment is called a C 9 axjs^AnxixbitaLwith this lundofsymmetry is called _a 
it orbital . Atomic orbitals of the s type can form only a molecular orbitals; atomic 

20 The Covalent Bond 





-c 2 

Figure 1.9 The symmetry of the electron distributions </>mo 2p * and 0MOap* - Rotational 
symmetry is C 2 . 

orbitals of the p type can form either a or -rr orbitals, depending on their orienta- 
tion relative to each other. Because the overlap of p o rjaitolsjntgrar.ting in the _?_ 
manner is smaller than overl ap in the <j manner, jthe, AiEJor jnteraction in n MO 
formatiorils^usually less than in g MO formation. 


Suppose that we wish to construct an LCAO bonding model for methane. We set 
up the problem by defining an x, y, z coordinate system and placing the carbon at 
the origin. The molecule is tetrahedral, as determined from the electron-pair 
repulsion model. The orientation of the molecule is arbitrary; we choose to 
arrange it as shown in 21, with the hydrogen atoms in the + x, +y, + z quadrant, 
the —x, —y, +z quadrant, the +x, —y, —z quadrant, and the — x, +y, —z 

+ x 

+ z 

+ y 


Hybrid Orbitals 21 

Figure 1.10 The valence atomic orbitals of the carbon and four hydrogens in methane. 

We have on each hydrogen a Is orbital, <p H is> ar >d on the carbon a 2s, 2p x , 
2p y , anc!2/> 2 (Figure 1.10). 

The Need for Hybrid Orbitals 

We could simply proceed to inspect these orbitals to see which overlap with each 
other, and then begin to make molecular orbitals in the way described in the 
previous section. Unfortunately, the situation is now quite complicated. The <p lsl 
orbital of hydrogen number 1 interacts with all four of the carbon valence orbitals. 
The quantum theory gives procedures for dealing with this situation; for 
calculations done with the aid of a computer, there is no disadvantage in using 
the orbitals in Figure 1.10 directly. But the algebraic manipulations required are 
cumbersome; we are looking for a simpler model that will allow us to see quickly 
and clearly what the final outcome of this complex set of interactions will be. 

Constructing Hybrids 

The strategy we adopt is to look first at the atomic orbitals of the central atom, 
and to decide on the basis of the geometry which orbitals are going to interact 
with an orbital on a given ligand atom. For methane set up as in 21, all four 
carbon orbitals will be involved in bonding to H x . We then simply_add together 
the four carbon orbitals to obtaina new orbhal^^^wrfichjvdll have. the shape 
shown Jn-FiguneT. 1 1. Thenew function is called ^hybrid orbital, and is designated 
in this instance as sp 3 because it is formedjfrom an .rand three./) orbitals. 

The process of forming hybrids is n ot the same. J.s. the orbital interaction 
process thai occurs on bringing two atoms together. There is no molecular orbital 
formation involved, because_we are still talking about only one atom, and there is 
no energy lowering. The energy of a hybrid orbital is between the energies of the 
orbitals from whicTTit is made^ rather than 15eihg higher or lower. 

The reader should convince himself that the following four ways of adding 
together the s and p orbitals of the carbon will give four hybrid orbitals, each 

22 The Covalent Bond 

identical in shape to Xsp 3 i> shown in Figure 1.11, but each oriented toward a dif- 
ferent one of the four hydrogen atoms : 

Xsp 3 1 = 9?2s + <P2p x + 9Vv + f 2 "= 

Xsp 3 2 = <p 2s - <P2 Px - q>2p y + <P2p s 

Xsp 3 3 = 9?2s + (flVx - <P2p„ ~ 92V:. 

Xsp 3 4 = <P2s - 92p x + 92p„ - <P2P Z 


The actual correct mathematical forms are not exactly as indicated in 
Equations 1.6. The sign of each term, which is the important quantity for our 
present purpose, is correctly represented there, but each orbital function must be 
multiplied by a coefficient. The method of finding the proper coefficients for any 
desired geometry is given in Appendix 1 to this chapter. 

Figure 1.11 The formation of an sp 3 hybrid by adding together the four valence atomic 
orbitals. Orbital shapes and locations of the nodes are approximate in these 
diagrams. For a more accurate description, see Wiberg, Physical Organic 
Chemistry, pp. 29-33. 

Hybrid Orbitals 23 




^so 3 i 

J *M0 , = >V, +*,„ 

Figure 1.12 Formation of a bonding molecular orbital from (p lsl and Xsp 3 i- 

^M0 0l =X s/ , h -f hl 





/ c 

H \ 


Figure 1.13 The energy relationships in MO formation from Xsp 3 i anc ' <Pisi- 

24 The Covalent Bond 

The advantage we gain by making hybrid orbitals is that we now have four 
new atomic orbitals on carbon, each one oriented directly toward one of the 
hydrogen atoms. Each hybrid will have a large overlap and therefore a large 
interaction with one, but only one, hydrogen. Our complicated original problem, 
in which each hydrogen Is orbital had to interact with all four carbon atomic 
orbitals, is now replaced by four separate but simple problems. 

MOs from Hybrid Orbitals 

We can now proceed to make molecular orbitals in the same way we did for H 2 . 
Figure 1.12 shows the form of the bonding molecular orbital obtained from <p lsJ 
and Xsp 3 i> there will also be an antibonding combination which has a node be- 
tween the atoms. The energy changes (Figure 1.13) follow the pattern we found 
in H 2 . The only difference is that now the two interacting atomic orbitals are not 
the same and have different energies. The energy difference in this instance is not 
large, and makes no fundamental change in our model. We shall return to this 
point in Chapter 10. Note that our new molecular orbitals have infinite-fold 
symmetry about the C — H axis, and so are u orbitals. 


k J 


Vl " *2* + ^Px + flPy Vl = ^ + *1Px ~ *V V 3 = ^ " ^Px + ^Py 

Figure 1.14 Formation of sp 2 hybrids from an s and two p orbitals. 

Hybrid Orbitals 25 

Figure 1.15 Formation of sp hybrids from an s and one p orbital. 

The reader should now complete the bonding model for CH 4 by construct- 
ing a bonding-antibonding pair for each of the other three interacting pairs of 
atomic orbitals. 

Other Types of Hybridization 

A hybridization scheme can be constructed for each of the various possible geo- 
metries about the central atom. The sp 3 hybridization discussed above gives 
hybrids oriented at 109.5° angles to each other, and is appropriate to tetrahedral 
atoms. For trigonal atoms, the two p orbitals lying in the plane containing the 
nuclei are combined with the s to yield three sp 2 hybrids, as shown in Figure 1.14. 
For a linear geometry, the appropriate hybridization is sp (Figure 1.15). 

The__relative contributions of s and p orbitals to the hybrids is different for 
the different types of hybridization. An sp 3 hybrid contains a larger proportion of 
p and a smaller proportion of s than an sp 2 , which in turn contains more p and 
less s than an sp. Since s electrons can_penetrate closer to the nucleus than p 
electrons, which Jiaye a node at the nucleus, s electrons are held more tightly. 
Therefore an atom is effectively more electronegative in bonds that use a larger 
proportion of s. Appendix 1 to this chapter gives a systematic procedure for 
specifying the proportions of s and p, and also shows how the s and p contribu- 
tions change with changing geometry. 

a And 77 Bonding. Ethylene 

The ethylene molecule will illustrate construction of a model containing both a 
and 7T bonding. The Lewis structure (22) shows that each carbon should be 
approximately trigonal. Therefore we need sp 2 hybrids on each carbon. Figure 


H H 


26 The Covalent Bond 

Figure 1.16 The basis orbitals for the a MO's of ethylene. 

1.16 shows these hybrids, together with the hydrogen Is orbitals. The orbitals are 
allowed to interact in pairs, each pair yielding a bonding and an antibonding a 
MO. There remain two p orbitals, one on each carbon, which were not used in the 
hybridization. These can overlap to form a -n bonding-antibonding pair; this 
process is the same as illustrated earlier in Figure 1.8. Now we have obtained five 
bonding and five antibonding a MO's and one bonding and one antibonding 
77 MO. These can all be put on an approximate energy-level diagram as in 
Figure 1.17, which also shows how the 12 valence electrons are assigned to the 
molecular orbitals in the electronic ground state. 

The energy levels shown in Figure 1.17 are not accurate; actually the a CH 
levels will be at different energies rather than all the same as shown in the figure. 



— H— 


Oj cu 





— 14— 


— H— 


— H— 



Figure 1.17 Energy-level diagram for the bonding model of ethylene. The ct ch levels are not 
actually all at the same energy, but are lower than 7r cc . 

Delocalized tt Bonding 27 

But the important point for most purposes is that the highest-energy bonding MO 
and the lowest-energy antibonding MO in ethylene will be the it and it* levels, 
with the ct's lower than the n and the ct*'s higher than the n*. 


In the allyl system (23), each carbon is trigonal, and each uses sp 2 hybrids to 
make bonds to its neighbors. The procedure outlined in the previous section is 


therefore adequate for constructing the a MO's. The system of a orbitals obtained 
is called the a framework. After constructing the a framework, a p orbital remains 
on each carbon. These/) orbitals are the basis orbitals for the tt system of molecular 

Formation of 77 Systems 

In allyl, the three basis/) orbitals can be symbolized as shown in 24. Now there is 
no way to avoid the problem of the central p orbital interacting with more than 
one other orbital. One approach is to go to the quantum theory rules and work 



through the prescribed procedures to find how the three orbitals will combine. 
The method, at an approximate level, is the Hiickel theory. It is described in detail 
in the references cited earlier (see footnote 2, p. 10), and a brief derivation and 
an example are given in Appendix 2. Here, we illustrate the results for some 
simple systems; later, in Chapter 10, we shall develop a method of obtaining the 
same results qualitatively in a simple way. 

The first rule„tO-xemember in making tt system orbitals is that the number 
of MO's is going to be the same as the number of basis/) orbitals used. Thus,Jhr 
allyl we shall get three 77 MO's. The lowest-energy one will be the combination 

f Md = Pi + Pi + p3 
It will have the shape shown in 25, and it will be bonding. 



28 The Covalent Bond 
The next-higher energy MQ_is 

It looks like 26 : 


4>uo 2 nas a node cutting across it and passing through the central carbon ; basis 
orbital p 2 does not contribute to this MO. This orbital is nonbonding." Its energy 
is the same as that of the basis orbitals themselves, so that electrons in it do not 
contribute to bonding. The third MO is 

yW, = Pi - Pa + P3 (1-9) 

and looks like 27 : 

It has a node between each bonded pair of carbons and is antibonding. Figure 
1.18 shows these n MO's in an energy-level diagram. 

In the allyl cation, with two n electrons, ifi uo is occupied; in the radical, 
with three w electrons, one electron is in the nonbonding i/ , mo 2 > an ^ m the anion, 
with four v electrons, there are two in ft U02 . Note that the nonbonding <Pmo 2 1S 
concentrated at the ends of the chain ; the molecular orbital pictures for these 
species thus correspond closely to the resonance pictures (see 8, 9, 10, p. 6), 
which show the charge or unpaired electron to be concentrated at the ends. 

Figures 1.19 and 1.20 show the n molecular orbitals for butadiene and 
pentadienyl. In each case the lowest-energy orbital has no vertical nodes, and 
each higher-energy orbital has one more vertical node than the orbital below it 
had, with the highest-energy orbital always having a node between every adja- 
cent pair of atoms. Chains with an odd number of atoms have a nonbonding 
orbital, in which there is no contribution from alternate p orbitals. 

The it molecular orbitals in these systems extend over several atoms, rather 
than encompassing only two, as have the MO's we considered earlier. Orbitals_ 
that extend over more than two atoms are said tO-he delocalized,. 


The concept of aromaticity has been extremely fruitful for both theoretical and 
experimental organic chemists. Aromatic compounds are cyclic unsaturated 
molecules characterized by certain magnetic effects and by substantially lower 
chemical reactivity and greater thermodynamic stability than would be expected 
from localized bond models. 

Aromaticity 29 

Basis orbitals 

Pi Pi P2 

Molecular orbitals 






*M0 3 =Pi-P2 + P3 




^M0 2 = Pt~P3 


*MO, =Pl+P2 + Pi 

Figure 1.18 The it MO's of the allyl system. The basis orbitals from which the n MO's are 
constructed are shown at the top of the figure, and below are the molecular 
orbitals in an energy-level diagram. 

Resonance and Aromaticity 

The familiar properties of benzene illustrate the characteristics of aromatic com- 
pounds. Benzene is much less reactive toward electrophiles, such as molecular 
halogens, than are simple olefins; and the heat evolved on hydrogenation is less 
by 37 kcal mole" 1 than predicted for a cyclic C 6 H 6 with three localized ethylene- 
type double bonds. Furthermore, the nuclear magnetic resonance spectrum of 
benzene and its derivatives shows the protons bonded to the ring to be experienc- 
ing a stronger effective magnetic field than do protons attached to simple 

As we have seen, these properties are accounted for in the resonance picture 
by modifying the model through inclusion of a second structure with double 
bonds in the alternative locations. 

30 The Covalent Bond 


Molecular orbitals 




rr 4 


■ Bonding 

Figure 1.19 The -n MO's for butadiene. 

The reader will also be aware that not all cyclic conjugated molecules for 
which such equivalent structures may be written share with benzene these 
special properties. For example, cyclobutadiene (28) eluded synthesis for many 
years; when finally prepared, it and its simple derivatives proved to be extremely 


reactive and capable of existence only when immobilized by freezing in an inert 

Aromaticity 31 

matrix at very low temperature. 8 Cyclooctatetraene, though a stable compound, 
does not have a planar ring ; whatever stabilization we might have expected it to 
gain from the derealization 29 <-► 30 is evidently not sufficient to cause the 

molecule to abandon its tub-shaped conformation (31) for the planar structure 
that would allow cyclic conjugation. 

The simple resonance theory fails to explain the singular lack of effective- 
ness of derealization in cyclobutadiene and cyclooctatetraene, but we may turn 
to molecular orbitals for the solution. 

77-Electron Theory and the Hiickel 4n + 2 Rule 

In order to construct a bonding model for a planar conjugated ring, we follow the 
procedure outlined for the allyl system in the previous section and make the 
choice of sp z hybridization on each carbon. The a framework is then constructed 
from these sp z hybrids and the hydrogen \s orbitals, leaving a p orbital on each 
carbon. We next concentrate on the interactions among these p orbitals.' 

Erich Hiickel developed this theory in the 1930s. He discovered that the 
energies of the -n molecular orbitals for any regular plane polygon with an even 
number of atoms will fall in the pattern 32. 9 A polygon with an odd number of 
atoms gives the pattern 33. These patterns, a single lowest level with higher levels 




8 (a) L. Watts, J. D. Fitzpatrick, and R. Pettit, J. Amer. Chem. Soc, 87, 3253 (1965); (b) O. L. 
Chapman, C. L. Mcintosh, and J. Pacansky, J. Amer. Chem. Soc, 95, 614 (1973); (c) G. Maier and 
M.- Schneider, Angew. Chem. Int. Ed., 10, 809 (1971). For a summary of attempts to prepare cyclo- 
butadiene, see (d) M. P. Cava and M. J. Mitchell, Cyclobutadiene and Related Compounds, Academic 
Press, New York, 1967. 

9 (a) E. Hiickel, Z Physik, 70, 204 (1931); (b) E. Hiickel, Z. Physik, 76, 628 (1932); (c) E. Hiickel, 
Z. Electrochem., 43, 752 (1937). 

32 The Covalent Bond 

Basis orbitals 

Molecular orbitals 









Figure 1.20 The 77 MO's for pentadienyl. 

in pairs of the same energy [degenerate pairs), is actually a consequence of the re- 
fold symmetry of the CnH^ rings. 

Hiickel noted that if electron pairs are filled into the energy-level pattern 32 
or 33, a closed-shell structure (all electrons paired) will result only when the total 
number of pairs is odd (total number of electrons = \n + 2, n = 0, 1, 2, . . .) ; if 
the number of pairs is even (total number of electrons = An, n = 0, 1,2,...), 

Aromaticity 33 

the last pair will be the only occupants of a doubly degenerate level and so one 
electron will go into each orbital with spins parallel. Diagrams 34 and 35 show 
the level filling for An + 2 and An electrons, respectively. 

34 35 

4« + 2 electrons 4« electrons 

(odd number of pairs) (even number of pairs) 

Because open-shell molecules are ordinarily highly reactive, the An electron rings 
should be chemically unstable. 

When the n electron energy of a cor rugated C^H,, ring is calculated from 
the energy-Ievel diagram , it is [found to be differejiLfrojnjthej^er^r^ calculated 
for anopen-chain CnH„ ± 2 polyene or from the^77,energy^)f_fl/2-elhylene_moJecules. 
T he difference is termed the resonance energy. I The simple Hiickel molecular 
orbital theory yields unre h ^bje energies, but more careful calculations show that 
the 4w + 2 rings are stabilized compared with the open-chain analog, whereas 
the An systems are destabilized^ 10 Theory thus provides an energy criterion for 
classification of cyclic conjugated systems as aromatic or antiaromatic : j\ 
molecule is aro matic J f it is tl^rnic^ynamically^jriQre-^staMe than expected for 
tKeopei>cHain analog, and __it_ _is_antiarojnalic if it is thermodynamically less 
stableT^A compound showing-neither- stabilization Jior-destabilization would be 
classed as~honaromatic. 

AT second criterion of aromaticity comes from analysis of the influence of a 
magnetic field on the tt electron cloud. Theory jmggests i_that_a jnagnetic field 
perpendicular to the ring plane will cause the electrons to behave as_thpuglLj;liey 
were cumulating" around the ring and generating their own. small magnetic field, 
which will be superimposed on the applied field, 11 The term ring current is com- 
monly applied to this phenomenon. 

The direction of this induced magnetic field depends on the number of ir 
electrons. In An j^2_rings it is in _th.e_direction opposite to the applied field (the 
rings are diamagnetic), whereas in An rings it is in the same direction as the applied 
field {paramagnetic rings). Figure 1.21 illustrates these two situations and shows 
how the induced fields affect the total field at protons attached to the ring. Be- 
cause the magnetic lines of force must make closed loops, the induced field is in 
opposite directions for protons inside and outside the ring. Note that in An + 2 

10 See, for example, (a) M. J. S. Dewar and G. J. Gleicher, J. Amer. Chem. Soc, 87, 685 ( 1965) ; for 
discussion of the various approaches to -n electron molecular orbital theory, see (b) Streitwieser, 
Molecular Orbital Theory for Organic Chemists, and (c) L. Salem, The Molecular Orbital Theory of Conju- 
gated Systems, W. A. Benjamin, Menlo Park, Calif., 1966. 

11 J. A. Pople and K. G. Untch, J. Amer. Chem. Soc, 88, 4811 (1966). 

34 The Covalent Bond 

4n + 2 
7T electrons 



7T electrons 


Figure 1.21 Induced fields caused by ring currents in cyclic conjugated molecules, (a) Dia- 
magnetic \n + 2 ring. The induced field Hi opposes the applied field H for 
protons inside the ring and adds to it for protons outside, (b) Paramagnetic 4n 
ring. The induced field H t adds to the applied field H inside but opposes it 
outside the ring. 

rings the induced field adds to the applied field for outside protons but is opposed 
to the applied field inside the ring. The situation is reversed in \n rings. 

Theory of aromaticity is not restricted to the simple planar conjugated rings. 
Any system that has extra stability by virtue of being cyclic would be classed as 
aromatic. The homoaromatics form one such category ; they are systems in which the 
77 system is interrupted at one or more points by a saturated center but in which 
geometry still permits significant overlap of the p orbitals across the insulating 
gap. 12 Although there are a number of homoaromatic systems known, it will be 
sufficient for our purposes to restrict attention to the monocyclic conjugated rings 
C n H n and their derivatives. These compounds are known as annulenes; the nomen- 
clature convention is to designate the ring size by a number in square brackets. 
Thus [njannulene is the ring C n H n . 

Some Examples of Aromatic and Antiaromatic 
Systems: Neutral Even-Membered Rings 

For benzene, [6]annulene, with six it electrons (4n + 2, n = 1), the theory 
clearly meets both tests. As we have pointed out, there is a substantial stabiliza- 
tion of about 37 kcal mole -1 compared with a hypothetical localized model. The 
familiar chemical properties also point to a strong tendency for maintenance of 
the six -n electron unsaturated system. The proton magnetic resonance spectrum 
of benzene and its derivatives shows the proton resonances in the range of 
8 = +7 to +8ppm (downfield from tetramethylsilane), 1-2 ppm lower than 
protons attached to nonbenzenoid double bonds. Referring to Figure 1.21a, we 
can see that the prediction is in agreement with this result. The induced field adds 

12 Review: S. Winstein, Quart. Rev., 23, 141 (1969). 

Aromaticity 35 

outside the ring so that a smaller applied field is required to reach resonance, 
hence a downfield shift. There is, of course, no possibility of having a proton inside 
a ring this small. 

Cyclobutadiene, [4]annulene, is so far too elusive for the kinds of investiga- 
tions one would like to be able to carry out. But the great difficulty that chemists 
have experienced in its preparation alone justifies the conclusion that it lacks any 
aromatic stabilization. The compound can now be prepared by oxidation of 
cyclobutadieneiron tricarbonyl (36) ; 13 it dimerizes instantaneously but is stable 

ZxJ ^- £J 




C C c 

O O o 


when prepared in a dilute argon matrix below 35°K. 14 Infrared and ultraviolet 
spectra have been recorded, but magnetic resonance presents a more difficult 
problem, and no pmr spectrum has been obtained. 

Ronald Breslow and his collaborators have given some attention to the 
problem of estimating the degree of destabilization of cyclobutadiene with respect 
to nonconjugated models. They have concluded from electrochemical measure- 
ments of oxidation-reduction potentials of the system 37 ^ 38, of which only 
the quinone 38 has the cyclobutadiene fragment, that the C 4 H 4 ring is desta- 
bilized by some 12-16 kcal mole -1 and so is definitely antiaromatic. 15 

+ 2e~ 


Cyclooctatetraene, as we have noted earlier, avoids the difficulty that we 
would predict it would encounter if it were planar. It takes up a nonplanar con- 
formation in which the double bonds are effectively isolated from each other by 
twisting ; in this way the p orbitals of one do not interact appreciably with those 
of the next. The molecule has conventional single and double bonds and behaves 
chemically like a typical olefin. One might argue that this evidence is only sugges- 
tive, because the angle strain which would be introduced were the ring to become 
planar could be the cause of its preferred shape. But as we shall see, the angle 

13 For other methods of preparation see (a) C. Y. Lin and A. Krantz, J. Chem. Soc. Chem. Comm., 1111 
(1972); (b) S. Masamune, M. Suda, H. Ona, and L. M. Leichter, J. Chem. Soc. Chem. Comm., 1268 
(1972); (c) see also note 8(a), p. 31. 

14 See note 8(b), p. 31. 

15 R. Breslow, D. R. Murayama, S. Murahashi, and R. Grubbs, J. Amer. Chem. Soc, 95, 6688 

36 The Covalent Bond 

strain is not sufficient to overcome the tendency toward planarity for an eight- 
membered ring with 4n + 2 n electrons. 

A number of larger cyclic conjugated systems have been prepared, many of 
them by Sondheimer and co-workers. 16 [10]Annulene and [12]annulene are 
subject to considerable steric difficulties and probably are not planar, but the 
larger molecules are big enough to accommodate hydrogen atoms inside the rings 
and so can have trans double bonds and still be planar or nearly so. Likely con- 
formations for some of these compounds are shown in Structures 39, 40, and 41. 

h ^r ^r ^r h 

H H H 


Annulenes as large as the 30-membered ring have been prepared, and many 
dehydroannulenes, which* contain one or more triple bonds, are also known. 

18 F. Sondheimer, Accts. Chem. Res., 5, 81 (1972). 

Aromaticity 37 

(These latter substances are actually intermediates in the preparation of the 
annulenes themselves.) 

These large rings, even the 4n + 2 ones, do not show the kind of chemical 
stability that benzene has, although [18]annulene does undergo electrophilic 
substitutions. Ring currents provide the most useful criterion for testing their 
aromaticity. The molecules have protons both inside and outside the ring. Con- 
formational equilibria such as those indicated in 39 and 40 exchange the inner 
and outer protons rapidly at room temperature, but at lower temperatures the 
rates are sufficiently slow that the two types of proton can be observed. The 
spectra provide a dramatic confirmation of theory. The [14], [18], and [22] annu- 
lenes, 4n + 2 systems, have outside proton resonances between about 8 — +7.8 
and S = + 9.6 ppm, shifts somewhat larger than those in benzene, whereas the 
inside protons appear between 8 = — 0.4 and 8 = — 3 ppm. 17 (Positive 8 values 
are downfield from tetramethylsilane (TMS) ; negative 8 values are upheld.) 
The 4n rings [16] and [24]annulene have outside protons at 8 = +4.7 to 
5 = +5.3 ppm and inside protons at much lower field, 8 = + 10 to 8 = +12 

Even-Membered Rings: 
Cations and Anions 

Addition of two electrons to, or removal of two electrons from, a \n antiaromatic 
ring converts it to a 4n + 2 system, which should be aromatic. Several examples 
of such ions are known. 

Tetramethylcyclobutadiene dication (43), has been prepared by Olah and 
co-workers by dissolving the dichloride (42) in a mixture of antimony penta- 

H 3 C. 

N s - - \ / 

+ 2C1" 

.CH 3 

/CH 3 


H 3 C X 

/CH 3 



SbF 5 , SO a 

H 3 C / 

X CH 3 

H 3 C 

42 43 

fluoride and sulfur dioxide at low temperature. 18 It was identified by its proton 
magnetic resonance spectrum, a single peak at 8 = +3.7 ppm. The tetraphenyl 
dication has also been observed. 19 A report of the dianion 44, a six n electron 
system, has appeared. 20 



Addition of two electrons to cyclooctatetraene yields the dianion 45, which 
shows a single peak in the proton magnetic resonance spectrum. 21 The conclusion 

17 See note 16. 

18 G. A. Olah, J. M. Bollinger, and A. M. White, J. Amer. Chem. Soc, 91, 3667 (1969). 

19 G. A. Olah and G. D. Mateescu, J. Amer. Chem. Soc, 92, 1430 (1970). 

20 J. S. McKennis, L. Brener, J. R. Schweiger, and R. Pettit, J. Chem. Soc. Chem. Comm., 365 (1972). 

21 T.J. Katz, J. Amer. Chem. Soc, 82, 3784 (1960). 

38 The Covalent Bond 

that the ion is a planar regular octagon is confirmed by the X-ray crystallographic 

Li, Na, or K 

+ 2M + 

structure determination of the 1,3,5,7-tetramethylcyclooctatetraenyl dianion, 
which shows the eight-membered ring in a planar conformation with equal bond 
lengths. 22 Note that the energy gain associated with establishment of the con- 
jugated An + 2 77 electron aromatic system is sufficient to overcome the angle 
strain, which tends to prevent a planar structure. 

Dianions of several of the large ring annulenes have also been prepared. 23 
The An + 2 system [18]annulene, which has outer protons at S = +9.3 ppm 
and inner protons at S = — 3 ppm, is converted by potassium to the dianion, a 
An system with outer protons at 8 = — 1 ppm and inner protons at S = +29 
ppm, the lowest field resonance known for a proton bound to carbon. (The largest 
known upfield shift, 8 = — 9 ppm, occurs for the inner protons of an 18 n electron 
(An + 2) monoanion. 24 ) 

Another intriguing ion, hexachlorobenzene dication (46), a four n electron 
system, has been observed by Wasserman and his collaborators. As predicted by 
the simple molecular orbital energy-level pattern, the ion has two unpaired 
electrons. 25 


Odd-Membered Rings 

Neutral rings composed of an odd number of C — H groups have an odd number 
of electrons and hence cannot be closed-shell molecules. In study of odd-mem- 
bered rings, attention has focused on ions with even numbers of electrons, obtained 
by processes like those indicated in Equations 1.11 and 1.12. Rings containing a 

22 S. Z. Goldberg, K. N. Raymond, C. A. Harmon, and D. H. Templeton, J. Amer. Chem. Soc, 96, 
1348 (1974). 

23 See note 16, p. 36. 

24 See note 16, p. 36. 

25 E. Wasserman, R. S. Hutton, V. J. Kuck, and E. A. Chandross, J. Amer. Chem. Soc, 96, 1965 
(1974). Careful theoretical analysis suggests that the open-shell systems, which simple theory predicts 
will have one electron in each of two degenerate levels, can distort from the regular polygon geometry 
by moving to a structure with alternating bond lengths, thereby removing the degeneracy and 
causing the electrons to pair in the lower level. This distortion seems to occur in some antiaromatic 
systems but not in others. 

Aroma ticity 39 

hetero atom that contributes two electrons to the n system are isoelectronic with 



the C — H ring anion of the same size. Rings containing one carbonyl group 
resemble the C — H ring cation of the same size because the electron-withdrawing 
carbonyl oxygen leaves the carbonyl carbon electron-deficient. According to 
theory, rings of 3, 7, 11, ....... members .should yield aromatic cations and anti- 
aromatic anions, whereas rings of 5, 9 3 13,... members should give aromatic 
anions and antiaromatic cations. 

The best-known examples in this series are the cyclopentadienyl anion (47) 
and the cycloheptatrienyl cation (48), both six n electron systems and both 
remarkably stable. 26 


Attempts to prepare cyclopentadienone (49), an analog of C 5 H 5 + , yield 
only the dimer (Equation 1.13). 27 Cycloheptatrienone (tropone, 50), on the 
other hand, is stable and readily prepared by a number of methods. 28 Cyclo- 



26 (a) Cyclopentadienide anion: P. L. Pauson, in Non-Benzenoid Aromatic Compounds, D. Ginsberg, 
Ed., Wiley-Interscience, New York, 1959; (b) cycloheptatrienyl cation: F. Pietra, Chem. Rev., 73, 
293 (1973). 

27 M. A. Ogliaruso, M. G. Romanelli, and E. I. Becker, Chem. Rev., 65, 261 (1965). 

28 See note 26(b). 

40 The Covalent Bond 

heptatriene is correspondingly reluctant to be converted to an eight tt electron 
anion; the acidity of cycloheptatriene (Equation 1.14) is less than that of cyclo- 
pentadiene (Equation 1.15) by roughly 20 powers often, 29 a difference in reaction 
free energies of some 27 kcal mole -1 . 


Q] + H 3 + (1.15) 

Three-mernbered ring systems have also provided examples of aromatic and 
antiaromatic behavior. Despite the very substantial angle strain, Breslow and his 
collaborators have succeeded in preparing a number of cyclopropenyl cations 
(51). 30 Cyclopropenone (52) has been isolated and is stable in pure form below 

O O 

52 53 

its melting point of -28 to -29°C and in solution at room temperature, 31 
even though the saturated analog cyclopropanone (53), which should be less 
strained, polymerizes rapidly in solution at room temperature by a self-addition 
to the carbonyl group which relieves some of the strain. 32 

The contrasting reluctance of the three-membered ring n system to take on 
four electrons is illustrated by the very low acidity of triphenyl cyclopropene (54), 
estimated to be roughly 18 powers often less than that of triphenylmethane. 33 
A number of ions and hetero-atom large ring systems are also known. 34 


1. (a) Write Lewis structures for each of the following molecules or ions. Show all ' 
significant contributing structures whenever there are more than one. 

29 See Table 3.1, pp. 146-147. 

30 See, for example, R. BreslowrH. Hover, and H. W. Chang, J. Amer. Chem. Soc, 84, 3168 (1962). 

31 R. Breslow and M. Oda, J. Amer. Chem. Soc, 94, 4787 (1972). 

32 N. J. Turro and W. B. Hammond, J. Amer. Chem. Soc, 88, 3672 (1966). 

33 R. Breslow and K. Balasubramanian, J. Amer. Chem. Soc, 91, 5182 (1969). 

34 See note 16. 

Problems 41 

(b) In each molecule that has a delocalized bonding system, identify the 
orbitals that interact to form the delocalized molecular orbitals. 

°X /° 

N— N 

</ x o 

K 2 C0 3 Sodium nitrate 

Allene (H 3 C) 3 OBF 4 

Butadiene Benzyl cation 

Sodium phenoxide Phenyl anion 

Nitrobenzene 3,5-di-toY-butyl-4-nitrophenoxide 

N— N— O 

2. What kinds of symmetry are possible for interactions of d orbitals ? 

3. In the pentadienyl radical, predict the distribution of the unpaired electron 
(a) from the resonance model, and (b) from the molecular orbital model. 

4. Construct a complete orbital model for-HN 3 , showing both a and n molecular 
orbitals, and giving an approximate energy-level diagram showing electron occupancy. 
Compare the MO model with the resonance model. 

5. Construct a MO model for twisted ethylene, in which the two CH 2 groups lie 
in mutually perpendicular planes. Why does the molecule prefer coplanarity ? 

6. Explain why dehydroannulenes, which have some of the double bonds of the 
annulene replaced by triple bonds, can be considered in aromaticity theory as equivalent 
to the parent annulene. What advantages might dehydroannulenes have over annulenes 
in the study of aromaticity ? 

Problems 7-11 require the material in Appendix 1. 

7. Verify that the hybrid orbital in Equation A1.9 (p. 46) is normalized for any 
values of m, 6, <f>. 

8. Write the expression for a normalized sp 2 hybrid orbital oriented along the line 
from the origin to the point ( — 2, 3, — 1). 

9. Write the expression for a normalized hybrid orbital with 28 percent s 
character lying in the xy plane at an angle of 60° from the x axis. 

10. If s,p x ,p y ,p z orbitals are to be hybridized, and the fractional s character of 
three hybrids are specified, what remains to be specified before the hybrid set can be 
written explicitly? 

11. What are the fractional s and/> characters of a pair of equivalent hybrids with 
an angle of 1 00° between them ? If the other two hybrids are required to be equivalent 
to each other, what are their fractional s and p characters, and what is the angle be- 
tween them? 

Problems 12 and 13 require the material in Appendix 2. 

12. Find the Huckel energy levels and molecular orbitals for butadiene, cyclo- 
butadiene, and pentatrienyl. 

13. In the Huckel theory the it electron energy is defined as the sum of the orbital 
energies of all the n electrons. Thus for ethylene, with two electrons in an orbital of 
energy /}, the n electron energy is 2/3. Resonance energy is the difference between the 
calculated 77 electron energy and the 77 electron energy the system would have if the 
electrons were in localized ethylene double bonds. Find the resonance energies for the 
systems in Problem 12. 

42 The Covalent Bond 


6. F. Sondheimer, Accts. Chem. Res., 5, 81 (1972). 

12 and 13. A. Liberies, Introduction to Molecular Orbital Theory, Holt, Rinehart, and Win- 
ston, New York, 1966; J. D. Roberts, Notes on Molecular Orbital Calculations, W. A. 
Benjamin, Menlo Park, Calif., 1962. 

Appendix 1 



In order to obtain correct expressions for hybrid orbitals, we first need to describe 
more precisely than has been done in Section 1 .2 some properties of orbitals. 
Recall that <p 2 , the square of an orbital function, gives the probability of finding 
the electron in each region of space. If we were to add up the values of this func- 
tion over all points, we would have the total probability of finding the electron, 
which should equal unity. Orbitals are ordinarily constructed so as to satisfy this 
requirement; when they are, they are said to be normalized. The normalization 
condition is Equation A 1.1, where dr signifies integration over all coordinates. 

Normalization : j 9s 2 dr — 1 ( A 1 . 1 ) 

A second condition, which does not apply generally to orbitals but which 
does apply to different atomic orbitals on the same atom is that they do not overlap 
with each other. The correct terminology for orbitals that have zero overlap is 
that they are orthogonal. We have seen that the overlap of two orbitals is found by 
integrating over space the product (pi(p 2 - Since our s and p orbitals, and also the 
resulting hybrids, are on the same atom, we require for any pair in the s, p set 
and also for any pair in the hybrid set that Equation Al .2 be satisfied : 

Orthogonality: ) (p t (pj dr = (A 1.2) 

We now write a general formulation for our set of hybrid orbitals. Each 
hybrid, xt, is going to be written as a sum of contributions from the s, p x , p y , p z 
atomic orbitals, each with a coefficient that tells the extent of its contribution. 

'The discussion partly follows C. Hsu and M. Orchin, J. Chem. Educ, 50, 114 (1973). 


44 Appendix 1 

The hybrids therefore have the form of Equations A 1.3. 

Xi = a n* + a i2p x + a 13 p y + aup; 

X2 = 021 s + a 22px + 023py + <224/>3 

X3 = fl 3i-* + a 32 p x + a 33 p y + a 3 ip z 

X4 = <*u s + a i2 p x + a i3 p y + a 44 /> 3 


We assume that s, p x , p y , p z are all normalized and mutually orthogonal. 
The requirement that the Xi will also be normalized and mutually orthogonal 
then leads to the following conditions : 

Normalization of y^\ 

an 2 + a l2 2 + a, 3 2 + a, 4 2 = 1 

Orthogonality of^, and^ y : a tl a n + a l2 a j2 + a i3 a j3 + a ti a,i = 


(The reader familiar with vectors will recognize that, if the xi are thought of as 
vectors written in terms of the set of unit vectors s, p x , p y , p z , Equation A 1.4 is 
just the requirement that xi be of unit length, and Equation A1.5 is the require- 
ment that the dot product Xi-Xy be zero.) 

Since the sums of squares of the a coefficients of a given hybrid is unity 
(equation A 1.4), it is reasonable to take the squares of the coefficients as giving 
the contributions of the orbitals of the s, p x , p y , p z set to the hybrids. We therefore 
define the fractional s character of hybrid xt as a a 2 and the fractional p character 
as a i2 2 + <z (3 2 + a (4 2 . The orthogonality and normalization conditions guarantee 
that the sum of squares of a coefficients down a column in A 1.3 will be unity, just 
as it is along a row; the fractional contribution of a given member of the s, p x , p y , 
p z set summed over all the hybrids (for example a xl 2 + a 2i 2 + a^ 2 + ^n 2 for 
the j-orbital contributions) therefore will always be unity. 

Equations A 1.3 can be put in a more convenient form in the following way. 
We note that because the s orbital is spherically symmetrical, the directional 

sin 6 cos 

Figure Al.l The vector v, of unit length, is expressed in polar coordinates in terms of unit 
vectors x, y, z as v = sin 6 cos <f> x + sin 6 sin <f> y + cos z. 

Hybrid Orbitals 45 

properties of a hybrid are entirely determined by the relative contributions of 
p x , p y , and p z . It is therefore convenient to think of three-dimensional vectors 
oriented along the directions in which we wish our hybrids to point. (It is 
important to understand that we are now talking about vectors in ordinary 
three-dimensional space.) 

These vectors can be written in terms of vectors along the x, y, and z direc- 
tions using polar coordinates 8 and <f>, as indicated in Equation A1.6 and illus- 
trated in Figure A 1.1. 

v = sin 9 cos (j> x + sin 9 sin <f> y + cos 9 z 


The reader can verify that v defined in this way is normalized (of unit length). 
Now we wish to write an expression for an orbital oriented along the direc- 
tion defined by vector v. This task is easily accomplished if we replace our unit 
vectors x, y, z by the orbital functions p x , p y , p z . These orbitals add just like the 
unit vectors to produce a new function, Equation A 1.7, with the usual ^-orbital 
shape, but pointing in the direction of v, as illustrated in Figure A1.2. Note that 
7] is normalized. 

r) = sin 9 cos <\> p x + sin 6 sin <j> p y + cos 9 p z (A 1.7) 

If we now want to introduce s character into the orbital ~q, the direction will 
remain as before; adding in some s only expands one lobe (on the side where s 
and Tj have the same sign) and contracts the other, at the same time moving the 
node away from the nucleus. The new orbital is most conveniently defined by 

Figure A1.2 The orbital yj, oriented in the direction of vector v (Figure Al.l), is expressed 
as a combination of the p x , p y , and p z orbitals by rj = sin 9 cos <f> p x + 
sin 9 sin <j)p y + cos 9 p z . Positive lobes are shaded, negative lobes are un- 
shaded. Orbital shapes are not accurately reproduced; see Wiberg, Physical 
Organic Chemistry, pp. 29-33, for more accurate contour diagrams. 

46 Appendix 1 

Equation A1.8, and the hybrid is illustrated in Figure A1.3. In Equation A1.9, 
■s+ I- v (Al-8) 


+ m 

1 + m 

1 + m 

s + 

1 + m 

{sin 6 cos <f> p x + sin 9 sin if> p y + cos 9 p s } 


we have simply substituted for tj by its equivalent from Equation A 1.7 in order to 
arrive at a general expression for the hybrid in terms of the original set s,p x ,p y ,p z . 
The reason for expressing the relative contributions of s and p in terms of the 
awkward-looking factors V 1/(1 + m) and Vm/(1 + m) is that this form 
guarantees that the generalized hybrid A 1.9 will be normalized. (See Problem 
1.7.) We have thus built in automatically one of the restraints on our hybrids. 
The quantity m is the hybridization index, and is the number that appears as the 
superscript in the standard designation of hybrid type. Thus an sp 3 orbital, m = 3, 
always has the form 

vT-S + vT { s > n cos <f> p x + sin sin <f> p y + cos 6 p z } 

an sp 2 orbital, m = 2, is always 

Vf-f + "V^F {sin 9 cos <f> p x + sin 9 sin <f> p y + cos />.J 

(Note that ordinarily one chooses a coordinate system in such a way that the sp 2 
hybrids will lie in, for example, the xy plane; then the angle 9 is 7r/2 and the 
coefficient of p z in the hybrids is zero. It is not necessary to follow this procedure, 
and the general sp 2 hybrid will have contributions from all three p orbitals.) 

We say that two hybrid orbitals are equivalent if they have the same hybridiz- 
ation index m. Recalling that the squares of the coefficients of a given orbital 
summed over the whole hybridized set must equal unity, we can easily see that 

Figure A1.3 The hybrid orbital x = "^1/(1 + m)s + Vm/(\ + m)t), or x = "^/O + m)s 
+ Vm/(1 + m){sm 6 cos <f> p x + sin6sin<f>p y + cos 6 p s }. 

Hybrid Orbitals 47 

the only way to have four equivalent hybrids is to let the coefficient of s be 
\/I in each ; these are the familiar sp a orbitals. 

We can use the generalized expression for hybrids to find the relation be- 
tween hybridization indices and angle between two hybrids xi an d x 2 (Equations 
ALIO). Since the expressions in braces are equivalent to ordinary three-dimen- 
sional vectors of unit length, the three-dimensional vector dot product, found by 

Xi = /■: s + I {sin 6x cos <f> 1 p x + sin 8 1 sin <f> x p M + cos 9i p z } 

/y 1 + m 1 /y 1 + m x 


I \ rnr 2 

X 2 = s + /- {sin 8 2 cos <f> 2 p x + sin 8 2 sin <f> 2 p y + cos 6 2 p 2 } 

y I + m 2 V 1 + m 2 

summing the products of coefficients appearing inside the braces, must be equal 
to the cosine of the angle a between the vectors (Equation Al.ll). b But the 
hybrids are directed along these vectors, so the angle between the hybrids is also 

cos a = sin 8 1 cos <f> 1 sin 9 2 cos <f> 2 + sin 9x sin ^ sin 8 2 sin <j> 2 + cos 8 X cos 9 2 (A 1.1 1) 

a. We now bring in the requirement A 1.5 that the two hybrids be orthogonal. 
This condition gives Equation A 1.1 2, which can be immediately simplified be- 

VI / 1 / m[ I m 2 
— / — + / — ■ / — {sin 8 X cos 0! sin 8 2 cos <f> 2 
1 + m 1 V 1 + m 2 /y 1 + mj -V 1 + m 2 

+ sin #! sin ^ x sin 8 2 sin <f> 2 + cos 8i cos 8 2 } ( A 1 . 1 2) 


cause the expression in braces is equal to cos a from Equation A 1.1 1. Equations 
A1.13 through A1.16 then follow. 

0= / / + / mi / — "^— {cos a} (A1.13) 

V l + % \ l + i»2 V i + ">i V i + m i 
I i / i - ^- ^ 

= / / [1 + ^SmlT/m^ cos a] (A1.14) 

V l + % \ l + «i 2 

0=1 + \/ r m^\/ r m^ cos a (A1.15) 


\/m x m 2 

If the two orbitals are equivalent, m 1 = m 2 = m, Equation A 1.1 6 reduces to the 
even simpler expression A 1.1 7. The angle between two equivalent hybrids completely 

cos a = — (A 1.1 7) 


" Proof may be found, for example, in G. B. Thomas, Jr., Calculus and Analytic Geometry, Addison- 
Wesley, Reading, Mass., 1953, p. 447. 

48 Appendix 1 

Figure A1.4 Orbitals %i an d X2 are t0 point along directions Vi and v 2 , with an angle of 
105° between them. 

Vj = x 

v 2 = —sin 15" x + cos 15° y 

determines the hybridization index, and conversely. We have just seen that four equi- 
valent hybrids must be sp 3 ; it is now clear that the angle between any two must 

cos a = — ^ 

a = 109.5° 

the tetrahedral angle. 

It is an easy matter to write the correct expressions for a pair of equivalent 
hybrids with a given angle a between them. Hybridization index m is found 
immediately from Equation A1.17. A direction [9 U ^) must be chosen for the 
first hybrid, and a direction (0 2 , <f> 2 ) for the second found such that the angle be- 
tween them will be a. The orientation of the hybrids with respect to the coordin- 
ate system is arbitrary; it will be easiest to set up the orbitals if they are oriented 
so that the first points along one of the axes (say x) and the second lies in one of 
the coordinate planes (say x, y), or if the two are placed in one of the coordinate 
planes with a coordinate axis bisecting the angle a. 

To illustrate with a concrete example, suppose that we wish to have 
a = 105°. In Figure A1.4, we orient the first hybrid along the x axis (along the 
direction v x = x) and the second at an angle of 105° to it in the xy plane (along 
the direction v 2 ). Equation A1.17 gives 

- = -cos 105° 

- = 0.259 




Hybrid Orbitals 49 
The hybrids are then 

I \ / 3.86 

* = V TTTse ' + JTTJM {p * ] (AL21) 

I i / 3.86 


Xl = V0.206* + V0?mp x (AI.23) 

* 2 = V0.206i + \ZO794{-0.259/> x + 0.966p y ] (A 1.24) 

The hybrids are <r/> 3 - 86 , the fractional j- character is 20.6 percent, and the frac- 
tional p character is 79.4 percent. 

Appendix 2 


The electronic state functions of a molecule are those functions *F which satisfy 
the Schrodinger equation : 

,#VF = £.¥ (A2.1) 

Here E e is the total electronic energy and 3^f e is the electronic Hamiltonian 
operator. 6 The state function T is a function of the coordinates of all the elec- 
trons. 3tif e is a prescription for carrying out on ¥" a sequence of mathematical 
operations (partial differentiation with respect to the various coordinates and 
division by electron-electron and electron-nuclear separations) that is deter- 
mined from the laws of mechanics and from the properties (number of electrons, 
number and positions of nuclei) of the particular molecule being considered. The 
Hamiltonian operator, though it may be quite complicated for a large molecule, 
can be written relatively easily; the unknown quantities in the equation are T 
and E e . In general, there will be many possible functions W that are solutions for a 
given #C e . Each of them represents a different possible state of the molecule, and 
each has its associated energy. (From this point on we shall consider the electronic 
ground state only.) Because the complexity of the many-particle molecular 
systems is so great, it is impossible to solve A2.1 for T and E. Approximate 
methods must be used if there is to be any hope of progress. 

" For further information consult the sources cited in footnote 2, p. 10. 

6 Equation A2.1 has already been simplified by making the assumption, known as the Born-Oppen- 
heimer approximation, that nuclear and electron motions can be considered separately. Equation 
A2.1 applies only to electron motions; the nuclei are considered to be in fixed locations. 


Molecular Orbital Theory 51 


The first approximation made in simplifying the task of solving for T is the 
orbital approximation. Each of the M electrons of the molecule is assumed to be 
described by a molecular orbital function i/> ; the total wave function for the elec- 
tronic state is the product of </i's for the individual electrons (Equation A2.2). c 

Y = fr(l)fc(2)fc(3) . . . + wa (M) (A2.2) 

The problem of finding the orbital functions </ij is commonly solved in one 
of two ways. Both use the variation principle. The variation principle states that 
whenever an approximate function is substituted for </r in the expression 

^°</. = Ej, (A2.3) 

where 2fP now refers to any Hamiltonian operator, the value of the energy E 
obtained will be greater than the true energy of the correct lowest energy wave 
function. Hence, the best result possible with an approximate wave function of a 
particular type will be obtained when it is chosen so as to minimize E. The more 
rigorous approach to finding the orbital functions is the Hartree-Fock-Roothaan 
method. It applies the variation principle to Equation A2.1, with Y expressed 
as in A2.2, and yields a new result of the form A2.3, where 3df becomes the 
Hartree-Fock or self-consistent field operator, ^scfj an d the molecular orbitals 
i/ij represent the best solution possible within the orbital approximation. d A 
simpler procedure is to assume an approximate Hamiltonian, ^a^rox, which 
can be put directly in place of J^in A2.3. Hence, both approaches lead to the 
form A2.3, which must now be solved for </i and E. 


The next approximation is the expression of each molecular orbital 1/1 as a linear 
combination of atomic orbitals (LCAO) (Equation A2.4), where <p y are atomic orbital 
functions and c j are coefficients that give the contribution of each atomic orbital 
to the molecular orbital. The cp y are the basis functions discussed in Section 1.2. 
Valence atomic orbitals are ordinarily chosen for the basis. 

* = 2 w ( A2 - 4 ) 

We always require that orbital functions be normalized. Because the proba- 
bility of finding the electron in orbital ift near a particular point is given by the 
value of i/i 2 at that point and because the total probability of finding the electron 

c When electron spin is properly taken into account, the total wave function for the state must be an 
antisymmetrized product of the orbital functions. Antisymmetrization automatically incorporates the 
Pauli exclusion principle. In Huckel theory, where orbitals are not properly antisymmetrized, it is 
necessary to add the extra restriction that electrons be assigned no more than two to an orbital and 
that spins of electrons occupying the same orbital be paired. 

i Because ^" SC f depends on its own solutions iji, an iterative procedure of successive approximations 
is required. For derivations, see the sources cited in notes 2 (f), and 2 (g), p. 10. 

52 Appendix 2 

somewhere must be unity, Equation A2.5 must hold, where dr indicates a multiple 

j f 2 dr = 1 (A2.5) 

integration throughout all space over all the coordinates of the electron. e It is an 
easy matter to normalize an orbital function; if ifi is not normalized, iplV^dr 
will be. In practice, normalized atomic orbital functions <pj are chosen initially; 
then the ^'s are normalized when Equation A2.6 is satisfied. 

2 c* = 1 (A2.6) 


We now return to Equation A2.3 and substitute into it Equation A2.4. We 
then obtain A2.7, where A^is the total number of basis orbitals being used. The 
variat ion principle now has to be applied to A2.7 to find the values of the c's 
which will give the best ip's possible with the chosen basis. The energy is mini- "I 
mized simultaneously with respect to all the c's by carrying out a partial differen- \ 
tiation with respect to each c and making the derivatives of the energy satisfy 
A2.8. The result, after some manipulations, is a set of N equations of the form 
A2.9, where the index i takes a different value for each equation. 

N N 

x> 2 w = E 1 c m ( A2 - 7 ) 


— = for each./' = 1, 2, . . ., N (A2.8) 

2 c t [ tf^ift dr = 2 Ec i J" <Pt<Pi d T (A2.9) 

1=1 ' y=i 

We now introduce the following new notation. 

\<p m dr = <^| v ,> = S„ (A2.10) 

J 1H#> 9 , dr = < w | JP| W > = H u (A2.1 1) 

S tj is the overlap integral, and H ti is called the Hamiltonian matrix element between 
basis functions i andj. We can now rewrite A2.9 as A2.12: 

| e,H u = I Ec,S tj (A2.12) 

Rearranging, we have : 

2 c,(H tj - ES it ) = (A2.13) 

* Because orbital functions can be complex (that is, they can contain the quantity V— 1), one must 
actually use ij>*ij> instead of if> 2 . The functions one ordinarily encounters in approximate molecular 
orbital theories are real ; therefore this distinction makes no practical difference for our purposes. 

Molecular Orbital Theory 53 

Remember that there are N of these equations, one for each of the N possible 
values of i. If we regard the e/s as unknowns, these equations constitute a set of N 
linear homogeneous equations in N unknowns. The set has solutions for those 
values of £ for which the determinant 

H xl — ESu H 12 — ES 12 H l3 — ESx 

M21 — -^"^21 "22 — ES22 • • ' 


is zero ; in more compact notation, 

det \H lf - ES„\ = (A2.15) 

This is the secular equation. 

Solution of the secular equation amounts to finding the roots of an iVth order 
equation in E. The N roots are the energies of the N molecular orbitals ; the 
forms of the orbitals in terms of the basis atomic orbitals <p, are found by substi- 
tuting each value of E, in turn, back into Equations A2.13 and solving for the c's 
using the additional condition that each MO tp t is to be normalized, 


2 c t * = 1 (A2.16) 

) = i 

Electrons are then assigned, two to each molecular orbital starting from the 
lowest energy. 

Standard computer methods are available to solve Equation A2.15 if 
numerical values can be found for H tj and S tj . The S it can be determined easily 
with the aid of the computer, but the H ih which represent the interactions be- 
tween the basis orbitals, are more difficult to obtain. A number of methods can 
be used to deal with this problem. 


The Hiickel method is the simplest of the quantitative MO techniques. It has the 
following characteristics : 

1. Only w electrons are treated. 

1. The basis consists of ap orbital on each carbon atom of the tt system. 

3. All overlaps, S ti , i i= j, are assumed to be zero ; overlaps S ti are unity 
because the basis orbitals are normalized. 

4. Interactions H tj , i ^ j, are assumed to be zero except for pairs of basis 
orbitals i and j that are on carbons directly bonded to each other. All H tj for 
bonded pairs are assumed to have the same value, which is not calculated but is 
simply called p. (^ represents an energy lowering and, therefore, is negative.) 

5. H ti , which represents the energy of an electron in the basis orbital i be- 
fore any interaction with its neighbors occurs, is the same for all j (because all 
basis orbitals are the same) . It is called a. 

54 Appendix 2 

The secular equation then takes the form of the N-by-N determinental Equation 
A2.17. The asterisk in row i, column j is zero if atom i is not bonded to atomj, 

- E 



and it is /? if i is bonded to j. A further simplification of the algebraic manipula- 
tions required is obtained by setting the zero of energy equal to a and the unit of 
energy equal to /?. (That is, we measure energy relative to a in units of j3.) Then 
we have Equation A2.18, where *, y is zero if i andj are not bonded and unity if 
they are. 

-E * * 
* -E * 



The Hiickel orbitals have a number of properties that make them parti- 
cularly convenient starting points for arguments of a qualitative or semiquantita- 
tive nature about conjugated systems/ Hiickel calculations are the only ones that 
are practical to do without the aid of a computer, and then only when deter- 
minants are of an order no larger than about four. 9 The Hiickel method gives 
rather poor energies and orbital functions but does reproduce faithfully sym- 
metry properties of orbitals. Despite its many deficiencies, the method has been 
successful in correlating a variety of experimental data and has pointed the way to 
much interesting experimental chemistry. 


As an example of the Hiickel method we will examine the allyl system. There are 
three basis orbitals, numbered as shown in 1. Atoms 1 and 2 are bonded to each 


fp\ fp2 <Ppi 


1 M. J. S. Dewar, The Molecular Orbital Theory of Organic Chemistry, McGraw-Hill, New York, 1969. 
' Symmetry properties can sometimes be used to reduce the size of determinants. 

Molecular Orbital Theory 55 

other, as are 2 and 3; 1 and 3 are not bonded. The secular equation is A2.19. 

-E 1 
1 -E 1 =0 (A2.19) 

1 -E 

Expansion of the determinant gives : 

-E 3 + 2E = 


E(E 2 - 2) = 

The roots are: 

E = -VI 

E = 

E = +V2 



The energies, relative to a, are therefore — a/2/S, 0, and + a/2/8 ; because /8 is a 
negative energy, the first of these is the highest energy and the third is the lowest. 
To find the orbitals, we substitute each E, in turn, into the set of Equations 

— c x E + c 2 + = 
Cx — c 2 E + c 3 = 
+ c 2 — c 3 E = 

E = — a/2 gives the relationships A2.24: 

c 2 = - V2 Cl 

C 3 = Ci 

The other information we have about the coefficients is the normalization 
condition : 



^1 "+" ^2 H~ ^3 — 


Combining Equations A2.24 and A2.25, we obtain the coefficients for the highest 
energy MO : 

ri = 1/2 _ 

c 2 = -V2/2 = -1/V2 

c 3 = 1/2 


The coefficients for the other orbitals are obtained in the same way starting with 
E = and E = + a/2. The orbitals are, in order of decreasing energy, measured 
relative to a as the zero of energy : 

E 3 = -V2fi fa= 1/2?,! - 1/V2 9£a + 1/2^3 

E 2 = _ ^ 2 = l/V2<p Pl - l/V2<p P3 

E, = +V2J3 fc = l/2 Vpi + llV2 Vp2 + 1/2^ 


These are the orbitals shown in Figure 1.18. 

56 Appendix 2 


The extended Huckel method, developed by Hoffmann," has the following 
characteristics : 

1. All valence orbitals are included in the basis. The method is not restricted 
to 77 systems. 

2. All overlaps S tj are calculated and included. 

3. Energies H it of an electron in each of the basis orbitals are estimated 
empirically from spectroscopic data. 

4. Interactions H if are approximated as a simple function of S if , H iU and 

This method provides a practical way of carrying out rapid calculations on 
moderately large organic molecules. Although energies are still not particularly 
reliable, energy differences within a series of similar compounds are revealing. 

Huckel and extended Huckel methods are termed semi-empirical because 
they rely on experimental data for the quantification of parameters. There are 
other semi-empirical methods, such as CNDO, MINDO, INDO, in which experi- 
mental data are still used, but more care is taken in evaluating the H if . These 
methods are self-consistent field procedures based on J^f 3CF . They are discussed 
in various works on molecular orbital theory.' 


Ab initio methods calculate all quantities needed from first principles and use no 
experimentally determined parameters. The computations require more machine 
time and are therefore more expensive than semi-empirical ones. Good 
energies can now be obtained for small molecules by these techniques. The reader 
is referred to specialized treatments for further information/ 

* R. Hoffmann, J. Chetn. Phys., 39, 1397 (1963). 

' See note 2, p. 10. 

' For an introduction, see W. G. Richards and J. A. Horsley, Ab initio Molecular Orbital Calculations 

for Chemists, Oxford University Press, London, 1970. 

Chapter 2 




In this chapter we review several aspects of the physical chemistry of organic com- 
pounds that are particularly useful in the investigation of reaction mechanisms. 


Because of the excellent introduction to stereochemistry that is included in most 
introductory organic textbooks, we shall limit our discussion to reviewing the 
meaning of a number of terms. The reader who wishes more information is 
referred to other sources. 1 

Two compounds are stereoisomers of one another if the bonding arrangement 
in one is identical to that in the other except in the way the atoms are oriented in 
space. Thus, 1 and 2, 3 and 4, 5 and 6, 7 and 8 are four pairs of stereoisomers. 
There are two types of stereoisomers: enantiomers and diasteriomers. 

Enantiomers are nonsuperimposable mirror images of one another. Thus, for 
example, .K-lactic acid (1) is the enantiomer of S-lactic acid (2). And allene 3 is 
the enantiomer of allene 4. Molecules that are not superimposable on their mirror 

1 For the best discussions in introductory textbooks, see: (a) R. T. Morrison and R. N. Boyd, 
Organic Chemistry, 3rd edn., Allyn & Bacon, Boston, 1973, pp. 73-80, 115-140, 225-246; (b) J. B. 
Hendrickson, D. J. Cram, and G. S. Hammond, Organic Chemistry, 3rd edn., McGraw-Hill, New 
York, 1970, pp. 175-230; (c) N. L. Allinger, M. P. Cava, D. C. Dejong, C. R.Johnson, N. A. Lebel, 
and C. L. Stevens, Organic Chemistry, Worth, New York, 1971, pp. 105-126. More thorough intro- 
ductions are available in the two small books; (d) G. Natta and M. Farina, Stereochemistry, 
Harper & Row, New York, 1972; (e) K. Mislow, Introduction to Stereochemistry, W. A. Benjamin, 
Menlo Park, Calif., 1966. A number of larger, more advanced treatments are also available. See, for 
example: (f) M. S. Newman, Steric Effects in Organic Chemistry, Wiley, New York, 1956; (g) E. L. 
Eliel, Stereochemistry of Carbon Compounds, McGraw-Hill, New York, 1962. 


58 Some Fundamentals of Physical Organic Chemistry 

images are chiral, whereas molecules that are superimposable on their mirror 
images are achiral. A tetrahedral atom with four different substituents is called a 
chiral center. Thus, the central carbons in R- and 5-lactic acids (1 and 2) are chiral 


H<3^0H HO-O-H 

CU 3 CH 3 

1 2 

H 3 C «Pr «Pr CH 3 

\ / \ / 

C=C=C C=C=C 

' X ^ ^ 

CH 3 HoC i-Pr iPr CH 2 CH 3 

H 3 C H H 3 C CH 3 

\ / \ / 

C=C C=C 

/ \ / \ 

H CH 3 H H 

5 6 

Br Br 

H-Q-Cl H-O-Cl 


C4H3 ^^13 

7 8 

centers. The allenes 3 and 4 are chiral molecules although they do not have a 
chiral center. A mixture that contains equal amounts of both enantiomers is 
called a racemic mixture. 

Stereoisomers that are not mirror images of each other are called dia- 
stereomers. Thus geometrical isomers (e.g., 5 and 6) are diastereomers, as are mole- 
cules that have two or more chiral centers but that are not enantiomers. For 
example, 7 and 8 are diastereomers of one another. 

A molecule that has two or more chiral centers so arranged that one-half of 
the molecule is the mirror image of the other half is achiral. Such a molecule is 
called a meso molecule. 

Let us now define three terms that refer to reactions: stereoselective, 
stereospecific and stereoelectronic. There has been a difference of opinion about 
the use of the first two; we shall use the definitions suggested by Zimmerman 2 
and now adopted by most authors. 

The terms stereoselective and stereospecific properly refer only to reactions 
in which diastereomerically different materials may be formed or destroyed dur- 
ing the course of the reaction. Stereoselective reactions are all those in which one 
diastereomer (or one enantiomeric pair of diastereomers) is formed or destroyed 

2 H. E. Zimmerman, L. Singer, and B. S. Thyagarajan, J. Amer. Chem. Soc. ,81, 108 (1959). 

Stereochemistry 59 

in considerable preference to others that might have been formed or destroyed. 
Thus, for example, bromination of trans-2-butene might give either racemic or 
7n£K>-2,3-dibromobutane. However, the meso compound is produced stereoselec- 
tively, as shown in Equation 2.1. Similarly, Equation 2.2 shows that cis-2- 

H CH 3 J, 

C=C + Br 2 y H 3 C^ ^H n o (2.1) 

h/ X h h ^ c ^ch 3 






CH 3 


butene on bromination gives only racemic 2,3-dibromobutane. Another example 


\„ „/ 


p=\ +Br 2 ► H 3 C^H + (2-2) 

H' H H 3 (X V H 


H 3 C H 


of a stereoselective reaction is loss of/>-toluenesulfonic acid 
(CH 3 ^ VS0 2 -0-H = TsOH) 

from ira/w-2-phenylcyclohexyl "tosylate" (Equation 2.3). Only cw-1-phenylcyclo- 
hexene is produced. Likewise, as Equation 2.3 shows, cu-2-phenylcyclohexyl 
tosylate also loses TsOH stereoselectively to form cw-l-phenylcyclohexene. 

In a stereospecific reaction diastereomerically different starting materials give 
diastereomerically different products. Thus the bromination of the 2-butenes 
(Equations 2.1 and 2.2) is stereospecific, since one geometrical isomer gives one 
product and the other isomer a diastereometrically different product. Elimination 
of TsOH from the two 2-phenylcyclohexyl tosylates, however, is not stereospecific. 

60 Some Fundamentals of Physical Organic Chemistry 

As Equation 2.3 shows, both compounds give the same product. All stereospecific 
reactions must be stereoselective, but the reverse is not true. 3 

H TsO/ v <A 

\ \ (2-3) 

H H 


The term stereoelectronic refers to the effect of orbital overlap requirements on 
the steric course of a reaction. Thus, because of stereoelectronic effects, the S N 2 
substitution gives inversion (see Section 4.2) and E 2 elimination proceeds most 
readily when the angle between the leaving groups is 0° or 180° (see Chapter 7, 
p. 369). Stereoelectronic effects also play an important role in pericyclic reac- 
tions, which are the subject of Chapters 11 and 12. 


A problem that has challenged chemists for years is the determination of the 
electronic influence that substituents exert on the rate and course of a reaction. 
One of the difficulties involved in determining electronic substituent effects is that 
if the substituent is located close to the reaction center it may affect the reaction 
by purely steric processes, so that electronic effects are masked; if placed far 
away in order to avoid steric problems, the electronic effects will be severely 

In 1937 Harnmett-reGogj«zed- 5_ rrratthc-ele€^«)fH^ 
X^jnight be assessed by_stu^in^jxaxJtioris..iiLa sidexhairi at Y in benzene 
derivatives (?Tand 10). 


9 10 

The substituent X is separated physically from the reaction site, but its electron- 

3 Reactions may be "partially", "90 percent," "60 percent," etc., stereoselective or stereospecific. 

4 For reviews see: (a) J. Shorter, Quart. Rev. {London), 24, 433 (1970); (b) P. R. Wells, Linear Free 
Energy Relationships, Academic Press, New York, 1968; (c) L. P. Hammett, Physical Organic Chemistry, 
2nd edn., McGraw-Hill, New York,(I97Q/pp. 347ff; (d) C. D. Ritchie and W. F. Sager, Prog. Phys. 
Org. Chem., 2, 323 (1964); (ej_J. E. Leffler and E. Grunwald, Rates and Equilibria of Organic Reactions, 
Wiley, New York, 1963; (f) H. H. Jaffe, Chem. Rev., 53, 191 (1953). For theoretical discussions see: 
(g) S. Ehrenson, R. T. C. Brownlee, and R. W. Taft, Prog. Phys. Org. Chem., 10, 1 (1973); (h) M. 
Godfrey, Tetrahedron Lett., 753 (1972); (i) S. Ehrenson, Prog. Phys. Org. Chem., 2, 195 (1964). 

6 L. P. Hammett, J. Amer. Chem. Soc, 59, 96 (1937). 

Linear Free-Energy Relationships 61 

donating or -withdrawing influence is transmitted through the relatively polariz- 
able it electron system. Th e Ha mmgtt_ approach is to take as a standard re action 
for_evaluation of substituent effects the dissociation of substituted benzoic acids 
( 9 and lly Vjj JCOOH) at 25*C"nTH 2 07Substitution of an electron-withdrawing 
group (such as nitro) in the para position of benzoic acid causes an increase in 
strength of the acid, while an electron-donating group (for example, amino) 
decreases the strength. The same substituents in the meta position have slightly 
different effects. Qrthn snh stituents are not inc luded^ because their proximity to 
t he reaction site introduces interactions not present if the subsjituent is at the 
meta or para positi on.^ 

If the free-energy change on dissociation of unsubstituted benzoic acid 
(X = H) is designated as AGo, the free energy on dissociation of a substituted 
benzoic acid (AG°) can be considered to be AG£ plus an increment, AAG°, con- 

AG° = AG° + AAG° (2.4) 

tributed by the substituent (Equation 2.4) . Because the substituent X will make 
different contributions at the meta and para positions, it is always necessary to 
designate the position of substitution. 

In order to bring the relationship (2.4) into more convenient form, a para- 
meter a is defined for each substituent according to Equation 2.5, so that equation 
2.4 becomes Equation 2.6. 

AAG° = -2.3037? To- (2.5) 

-AG° = -AG° + 2.303RTo (2.6) 


By using the relationship 2.7 between free energy and equilibrium, Equation 2.6 
can be rewritten as Equation 2.8, which in turn simplifies to Equation 2.9. 

- AG° = 2.303/? riog 10 K (2.7) 

2.303/? riog 10 K = 2.3037? riog 10 K + 2.3037? To (2.8) 

i logic -f =pK - P K = a \ (2.9) 

Table 2.1 lists a constants for some of the common substituents. 

If we now examine the effect of substituents on another reaction, for example 
acid dissociation ofphenylacetic acids (Equation 2.10), we can anticipate that the 

XC 6 H 4 CH 2 COOH + H 2 ^^ XC 6 H 4 CH 2 COO- + H 3 + (2.10) 

various substituents will exert the same kind of effects on these equilibrium con- 
stants as they did on the benzoic acid equilibrium constants; but_tne_greater 
se paration betw een substitution site an d reaction site in t he phenylacetic acid s 
makes _ the, reaction_j£SS-.-S£n.gitive to tne su bstituent effects. The increment 
2.303i?7cr, which was appropriate for benzoic acid dissociations, must now be 
multiplied by a factor £_which_ rhararteri zes thcsensitivit y of t he nemL reaction to 
electron donation and wit bdrawaL-We can therefore write Equation 2.11, 

-AG°' = -AG?' + 2.303/? Tpo (2.11) 

AG°' is the free-energy change for the new reaction with substituent X and 

6 The ortho effect is not entirely steric in origin. See M. Charton, Prog. Phys. Org. Chem., 8, 235 (1971). 

62 Some Fundamentals of Physical Organic Chemistry 

Table 2.1 a Values of Common Substituents 





a +a 

a~ a 

N(CH 3 ) 2 





NH 2 





CH 3 










C e H 6 





OCH 3 















C0 2 H 









— • 











C0 2 R 





CF 3 










N0 2 





Source: Values are those given by C. D. Ritchie and W. F. Sager, Prog. Phys. Org. Chem., 2, 323 
(1964). Reproduced by permission of Wiley-Interscience. 

° <j + and o~ values are given for para substituents only. <j + values for some meta substituents have 
been measured, but because direct resonance interaction between meta substituents is impossible 
they do not differ appreciably from the <j mMa values. 

AGq' is the free-energy change for the new reaction with no substituents. Re- 
writing Equation 2.1 1 as before, we have the relationship in the more useful form 
of Equation 2.12: 

i K ' 
logio -g7 = pa 


Equations 2.1 1 a nd 2.12 express a linear r elationshijaof free ener gies known as the 
Hammett jt-£ relationship^ or simpjy_as the Hammett equation. It can be 
arirjl jgH to reaction jsy^ofLsub&t ituted aromat ic compounds as well as to equili- 
brium constants, and we shall find that it is a very useful tool for obtaining inform- 
ation about reaction mechanisms. (See, for example, Problem 2.1.) 

Usually the most convenient way to use the Hammett equation is to plot 
log KjK , or just log K (for equilibria) or log kjk , or just log k (for rates) of the 
reaction of interest on the vertical axis and a values for the substituents on the 
horizontal axis. A straight line indicates that the free-energy relationship of 
Equation 2.11 is valid. The slopej rf the line is p for the reaction. A posi tiye_yalue 
of j>jneans that jhe reaction responds^tq sjibstituents^n the :_same sense ; as does 
benzoi^ac jduonization; thatis»tfiff equilibrium c onstant for r eaction rate)as_in- 
creased by elec tr < ?n-witrHraw' ri ff ^""p" Tf p > 1. then the reaction i sjnoxe^ejisi- 
t ive tn th e pffcrt of th«-9ubstrtuen4-tlmriijejizpic acid dissociation; if 0_ <_fl__< 1, 
t hen elert rnn^wjijiHrawing-gToijps stilLincrease th^j^^^r^cjuilibrium _ constant 
but less than in benzoic_acid ^^s^c^^ion^^_ne^^iyje_p_shows that electron- 
H r»n a ti n g^roups~mcre ase-the-jeacboJx. constant. A small^^fteri^me^ansjhat the 

mechanism of thcj^^Qn^jiwijh^ejLradical^ 

state with Iittle_chargejeparation. Sometimes the plot of log k vs. a changes slope 

more or less abruptly as substituents are varied, so that two straight lines are 

Linear Free-Energy Relationships 63 

0.2 0.4 0.6 O.i 

Figure 2.1 Plot of KjK vs. a constants for dissociation of X — C a H 4 CH 2 COOH ( x ) and of 
X— C 6 H 4 CH 2 CH 2 COOH (O). The data are from J. F. J. Dippy and J. E. 
Page, J. Chem. Soc. , 357 (1938), and the p- values from a least-squares analysis of 
the data by H. H. Jaffe, J. Chem. Phys., 21, 415 (1953). 

obtained. The reason for this behavior usually is that the mechanism is changing 
in response to the varying electron demand of the substituents. 

Figure 2.1 shows the results of application of the method to ring-substituted 
phenylacetic and 3-phenylpropionic acids. The p values are positive for both 

Table 2.2 p Values for Acid Dissociations 



Temp (°C) 




H 2 






N0 2 

C 2 H 5 OH 

H a O 







Source: H. H. Jaffe, Chem. Rev., 53, 191 (1953), where more complete data may be found. Repro- 
duced by permission of the American Chemical Society. 

64 Some Fundamentals of Physical Organic Chemistry 

Table 2.3 p Values Derived from Rates of Heterolytic Reactions 

Solvent Temp (°C) p 

i O 

X y_c— och 3 + oh- 



r- Y-C— OC 2 H 3 + H + > X \-i 


C— OH 


^kc-ci +H2 o^ ^y 




C— OH 


60% acetone, 25 

60% acetone, 100 

50% acetone, 

95% ethanol, 20 

)TA_ C _ H + HCN y X )~ C - H 

\=/ ^= / CN 

¥~\-l^~\ + C 2 H 5 OH > A^V_ c ^ r A ethanol; 25 






Source: H. H. Jaffe, Chem. Rev., 53, 191 (1953), where more complete data may be found. Repro- 
duced by permission of the American Chemical Society. 

reactions but decrease in magnitude as the substituted ring is placed farther from 
the reaction site. Tables 2.2 and 2.3 list several additional p values for the correla- 
tion of equilibrium constants and reaction rate constants, respectively. Note, for 
example, in Table 2.2 that p for the dissociation of substituted benzoic acids is 
much higher in ethanol than it is in water. This is because acid strength in the less 
ionizing solvent, ethanol, is more dependent on any help it can get from sub- 
stituents than it is in water. 

a + and a Constants 

When the reaction site comes into direct resonance with the substituent, the a 
constants of the substituents do not succeed in correlating equilibrium or rate 
constants. For example a/>-nitro group increases the ionization constant of phenol 
much more than would be predicted from the o- p _ N02 constant obtained from the 
ionization of />-nitrobenzoic acid. The reason is readily understood when one 
realizes that the />-nitrophenoxide ion has a resonance structure (11) in which 
the nitro group participates in through-resonance' 1 with the O - . The extra stabiliza- 
tion of the anion provided by this structure is not included in the o- p _ N02 constant 







' This term was introduced by J. Clark and D. D. Perrin, Quart. Rev. (London), 18, 295 (1964). 

Linear Free-Energy Relationships 65 

because the COO" group in the benzoate anion cannot come into direct reso- 
nance interaction with any ring substituent. Similarly, a />-methoxide group is 
much more effective at increasing the rate of ionization of triphenylmethyl 
chloride than would be predicted from the <7 p _ OCH3 constant (see Equation 2.13). 

</> <f> ^_^ $ 

H 3 CO-d y- C— CI > CH 3 0—<f \-C + -< > CH 3 6=< \=C 

<t> 4> <t> 


Several investigators found 8 that rate and equilibrium constants can be 
better correlated by the Hammett equation if two new types of a constants are 
introduced. When there is through-resonance between a reaction site that be- 
comes electronnrich lincTa sujjstituent electron-withdrawing by resonance, the 
a~ constant should be used. The standard reactions for the evaluation of a~ con- 
stants are the ionizations of para-substituted phenols and of para-substituted 
anilinium ions. 9 The o- + constant should be used whenever a jsubstituent electron- 
don ating by reson ancgJs_^a ra to a reaction site that become^rlectron-dencient, 
ancTwhen through-r^sonanceis possible. between the two groups. The standard 
reaction for the evaluation of o- + is the solvolysis of para-substituted /-cumyl 
chlorides in 90 percent aqueous acetone (Equation 2.14). 10 Table 2.1 lists a 
number of a + and a~ constants. 

CH 3 CjH 3 CH 3 

Cjrl3 LH3 LHs 

Figure 2.2, in which a constants are plotted against log k/k , for the bromina- 
tion of monosubstituted benzenes, shows an example of the usefulness of these 
new parameters. As can be seen from Structures 12 and 13 — which are represen- 
tations of the intermediates in the ortho and para bromination of anisole — sub- 
stituents electron-donating by resonance ortho or para to the entering bromine 
can stabilize the positive charge in the intermediate and therefore also in the 
transition state by through-resonance. 

OCH3 + OCH 3 

+ + 

12 13 

In Figure 2.2a, in which Hammett a constants are plotted, there is only a scatter 
of points; but in Figure 2.2b a + parameters are used and a straight line is 

8 For reviews see (a) Note 4(d), p. 60; (b) L. M. Stock and H. C. Brown, Advan. Phys. Org. Chem., 
1,35 (1963). 

9 See note 4(f), p. 60. 

10 H. C. Brown and Y. Okamoto, J. Amer. Chem. Soc, 80, 4979 (1958). 

66 Some Fundamentals of Physical Organic Chemistry 



O p-OMe 

















10 - 








Figure 2.2 Bromination of monosubstituted benzenes in acetic acid. From H. C. Brown and 
Y. Okamoto, J. Amer. Chem. Soc, 80, 4979 (1958). Reprinted by permission of 
the American Chemical Society. 

a n and o-° Constants 

cr + and ct~ constants have been widely and successfully used. However, they have 
also been strongly criticized by Wepster 11 and by Taft. 12 Both investigators pre- 
dicted that the ability of a substituent to interact with a reaction site by resonance 
should depend on the exact nature of the reaction as well as on the substituent 
and there should, therefore, be a whole spectrum of a values for every substituent. 
Wepster introduced the o- n constant as the "normal" o- value, representative only 
of inductive effects and free of all resonance effects. The constants for m-Cl, 
ffl-CH 3 , and m-N0 2 were taken by Wepster as primary a 11 values. 13 The cr para 
constants were rejected because, even in the absence of through-resonance, 
resonance can effect the electron supply at the site of reaction. (Consider, for 
example, the contribution from Structure 14 to the anion of jfr-nitrobenzoic acid. 








There is no through-resonance between the nitro group and the negative charge 
on the carboxylate group. However, the partial positive charge, which results 
from electron-withdrawing resonance by the nitro group, on the ring carbon that 
bears the carboxylate does stabilize the negative charge.) Using only the primary 
o n values, p for any reaction of interest is calculated. Once p for a reaction is 
known, the a constants of all other substituents for that reaction can be found. 

11 (a) H. van Bekkum, P. E. Verkade, and B. M. Wepster, Rec. Trav. Chim. Pays-Bas, 78, 815 (1959) ; 
(b) A.J. Hoefnagel, J. C. Monshouwer, E. C. G. Snorn, and B. M. Wepster, J. Amer. Chem. Soc, 95, 
5350 (1973). 

12 R. W. Taft, Jr. and I. C. Lewis, J. Amer. Chem. Soc, 80, 2436 (1958); 81, 5343 (1959); R. W. Taft, 
Jr. and I. C. Lewis, Tetrahedfbn, 5, 210 (1959). 

13 The a constants obtained for substituents electron-donating by resonance that are para to a 
reaction site that becomes electron-rich, and for substituents electron-withdrawing by resonance that 
are para to a reaction site that becomes electron-deficient, were also taken as a n values, since in these 
cases there would be no stabilization by resonance. 

Linear Free-Energy Relationships 67 

Table 2.4 <r n and a° Values 


<T n 



a n 


m-CH 3 



m-COCH 3 






m-N0 2 












/>-N0 2 









Source: P. R. Wells, Linear Free Energy Relationships, Academic Press, New York, 1968. Reproduced 
by permission of Academic Press and P. R. Wells. 

The spectrum of o- values for a single substituent that was predicted was indeed 

Taft separated the resonance from the inductive substituent effects and pro- 
posed Equation 2.15. The inductive parameter, o- 7 , is based on a* obtained from 
aliphatic systems (see p. 68). 14 

a = o- R + a, 


The constant a° is another "normal" substituent constant determined by choosing 
only reaction series in which at least one methylene group insulates the reaction 
site from the aromatic ring. The resonance parameter, o-^, is determined from 
Equation 2.15 and is the resonance contribution of a substituent when it is not 
directly conjugated with the reaction site. 15 Table 2.4 lists a number of a n and o-° 
values. Note the close correspondence between the two. 

Linear Free-Energy Relationships 
for Aliphatic Systems — a* Constants 

In the 1 950s Taft devised a method of extending linear free-energy relationships 
to aliphatic systems. 16 He suggested that, since the electronic nature of substi- 
tuents has little effect on the rate of acid-catalyzed hydrolysis of meta- or para- 
substituted benzoates (p values are near 0, see Table 2.3), the electronic nature of 
substituents will also have little effect on acid-catalyzed hydrolysis of aliphatic 
esters. All rate changes due to substituents in the latter reactions are, therefore, 
probably due to steric factors. 17 Taft defined E s , a steric substituent constant, by 
Equation 2.16 

log - 



in which k and k are the rate constants for hydrolysis of XCOOR and 
CH3COOR, respectively, and in which the subscript A denotes acid-catalyzed 

14 The ci[ constant is defined as cr; (x) = 0.54<t* (XO H2>- 

15 See note 12, p. 66. 

16 Taft followed a suggestion of Ingold (C. K. Ingold, J. Chem. Soc, 1032 (1930). R. W. Taft, Jr., 
J. Amer. Chem. Soc, 74, 2729, 3120 (1952); 75, 4231 (1953). 

17 For criticisms of this assumption see notes 4(a) and 4(f), p. 60. 

68 Some Fundamentals of Physical Organic Chemistry 

hydrolysis. Table 2.5 gives a number of E s values. The rates of other reactions in 
which the polar effect of substituents is small can be correlated by E s . 18 

Now that the steric parameter can be evaluated, the inductive parameter is 
available. Taft noted that the transition-state structures for acid- and base- 
catalyzed hydrolysis of esters (15 and 16, respectively) differ from each other 
by only tiny protons. Therefore the steric effect of a substituent should be approx- 






-C ■•• OR 

X— C-OR 

6h 2 




imately the same in the two types of hydrolysis. But in base-catalyzed hydrolysis 
the electronic influence of a substituent cannot be neglected, as can be seen from 
the large values of p for base-catalyzed hydrolysis of m- or /^-substituted ben- 
zoates (Table 2.3). The polar substituent constant, a*, was therefore defined as 

X^O/B V^o/a 



Table 2.5 Steric and Polar Parameters for Aliphatic Systems 

X ^ a* 


CH 3 

CH 3 CH 2 

t-C 3 H 7 

i-C 4 H e 




C1CH 2 

ICH 2 

C1 2 CH 

C1 3 C 

CH 3 OCH 2 


C 6 H 5 CH 2 CH 2 


C 6 H S 

Source: J. Shorter, Quart. Rev. (London), 24, 433 (1970), using data of R. W. Taft, in Steric Effects in 
Organic Chemistry, M. S. Newman, Ed., Wiley, New York, 1956, chap. 13. Reproduced by permission 
of the Chemical Society, Wiley-Interscience, and J. Shorter. 

+ 1.24 

+ 0.49 


















+ 1.05 


+ 0.85 


+ 1.~94 


+ 2.65 


+ 0.52 


+ 0.215 


+ 0.08 


+ 0.36 


+ 0.60 

18 Better correlations are usually obtained by using modified steric parameters that recognize a 
contribution to E s from the hyperconjugative effect of a hydrogens. See note 4(a), p. 60. T. Fujita, 
C. Takayama, and M. Nakajima, J. Org. Chem., 38, 1623 (1973). 

Linear Free-Energy Relationships 69 

pK or log k 


+ 1.0 

+ 2.0 

Figure 2.3 The divisions on the ordinate are 1.00 units of pA" or log k apart. The relative 
positions of the lines with respect to the ordinate are arbitrary. A: pK, aliphatic 
carboxylic acids (XC0 2 H), water 25°C vs. a*. B: log k, catalysis of dehydration 
of acetaldehyde hydrate by XCO z H, aqueous acetone, 25°C vs. a*. From J. 
Shorter, Quart. Rev. (London), 24, 433 (1970). Reprinted by permission of J. 
Shorter and The Chemical Society. 

The subscript B denotes base-catalyzed hydrolysis, and the factor 2.48 is present 
in order that the a and cr* constants of a substituent will have approximately the 
same value. Table 2.5 lists a number of cr* constants. 19 

Taft found that the rate or equilibrium constants for a variety of reactions of 
aliphatic compounds conform to Equation 2.18 or Equation 2.19, respectively. 

log— = a*p* 

log — = a*p* 



For example, Figure 2.3 shows plots of the a* constants of X vs. log pK of ali- 
phatic carboxylic acids (XCO a H) and vs. log k for the dehydration of acet- 
aldehyde hydrate by XCO z H. Deviations from Equations 2. 18 and 2. 19 occur when 
the rate of reaction or position of equilibrium becomes dependent on steric factors. 
For example, Taft studied the enthalpies of dissociation, AH d , of the addition com- 
pounds formed between boron trimethyl and amines (X 1 X 2 X 3 N) and found 
that when the amine is ammonia or a straight-chain primary amine the dissocia- 
tion conforms to Equation 2.20, in which 2 CT * is the sum of the cr* values for the 

AA// d = (2>*)/°* (2.20) 

19 Note that in Table 2.5 all alkyl groups have small negative a* values. It has been argued that these 
values, which often do not give good rate and equilibrium constant correlations, should properly be 
zero for all alkyl groups. For a review see note 4(a), p. 60. But also S. Fliszar, J. Amer. Chem. Soc, 
94, 1068 (1972). 

70 Some Fundamentals of Physical Organic Chemistry 



Figure 2.4 Chemical shift of cationic carbon in 17 vs. <j + . From G. A. Olah, R. D. Porter, 
C. L. Jeuell, and A. M. White, J. Amer. Chem. Soc, 94, 2044 (1972). Reprinted 
by permission of the American Chemical Society. 

groups X 1 , X 2 , and X 3 . But branched-chain and secondary or tertiary amines 
show marked deviations. These deviations were attributed directly to steric strain 
in the complex. 20 

The widest applicability of a* is found when Equation 2.21 is used. 8 is a 
proportionality constant representative of the susceptibility of the reaction to 
steric factors. Equation 2.21 states that the free energy of activation of a reaction 
with a substituted compound relative to that with an unsubstituted compound 
depends on independent contributions from polar and steric effects. 

log— = a*p* + SE S 


Physical phenomena other than rates and equilibrium constants can be 
correlated by Hammett-type relationships. For example, as Figure 2.4 shows, in 
13 G nuclear magnetic resonance spectroscopy (called Cmr) the chemical shift 
of the cationic carbon in 17 is correlated by Brown's a + values. 21 And the G=0 

infrared stretching frequency in XCOCH 3 correlates well with Taft's a* values. 22 

20 Taft, J. Amer. Chem. Soc, 75, 4231 (1953). 

21 G. A. Olah, R. D. Porter, C. L. Jeuell, and A. M. White, ./. Amer. Chem. Soc, 94, 2044 (1972). 

22 D. G. O'Sullivan and P. W. Sadler, J. Chem. Soc, 4144 (1957). 

Thermochemistry 71 

The Hammett and Taft equations are not the only linear free-energy 
relationships known. We shall encounter others — for example, the Bronsted 
relations, and the Grunwald-Winstein and Swain-Scott equations later in this 


Of importance to the problem of relating structure and reactivity is the therm- 
ochemistry of the reaction — that is, the net enthalpy and entropy changes that 
occur upon the making of new bonds and the breaking of old ones. If we consider 
the reaction in Equation 2.22, for example, a large positive standard free-energy 

A + B^C + D (2.22) 

change for the reaction, AG°, means that it will not take place. On the other hand, 
if AG° is large and negative, the likelihood is that it will occur. 24 AG in turn is a 
function of A//° and AS° the standard enthalpy and entropy of reaction, respec- 
tively (Equation 2.23). 

AG" = AH° - TAS° (2.23) 

AH° is a function of the heats of formation of the molecules being formed or 
destroyed, and AS° is a function of the entropies of the molecules being formed 
or destroyed. 25 Thus for the reaction in Equation 2.22, 

AH" = AH° f (C) + AH° (D) - AH° f (A) - AH° (B) (2.24) 

where AH° f (X) is the standard heat of formation of X. Similarly, 

AS° = S° (C) + S° (D) - S° (A) - S° (B) (2.25) 

where £°(X) is the standard entropy of X. 26 

Experimental heats of formation are not available for all compounds, but, 
by Benson's additivity rules, A/// for any molecule in the gas phase can be cal- 
culated. When an accurate experimental value is known, the calculated value is 
almost always to within a few tenths of a kilocalorie of it, and usually the agree- 
ment is even better. 

Benson's approach is to determine the AH° f of a molecule by adding together 
the AH°/s of the various groups in the molecule. A group is denned as an atom 
and its ligands. For example, CH 3 CH 3 is made up of two identical groups. The 
central atom in the group is carbon, and the ligands are carbon and three 

23 (a) S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. Rodgers, 
R. Shaw, and R. Walsh, Chem. Rev., 69, 279 (1969) ; (b) S. W. Benson, J. Chem. Educ, 42, 502 (1965). 

24 Even if AG is a large negative quantity the reaction is, of course, not necessarily fast. The rate 
depends on the activation barrier that the reactants must overcome to reach the transition state. If 
the barrier is too high, then no matter how exothermic the reaction is, it cannot take place. However, 
in the absence of special effects there is usually a qualitative correlation between a reaction's net 
energy change and its energy of activation. This point is discussed further in Section 2.6. 

25 The enthalpy change involved in the formation of one mole of a substance from the elements is 
called the heat of formation of the substance. The standard heat of formation is the heat of formation 
when all substances in the reaction are in their standard states. 

26 The standard entropy of a substance is its entropy in the state specified based on S" = at C K. 

72 Some Fundamentals of Physical Organic Chemistry 

hydrogens. By Benson's notation this group is designated C-(H) 3 (C) : the central 
atom in the group is given first and then the ligand atoms in parentheses. AH° f of 
each group is calculated from experimentally determined AHf'% of compounds 
that contain that group. Then A/// for a new molecule in the gas phase is obtained 
by simply adding together the contributions from each group. AH° for the 
C-(H) 3 (C) group is - 10.08 kcal mole -1 ). Thus ethane is calculated to have a 
AH° f of —20.16 kcal mole -1 . Propane also has two C-(H) 3 (C) groups and a 
C-(H) a (C) a group (A//° = -4.95 kcal mole" 1 ). Therefore AH°, (CH 3 CH 2 CH 3 ) 
= -20.16 - 4.95 = -25.11 kcal mole" 1 . The experimental AH°/s for ethane 
and propane are —20.24 and -24.82 kcal mole -1 , respectively. Benson's addi- 
tivity rules do not apply to condensed-phase compounds because of the contri- 
bution of solvation and of lattice and hydrogen bond energies to A//°(X) in the 
liquid and solid phases. These contributions are, of course, not additive. 

Tables 2.6 through 2.10 (see pp. 75-83) list AH° values for a large number 
of groups (see Section 9.1 for additivity data for radicals). In these tables, C d 
refers to a carbon that is forming a carbon-carbon double bond. The notation 
C d -(H) 2 (C d ) is shortened to C d -(H 2 ), since all carbon-carbon double bonds are 
between two sp 2 carbons. Similarly, C t — (X) refers to a carbon triply bonded to 
another sp carbon and to an X ligand; C B -(X) refers to an aromatic ring carbon 
bonded to two other ring carbons and to a substituent X; and C a refers to the 
central carbon of the allenic group C=C=C. Other group abbreviations are 
noted at the end of the appropriate table. 

In simply adding together the AH° f 's of all the groups in a molecule to ob- 
tain the AH° of the molecule, we make the assumption that only the nearest 
neighbors of a bond affect that bond. This is not always true, and we shall now 
discuss the more important corrections that must be applied if the group additivity 
scheme for molecular enthalpies is to be used successfully. 


In an alkane, gauche interactions may raise the enthalpy content of the molecule. 
The correction is made as follows. Arrange the alkane in its most stable conforma- 
tion, sight along each of the nonterminal chain carbon-carbon bonds, and count 
the number of gauche interactions. Then add +0.80 kcal mole -1 to the cal- 
culated AH° f of the compound for each gauche interaction. Thus, for example, in 
its most stable conformation rz-butane (18) (and all unbranched open-chain 
alkanes) has no gauche interactions, and no gauche corrections should be applied. 
The most stable conformer of 2,3-dimethylbutane (19) has two gauche interac- 
tions. Thus to obtain the AH for the molecule, we add together the group AH° f 

CH 3 



H N 


-^ H 

H N 


^/CH 3 



H 3 C/ 

<X H 

CH 3 

CH 3 





contributions and + 1.60 for two gauche corrections: 

Thermochemistry 73 

4C-(H) 3 (C) = -40.32 
2 C-(H)(C) 3 = -3.80 
2 gauche corrections = + 1.60 
AH° f (2,3-dimethylbutane) = -42.52 kcal mole" 1 

The experimental value is —42.49 kcal mole -1 . 


There are two types of corrections that are sometimes necessary in calculating 
A//° for alkenes. For a compound that contains a cis double bond, a correction 
factor of + 1.00 must be added. (If one or both of the cis substituents is f-butyl, 
the correction factor is larger: see Table 2.6, footnote a.) For example, the A//° 
(cij-2-butene) is calculated as follows: 

2C-(H 3 )(C) = -20.16 
2C d -(H)(C) = +17.18 
1 cis correction = + 1.00 
AH° f (m-2-butene) = - 1.98 kcal mole" 1 

The experimental value is — 1.67 kcal mole -1 . Note that there is no A//° for 
C-(H) 3 (C d ) in Table 2.6; a methyl bonded to an sp 2 carbon has the same A//^ 
group value as a methyl bonded to an sp 3 carbon. This assumption was made in 
the original determination of A//° group values. 

If one side of the double bond is substituted as in 20 or 21, in which R 
stands for an alkyl group, an alkene gauche correction of 0.50 kcal mole -1 must 
be added. Thus the calculated A//£ for 2,3-dimethylbut-l-ene (22) is as follows: 

3 C-(H) 3 (C) = 

1 C a -(H) 2 = 

1 C d -(C) 2 = 

1 C-(C d )(C 2 )(H) = 

1 alkene gauche correction = 

+ 6.26 

+ 10.34 
+ 0.50 

AH} j;2,3-dimethylbut-l-ene) = 

-14.62 kcal mole -1 

ital value is — 15.85 kcal mole 


R R 

CH 3 

R— C— C= R— C— C = 

11 II 
H R R R 


1 1 
H CH 3 

20 21 



In alkylated benzenes a correction factor of 0.57 must be applied if two substi- 
tuents are ortho to each other. For example, A.H° f of 1,2-dimethylbenzene is 
calculated as follows: 

4 C B -(H) = + 13.20 

2 C B -(C) = +11.02 

2 C(H) 3 (C) = -20.16 

1 ortho correction = +0.57 

AH} (1,2-dimethylbenzene) = +4.63 kcal mole" 

74 Some Fundamentals of Physical Organic Chemistry 

The experimental value is +4.54 kcal mole -1 . 

Note again, C-(H) 3 (C B ) is assumed to be equal to G-(H) 3 (C). 


Correction factors must be applied for ring strain. These are given in Table 2.6. 
Contributions to kH° f due to gauche interactions between substituents and be- 
tween substituent and ring must also be taken into account. (Contributions from 
ring-ring gauche interactions are included in the ring strain.) Thus, for example, 
in the most stable conformation of trans- 1 ,4-dimethylcyclohexane (23) both 
CH 3 's are equatorial and no gauche interactions exist between the methyl and 
the ring carbons. In m-l,4-dimethylcyclohexane (24), one of the methyls must 
be axial. Sighting along the C^Ca bond, as in 25, we see that there is one 

GH ; 





methyl-ring gauche interaction. Likewise, sighting along the Cj-Cg bond as in 
26, we see another methyl-ring gauche interaction. Thus &H° f (m-l,4-dimethyl- 







H ^ 

cyclohexane) is calculated as follows: 

2 C-(H) 3 (C) 

4 C-(H) 2 (C) 2 

2 C r (H)(C) 3 

cyclohexane ring strain 

2 alkane gauche corrections 

A//° (cis- 1 ,4-dimethylcyclohexane) 


- 20.16 

- 3.80 

+ 1.60 

= -42.16 kcal mole- 1 

The experimental value is —42.22 kcal mole -1 . (The calculated value for the 
trans isomer is ( — 42.16 — 1.60) = —43.76 kcal mole -1 , and the experimental 
value is — 44. 1 2 kcal mole ~ 1 . 

Compounds Containing Heteroatoms 

The examples we have discussed have all been hydrocarbons, and all the group 
enthalpy values have been obtained from Table 2.6. However, by using Tables 
2.7-2.10, AH] for a wide variety of compounds containing N, O, S, and the halo- 
gens can be calculated. The procedure is just the same as for the hydrocarbons ; 
all necessary correction factors are given in the tables. In the reference from which 
Tables 2.6-2.10 are taken, there are tables giving group enthalpy and entropy 
values for still other types of heteroatoms. There the reader can also find a very 

Table 2.6 Hydrocarbon Groups 

Thermochemistry 75 



C-(H) 3 (C) 



C-(H) 2 (C) 2 



0-(H)(G) a 



C-(C) 4 



C d -(H) 2 



C a -(H)(C) 



C«-(C) a 



C d -(C d )(H) 



C d -(C d )(C) 



[C a -(C B )(H)] 



C d -(C B )(C) 



[C d -(C t )(H)] 



C-(C d )(C)(H) 2 



C-(C d ) 2 (H) 2 



C-(C a )(C B )(H) 2 



C-(C t )(C)(H) 2 



C-(C B )(C)(H) 2 



C-(C d )(C) 2 (H) 



C-(C t )(C) 2 (H) 



C-(C B )(C) 2 (H) 



C-(C d )(C) 3 



C-(C B )(C) 3 









C t -(C d ) 



C t -(C B ) 



c B -(H) 



C b -(C) 



C B -(C d ) 



[C B -(C t )] 






C a 



Next-Nearest Neighbor Corrections 

Alkane gauche correction 


Alkene gauche correction 


cis Correction 



ortho Correction 



Corrections to be Applied to Ring Compound Estimates 

Ring (a) 



Cyclopropane (6) 





Cyclopropene (2) 



Cyclobutane (8) 



Cyclobutene (2) 



Cyclopentane (10) 



Cyclopentene (2) 





Cyclohexane (6) 


Cyclohexene (2) 



76 Some Fundamentals of Physical Organic Chemistry 

Table 2.6 {Continued) 

Ring (a) A7/? 298 Sl ea 





Cycloheptane (1) 







Cycloheptatriene-1,3,5 (1) 



Cycloctane (8) 







Cyclooctatriene- 1,3,5 










Spiropentane (4) 



Bicyclo[1.1.0]butane (2) 



Bicyclo [2.1.0] pentane 




Bicyclo[4. 1 .0]heptane 


Bicyclo[5. 1 .OJoctane 


Bicyclo[6. 1 .0]nonane 


Source: S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. 
Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69,279 (1969). Reproduced by permission of the Ameri- 
can Chemical Society. 

" When one of the groups is /-butyl, cis correction = 4.00; when both are /-butyl, cis correction = 
~ 10.00; and when there are two corrections around one double bond, the total correction is 3.00. 
6 + 1.2 for but-2-ene, for all other 2-enes, and —0.6 for 3-enes. 

Table 2.7 Oxygen-containing Groups 

Group AH° f S° 


CO-(0)(C d ) 

CO-(0)(C B ) 



CO-(C d )(H) 

CO-(C B ) 2 


[CO-(C B )(H)] 

CO-(C) 2 


CO-(H) 2 

0-(CO) 2 


[0-(CO)(C fl )] 






























Thermochemistry 77 

Table 2.7 {Continued) 

Group AH°, 




0-(C a ) 2 


0-(C a )(C) 


0-(C B ) 2 


0-(C B )(C) 


[0-(C B )(H)] 



0-(C) a 






C a -(CO)fO) 


C a -(CO)(C) 




[C a -(0)(C a )] 




[C a -(0)(H)] 







C-(CO) 2 (H) 2 


C-(CO)(C) 3 


C-(CO)(C) 2 (H) 



C-(COVC)(H) 2 



[C-(CO)(H) 3 ] 

- 10.08 


C-(0) 2 (C) 2 


C-(0) 2 (C)(H) 


C-(0) 2 (H) 2 


C-(0)(C B )(H) 2 



C-(0)(C a )(H) 2 


C-(0)(C) 3 



C-(0)(C) 2 (H) 



C-(OKC)(H) 2 



[C-(0)(H) 3 ] 

- 10.08 



Ether oxygen gauche 


Ditertiary ethers 





26.4 27.7 






78 Some Fundamentals of Physical Organic Chemistry 

Table 2.7 (Continued) 

Group AH° S° 



o o o 

o o x o 

o o o 





O 6.0 

O 3.4 




Source: S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. 
Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69, 279 (1969). Reproduced by permission of the Ameri- 
can Chemical Society. 

Table 2.8 Nitrogen-containing Groups' 1-6 

Group AHJ 

[C-(N)(H) 3 ] 

C-(N)(C)(H) a 

C-(N)(C) 2 (H) 

C-(N)(C) 3 

C-(N A )(C)(H) 2 








(-34.1) d 



Thermochemistry 79 

Table 2.8 {Continued) 

Group &H° 

C-(N A )(C) a (H) 

C-(N A )(C) 3 

N-(C)(H) 2 

N-(C) a (H) 

N-(C) 3 

N-(N)(H) 2 


N-(N)(C) 2 




Nr-(C B )« 

N-(C B )(H) 2 

N-(C B )(C)(H) 

N-(C B )(C) a 

N-(C B ) 2 (H) 


N a -(N) 



N-(CO)(H) a 


N-(CO)(C) 2 


N-(CO) a (H) 

N-(CO) 2 (C) 

N-(CO) a (C B ) 

C-(CN)(C)(H) 2 

C-(CN)(C) a (H) 

C-(CN)(C) a 

C-(CN) 9 (C)a 

C d -(CN)(H) 

C d -(CN) 2 

C d -(NO a )(H) 


C t -(CN) 

C-(N0 2 )(C)(H) 2 

C-(N0 2 )(C) 2 (H) 

G-(NO)a(C) a 

C-(NO a )a(G)(H) 


0-(NO) 2 (C) 

Corrections to be Applied to Ring Compound Estimates 

Ethylene imine 

^j 27.7 (31.6)° 


I I (26.2)" (29.3)" 

*— NH 







































(3.9) d 

+ 0.4 



















(48.4) d 


(26.9) d 







80 Some Fundamentlas of Physical Organic Chemistry 
Table 2.8 (Continued) 

Group A// ; 




6.8 26.7 







Source: S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. 
Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69, 279 (1969). Reproduced by permission of the Ameri- 
can Chemical Society. 

a Ni = double-bonded nitrogen in imines; Nj-(C B ) = pyridine N. N A = double-bonded nitrogen 

in azo compounds. 

6 No cis corrections applied to imines or azo compounds. 

c gauche corrections of +0.8 kcal mole -1 to AH" f applied just as for hydrocarbons. 

" Estimates. 

' For ortho or para substitution in pyridine add — 1.5 kcal mole" ' per group. 

Table 2.9 Halogen-containing Groups 

Group A#° S°~ 

C d -(F) 2 

C d -(Cl) a 

C d -(Br) 2 


C d -(F)(Br) 

C d -(Cl)(Br) 

C d -(F)(H) 

C d -(C1)(H) 


C a -(I)(H) 

C t -(C1) 

C t -(Br) 

C B -(F) 






















Thermochemistry 81 

Table 2.9 {Continued) 

Group AH° f S° 










C-(C B )(F) 3 



C-(C B )(Br)(H) 2 


C-(C B )(I)(H) 2 


G-(F) 3 (C) 

- 158.4 


C-(F) 2 (H)(C) 



C-(F)(rD 2 (C) 



C-(F) 2 (C) 2 



C-(F)(H)(C) 2 



C-(F)(C) 3 


C-(F) 2 (C1)(C) 

- 106.3 


C-(C1) 3 (C) 



C-(C1) 2 (H)(C) 



C-(C1)(H) 2 (C) 



C-(C1) 2 (C) 2 


C-(C1)(H)(C) 2 



C-(C1)(C) 3 



C-(Br) 3 (C) 


C-(Br)(H) 2 (C) 



C-(Br)(H)(C) 2 


C-(Br)(C) 3 



C-(I)(H) 2 (C) 



C-(I)(H)(C) 2 



C-(I)(C) 3 





N-(F) 2 (C) 


C-(C1) (C)(0)(H) 



Corrections for Next-Nearest Neighbors 

ortho (F)(F) 5.0 

ortho (CI) (CI) 2.2 

ortho (alk) (halogen) 0.6 

cis (halogen) (halogen) (0) 

cis (halogen) (alk) (0) 

gauche (halogen) (alk) 0.0 
gauche (halogen) 

(exclusive of F) 1 .0 

gauche (F) (halogen) 0.0 

Source: S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. 
Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69, 279 (1969). Reproduced by permission of the Ameri- 
can Chemical Society. 

Table 2.10 Sulfur-containing Groups 

Group AH° f S° 

[C-(H) 3 (S)] 

C-(C)(H) 2 (S) 

C-(C) 2 (H)(S) 

C-(C) 3 (S) 

C-(C B )(H) 2 (S) 


- 10.08 










82 Some Fundamentals of Physical Organic Chemistry 

Table 2.10 {Continued) 

Group AH°, ~S° 


[C a -(H)(S)] 

C a -(C)(S) 



S-(C) 2 

S-(C)(C a ) 

S-(C d ) a 

S-(C B )(C) 

S-(C B ) 2 


S-(S)(C B ) 

S-(S) 9 

[C-(SO)(H) 3 ] 


C-(C) a (SO) 

C-(C a )(SO)(H) 2 


SO-(C) 2 

SO-(C B ) 2 

[G-(S0 2 )(H) 3 ] 

C-(C)(S0 2 )(H) 2 

C-(C) 9 (SO a )(H) 

G-(C) s (SOa) 

C-(C a )(S0 2 )(H) 2 

C-(C B )(SO a )(H) 2 

[0 B -(SO 2 )] 

C a -(H)(S0 2 ) 

C a -(C)(S0 2 ) 

SO a -(C) 2 

S0 2 -(C)(C B ) 

SO a -(C B ) 2 

[S0 2 -(C d )(C B )] 

S0 2 -(C d ) 2 

S0 2 -(S0 2 )(C B ) 



G-(S)(F) 3 


[GS-(N) 2 ] 

N-(CS)(H) a 


N-(S)(C) a 

[SO-(N) 3 ] 

N-(SO)(C) a 

[S0 2 -(N)J 

N-(S0 2 )(C) 2 

Organosulfur Compounds Ring Corrections 






- 12.41 


























- 10.08 


































Ring (a) ., AH 

(a) A (2) 17.7 29.47 

Thermochemistry 83 

Table 2.10 (Continued) 

Ring (a) A/// S° 

19.37 27.18 

1.73 23.56 








V 2 ) 






(h, Q 



(i) «r > 








Source: S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, A. S. 
Rodgers, R. Shaw, and R. Walsh, Chem. Rev. , 69, 2 79 ( 1 969) . Reproduced by permission of the Ameri- 
can Chemical Society. 

large number of compounds listed with their estimated and observed enthalpies 
and entropies of formation. 


In this section we have so far emphasized only the A//° and A//° of the reaction 
components. This is because the entropy change in many reactions is small and 
can often be neglected in comparison to the enthalpy change. When S°'s are of 
interest, they too can be estimated by Benson's additivity rules. In order to cal- 
culate 5° for a molecule, the group S° contributions are added together just as 
they are for A///, but now a correction for the overall rotational symmetry (a) of 
the molecule must be added. The correction is — R In a, where a is the product 

84 Some Fundamentals of Physical Organic Chemistry 

of all the rotational degeneracies of the molecule. For example, in acetone the 
molecule as a whole has a twofold axis of symmetry (this is called the external 
axis) . Each of the two methyl groups has a threefold axis of symmetry (called 
internal axes) . Thus for acetone a is 2 x 3 x 3 and S° is calculated: 

2 C-(H) 3 (C) = +60.82 

1 CO-(C) 2 = + 15.01 

-Rlna = -Rln 18 = -5.74 

S° (acetone) = + 70.09 cal mole" 1 "K" 

The experimental value is 70.5 cal mole -1 °K _1 . 

If a molecule is optically active, R In n must be added to its entropy estim- 
ate, where n is the total number of stereoisomers of equal energy. 

Guide to the Use of the Group Tables (Tables 2.6-2.10) 

1, kH° { and 5° are the heat of formation and entropy, respectively, of a 
group when that group is in a molecule in its standard state of hypothetical ideal 
gas at 1 atm pressure and 25°C. All values of Ai/^ are in kilocalories per mole, 
and all values of S° are in calories per mole per degree (K). For a simple method 
of converting S° and A//^ to other temperatures, see Benson et al., Chem. Rev., 69 
(1969), p. 313. 

2. In order to assign values to all groups, some groups have had to be 
assigned arbitrary values. Groups in brackets in Tables 2.6-2.10 are those 
groups. Estimated values obtained from a single compound are in parentheses. 


The thermochemical additivity scheme outlined in the previous section is based on 
gas-phase data. Since most organic reactions are carried out in solution, it would 
be most useful to be able to understand and predict the thermochemical changes 
that molecules, ions, and transition states undergo when dissolved in various 
solvents. Our knowledge of the structure of liquids and of their interactions on the 
molecular level with solutes is still too incomplete to permit more than a very 
rough qualitative answer to this problem. We shall proceed by discussing briefly 
the influence on solvent properties of the most important parameters characteriz- 
ing liquids. 

Dielectric Constant 

The first property of solvents to be considered is the dielectric constant, e. The 
dielectric constant of a substance measures the reduction of the strength of the 
electric field surrounding a charged particle immersed in the substance, com- 
pared to the field strength around the same particle in a vacuum. The dielectric 
constant is a macroscopic property; that is, its definition and measurement 

27 The following discussions of solvent effects will provide further information: (a) T. C. Waddington, 
Non-Aqueous Solvents, Thomas-Nelson, London, 1969; (b) E. M. Kosower, An Introduction to Physical 
Organic Chemistry, Wiley, New York, 1968, p. 259; (c) T. C. Waddington, Ed., Non-Aqueous Solvent 
Systems, Academic, London, 1965; (d) E. S. Amis and J. F. Hinton, Solvent Effects on Chemical Pheno- 
mena, Academic, New York, 1973 ; (e) J. F. Coetzee and C. D. Ritchie, Eds., Solute-Solvent Interactions, 
Marcel Dekker, New York, 1969; (f) A. J. Parker, Chem. Rev., 69, 1 (1969). 

Solutions 85 

assume that the substance of interest is continuous, with no microscopic struc- 
ture. Electrostatic attractions and repulsions between ions are smaller the higher 
the dielectric constant, and ions of opposite charge therefore have a greater ten- 
dency to dissociate when the dielectric constant is larger. Table 2. 1 1 lists dielec- 
tric constants for some common solvents. 

The dielectric constant gives only a rough guide to solvent properties, and 
does not correlate well with measured effects of solvents on reaction rates. It is 
nevertheless useful for making a division of solvents into two broad categories : 
polar and nonpolar. In nonpolar solvents, e < ~ 15, ionic substances will be 
highly associated. Indeed, they will be very sparingly soluble in most of these 
solvents except as, for example in the case of acetic acid, when hydrogen bonding 
is available, and even then solubility is low. Ionic substances are more soluble in 
solvents of high dielectric constant, and the ions are dissociated. 

Dipole Moment and Polarizability 

In order to gain a better understanding of solution phenomena, it is necessary to 
evaluate solvent properties on the molecular level. Here the most important 
properties are the dipole moment, p, and the molecular polarizability. Values 
are listed in Table 2.1 1. 

The dipole moment measures the internal charge separation of the molecules 
and is important in evaluating how the solvent molecules will cluster around a 




Q) F\ ^(E3a 


Figure 2.5 Ordering of solvent molecules around (a) a dipolar solute molecule and (b) a 
solute positive ion. The orientation will be most pronounced in the innermost 
shell of solvent molecules and will become increasingly random as distance from 
the solute particle increases. The strength of the interaction will depend on the 
molecular sizes and shapes and on the magnitudes of the dipole moments of both 
solutes and solvent particles. 

86 Some Fundamentals of Physical Organic Chemistry 

solute particle that itself has a dipole moment or a net charge. The solvent di- 
poles will tend to orient themselves around the solute in the manner indicated 
in Figure 2.5. The first solvent layer will be the most highly ordered, with ran- 
domness increasing as the influence of the solute particle decreases with increasing 
distance. A smaller solute ion will generate a more intense electric field than will 
a large one, and so will have a stronger and more far-ranging capacity to orient 
solvent dipoles around it. In the solvent molecule itself, one end of the dipole may 
be exposed while the other end is buried inside the bulk of the molecule. In 
dimethylsulfoxide, for instance, the negative oxygen end of the dipole is exposed 
(27), whereas the positive end is not; this solvent interacts much more strongly 

H S« + H 

X X 

H H i H 


with the cations of an ionic solute than with the anions. Formation of solvation 
layers around the solute particles will be accompanied by heat evolution (nega- 
tive A//) and an increase in order (negative AS). 

Table 2.11 Dielectric Constant, Dipole Moment, and Molecular 
Polarizability for Selected Solvents' 1 

fi Polarizability 

Solvent €° (debyes) (cm 3 x 10 24 ) 

Nonpolar Protic d 


|| 6.15 e 1.68 5.16 

CH 3 — C— OH 

(CH 3 ) 3 C— OH 12.47 1.66 8.82 

CH 3 — (CH 2 ) B — OH 13.3 1.55 12.46 


15.0 1.86 11.33 


9.78' 1.45 11.11" 

Nonpolar Aprotic 

CC1 4 2.24« 10.49 

n-C 8 H 14 

<yc/o-C e H 12 
<f>— H 
(C a H 6 ) 2 

12.4" 2.37 9.55 




2.02 e 








Solutions 87 

Table 2.11 (Continued) 



(cm 3 x 10 24 ) 






GH3O — GrigGrig — 

OCH 3 




CH 3 0— (CH 2 CH 2 - 

-O— ) 2 CH 3 




Dipolar Protic 

H. 2 O fc 












C 2 H 5 OH 










Dipolar Aprotic 






CH3 — C — GH3 





H— C— N(CH 3 ) 2 






GH3 — S — CH 3 

CH 3 — CN 




CH 3 N0 2 






(CH 3 ) 2 N— P— N(CH 3 ) 2 




N(CH 3 ) 2 


" With the exception of the polarizabilities, data are from J. A. Riddick and W. B. Bunger, 

Organic Solvents, 3rd ed., Vol. II of A. Weissberger, Ed., Techniques of Chemistry, Wiley-Interscience, 

New York, 1970. Other physical constants may also be found in- this source. 

b T = 25°C except where noted. 

c Calculated from the refractive index n according to the formula 

Polarizability = 

1 M 3 

n 2 + 2 d 4ttN 

where M = molecular weight; d = density; and N — Avagadro's number. See E. A. Moelwyn- 

Hughes, Physical Chemistry, 2nd ed., Pergamon Press, Elmsford, N.Y., 1961, p. 382. T = 25°C except 

where noted. 

" The dividing line between nonpolar and dipolar solvents is arbitrarily set at t = 15. See A. J. 

Parker, Chem. Rev., 69, 1 (1969). 

' T = 20°C. 

' T = 60°C. 

» T = 45°C. 

* T= 21°C. 
1 T = 16°C. 
' T = 30°C. 

* Data from A. J. Parker, Chem. Rev., 69, 1 (1969). 

88 Some Fundamentals of Physical Organic Chemistry 

Polarizability is a measure of the ease with which the electrons of a molecule 
are distorted. It is the basis for evaluating the nonspecific attraction forces 
(London dispersion forces) that arise when two molecules approach each other. 
Each molecule distorts the electron cloud of the other and thereby induces an 
instantaneous dipole. The induced dipoles then attract each other. Dispersion 
forces are weak and are most important for the nonpolar solvents where other 
solvation forces are absent. They do, nevertheless, become stronger the larger 
the electron cloud, and they may also become important for some of the higher- 
molecular-weight polar solvents. Large solute particles such as iodide ion interact 
by this mechanism more strongly than do small ones such as fluoride ion. 
Furthermore, solvent polarizability may influence rates of certain types of reac- 
tions because transition states may be of different polarizability from reactants 
and so be differently solvated. 

Hydrogen Bonding 

Hydrogen bonding probably has a greater influence on solvent-solute interac- 
tions than any other single solvent property. Solvents that have O — H or N — H 
bonds are hydrogen bond donors, whereas most hydrogens bound to carbon are 
too weakly acidic to form hydrogen bonds. Any site with unshared electrons is a 
potential hydrogen bond acceptor, although the more strongly basic and the less 
polarizable the acceptor site the stronger will be the hydrogen bond. 28 

We class as protic those solvents that are good hydrogen bond donors and as 
aprotic those that are not. 29 Since the protic solvents have hydrogen bound to 
oxygen or nitrogen, they are also good hydrogen bond acceptors; the aprotic 
solvents may or may not be hydrogen bond acceptors. 

Because negative ions have extra electrons, they are hydrogen bond accep- 
tors and can be expected to be strongly solvated by protic solvents. Many neutral 
molecules also contain basic sites that will act as acceptors. Aprotic solvents, on 
the other hand, will be less able to solvate negative ions and basic molecules. 
Positive ions will ordinarily be solvated by dipolar interactions with the polar 
solvents, whether protic or not. Protic solutes will ordinarily interact by hydrogen < 
bonding with protic solvents. 

Solvent Structure 

Dipole-dipole interactions between solvent molecules, and, in the case of protic 
solvents, intermolecular hydrogen bonding, lead to a certain amount of structure 
in pure solvents. Water, which is both an excellent hydrogen bond donor and 
acceptor, is perhaps the foremost example. It exhibits structure very like that in 
the ice crystal over rather extended regions, although of course the structure is 
a dynamic one in the sense that molecules are continually leaving and joining the 
structured regions. 

When a solute is introduced into a solvent, the structure of the solvent will 
be disturbed in some way, and it will be the energy and entropy changes that 
accompany this disturbance, together with those arising from the new interactions 

For further discussion of these concepts see Section 3.5. 

Note that aprotic solvents may nevertheless contain hydrogen. 

Solutions 89 

of solvent with solute, that determine the thermodynamic properties of the solu- 
tion. Thermodynamic measurements yield the total enthalpies and entropies of 
solution, or of transfer of a solute from one solvent to another, but do not reveal 
the origin of the changes. Some of the data are difficult to interpret, and no really 
satisfactory theory is available. For example, negative entropies of solution show 
that there is a net increase in the amount of ordering upon dissolving nonpolar 
solutes in water, whereas exothermic enthalpies indicate favorable energy changes. 
These results are just the opposite of what one might have predicted by arguing 
that the main effect of introducing a nonpolar molecule would be to break up the 
water structure and hence to raise the energy while decreasing order by breaking 
hydrogen bonds. Ions (except for very small ones such as Li + ) cause a net 
decrease in the amount of structure, even though there must be a considerable 
amount of organization of water molecules around the ion. 30 These phenomena 
clearly require further investigation. 

Protic and Dipolar Aprotic Solvents 

It is useful to classify the more polar solvents (e > ~ 15) into two categories 
depending on whether they are protic or aprotic. It is found that reactions 
involving bases, as for example S w 2 substitutions (Chapter 4), E 2 eliminations 
(Chapter 7), and substitutions at carbonyl groups (Chapter 8), proceed much 
faster in dipolar aprotic than in protic solvents, typically by factors of three to 
four powers often and sometimes by as much as six powers often. 31 

The phenomenon can be explained by considering the various aspects of 
solvent-solute interactions that we have discussed. The reactions typically take 
place through the attack of an anionic reagent on a neutral molecule. The protic 
solvents solvate the anions strongly by hydrogen bonding, whereas the aprotic 
solvents cannot. Furthermore, the aprotic dipolar solvents, although they 
ordinarily have large dipole moments, are relatively ineffective at solvating the 
negative ions by dipole interactions because the positive ends of the dipoles are 
usually buried in the middle of the molecule. The dipolar aprotic solvents, on the 
other hand, are effective at solvating the positive counter ion because the nega- 
tive end of the dipole is ordinarily an exposed oxygen or nitrogen atom. The 
result of these differences is that the anions are more free of encumbrance by 
solvation in the dipolar aprotic solvents, and less energy is required to clear sol- 
vent molecules out of the way so that reaction can occur. 

Measures of Solvating Ability 

Because solvent-solute interactions are so complex, relatively little progress has 
been made in understanding them quantitatively from first principles. A useful, 
if somewhat unsatisfying approach, is to assign parameters characterizing solvat- 
ing ability on the basis of the measurement of some chemical or physical property 
that, one hopes, is closely related at the molecular level to the phenomenon under 

One approach is to take the rates of a particular standard reaction in various 

30 E. A. Arnett and D. R. McKelvey, in Solute-Solvent Interactions, Coetzee and Ritchie, Eds., p. 349. 

31 See note 27(f), p. 84. 

90 Some Fundamentals of Physical Organic Chemistry 

solvents as characterizing the solvents, and then to see whether these parameters 
will yield a linear correlation with rates of some closely related reaction in those 
same solvents. This method is the basis of the Grunwald-Winstein = Y scale, which 
we shall discuss further in Chapter 5. Another method is to measure the energy 
change of an electronic transition in a reference molecule between two states that 
differ in their ability to interact with solvent. Kosower's Z scale is of this kind. 32 
These solvent scales are linear free-energy relationships entirely analogous to 
those discussed in Section 2.2. They give only limited insight into the molecular 
basis of solvation, but are particularly useful in assessing reaction mechanisms. 


The study of reaction rates has two purposes: first, to compare the form of the rate 
equation with predictions of the various mechanisms under consideration, and 
second, to measure numerical values of rate constants and to interpret them in 
terms of elementary reaction steps. 

The Rate Equation 

The interpretation of kinetic data begins with a hypothetical sequence of ele- 
mentary reaction steps, each characterized by two microscopic rate constants, one for the 
forward and one for the reverse reaction. From this proposed mechanism a rate 
equation is derived, predicting the dependence of the observed reaction rate on 
concentrations and on microscopic rate constants, and its form is tested against 
the observations. If the form of the rate equation meets the test of experiment, it 
may be possible to derive from the data numerical values for the microscopic rate 
constants of the proposed elementary reaction steps. While inconsistency is clear 
grounds for modifying or rejecting a mechanistic hypothesis, agreement does 
not prove the proposed mechanism correct. 

The unimolecular reaction Suppose we postulate that a given reaction 
consists of the single step 

A , B (2.26) 

The rate of disappearance of A, — d[K]jdt, is given by Equation 2.27 and the rate 
of disappearance of B, — d[B]/dt, by Equation 2.28. 33 

—7^ = *i[A] - ft-![B] (2.27) 


-^ = -*i[A] + A_i[B] (2.28) 


For the rate equation to compare with experiment we could choose either of 
these, depending upon whether the time dependence of [A] or of [B] is more 
convenient to measure. _ 

32 Kosower, An Introduction to Physical Organic Chemistry, p. 293. 

33 It is merely a matter of convenience whether rates are expressed as rates of appearance, +rf[X]/<#, 
or as rates of disappearance, — d[X.]/dt, of a reactant or product. 

:tics 91 

Equations 2.27 and 2.28 constitute a mathematical model for the dynamics 
of the reaction of interest. Note that the p rfdjVwl rntffi of change of the r.ons ti- 
tuen U:oncentrati' ons are given hy sums of ter ms, each of which contains onlyj;he 
firgf pnwpr nfnnp nf the mncentra ti'nns The predict ed kinetics is therefore sa id to 
he-ftrst-order^. In this example of a single-step mechanism, the origin of the predic- 
tion of first-order kinetics is that A changes to B and B to A without the interven- 
tion of any third substance. An elementary reaction step in which a single 
substance changes to some other substance or substances without the intervention 
of anything else is said to be a unimolecular step. It is essential to maintain a dis- 
tinction between molecularity, a concept applying to the nature of a single step in 
the mechanistic hypothesis, and kinetic order, a term describing the experimentally 
determined dependence of rate of the reaction (which may be a complex series of 
steps) on concentration. The mechanistic chemist uses kinetic order along with 
other tools to try to establish a probable sequence of steps and the molecularity of 
each, but the relationship between kinetic order and molecularity is often not as 
simple as in the example of Equation 2.26. 

Rate equations like 2.27 and 2.28, obtained from a proposed set of ele- 
mentary reaction steps, are differential equations. Although for our purposes in 
this book we shall require only differential rate equations, it is usually more 
convenient in interpreting raw experimental data to have the equations in 
integrated form. Methods of integration of rate equations can be found in the 
literature. 34 

Macroscopic and microscopic rate constants Except in the simplest 
mechanisms, the observed rate constant for the reaction as a whole will not 
correspond to any one of the microscopic rate constants k characterizing the 
individual steps. The term observed rate constant, k obs , is used for the overall rate 
constant for the complete reaction. 

Simplification of kinetic equations It is a common practice in writing 
mechanisms to simplify them by making various assumptions about the relative 
size of rate constants. Such assumptions are justified on the basis of the same 
chemical intuition that led to the mechanistic proposal in the first place, and are 
properly regarded as part of the mechanism. Suppose, for example, that in 
Equation 2.26 we had reason to believe that the reaction of B to A was sufficiently 
slow that it would not occur to a measurable extent over the time scale being used 
to study the kinetics. We might then feel justified in omitting the k _ ^ step altogether 
and writing Equations 2.29 and 2.30: 

A *' > B (2.29) 

-^3. = *![A] (2.30) 


The predicted kinetics is still first-order, but the equation is simpler. Now the 
observed rate constant is identical with the microscopic constant k x . 

34 See for example (a) K. J. Laidler, Chemical Kinetics, 2nd ed., McGraw-Hill, New York, 1965, 
chap. 1 ; (b) G. M. Fleck, Chemical Reaction Mechanisms, Holt, Rinehart, and Winston, New York, 1971. 

92 Some Fundamentals of Physical Organic Chemistry 

The principle of microscopic reversibility, required by the laws of thermo- 
dynamics, specifies that there must be a reverse for every microscopic process. It is 
therefore strictly speaking incorrect to omit reverse steps, and doing so is justified 
only when the omitted reverse step is occurring so slowly as to have no observable 
effect on the reaction during the time it will be under observation. 

The bimolecular reaction We move next to a slightly more complex 
case, a single step with more than one reactant (Equation 2.31). The rate equa- 
tion is 2.32; if the reverse reaction may be safely omitted, these equations sim- 

A + B ^=^ C + D (2.31) 



= *![A][B] - *.![C][D] (2.32) 

plify to 2.33 and 2.34. The reaction2;33_is_/i/mo/gcuZarj_IrUeraction^f A with B is 
r equired. The predictedkT netic hehavinr (Equat ion 2.34 ) is_£ecand=grder overall, 

A + B — ^-> C + D (2.33) 



*i[A][B] (2.34) 

first-order in JAl ■■.and— fiist-prder. in {B^_and the observed second-order rate 
con stant, A: ohs , is equ al to the microscopic constant k x . 

The pseudo first-order reaction It may be possible in a reacti on in 
which two substances take part to arrange that one concentration is effectively 
constantcluririg pie kinetic experiment. The most obvious example is when one 
reactant can be buffered, asTn" aii" "acid-catalyzed process, but it caii ^alsojbe _ 
aco^plished^imply_bj/j2aj^^jrgagen t B pre seirtinlarge excess over A , so_that 
the proportional chang g_in.[B] is very s mall while the proporti onal changejn [A] 
is large. Then the constant c oncentra tion becomes effectively_ part of the rate 
constant an oVdie^ra^eguation 2-34 reduces to 

--^ = *ob.[A] (2.35) 


*„bs = *i[B] [B] constant (2.36) 

The predicted kinetic behavior under these circumstances is therefore first-order, 
with a first-order k oba related to the microscopic second-order constant k-^ by 
Equation 2.36. Such reactions are said to follow pseudo first-order kinetics. 

Multistep Reactions 

Kinetic treatment is more difficult for mechanisms with more than one element- 
ary step. Here we shall restrict the discussion to two commonly encountered 
special cases. Let us look first at a simple two-step process (Equations 2.37 and 
2.38) in which we are justified by the chemistry in ignoring reverse reactions. 

A — ^— B ON (2.37) 

B — ^->- C hW (2.38) 

Kinetics 93 

SjrjjrjosjM^hat jhe_s^c^^ nrs ^L Y^ wo uld ex pe ct on 

the bjy^_piLaJ3~int«iti¥e-appxaach_.^ 

p end o nly_o n k 1: because every^^jm>kc^l€-4hatisJhrxiied-ixi- the in i t ia l s l ow -Slep 

goesJnstantly Jo C. We would, say sunder the^e-circumstanees-thaJ: the iirst. step is 

r ate-determ ining. 

The stationary-state approximation Kinetic analysis of Equations 
2.37-2.38, first step rate-determining, takes the following form. Because B is 
consumed as fast as it forms, its concentration is always very close to zero and 
therefore approximately constant. We assume that 

M = (2.39) 


This assumption is known as the stationary -state approximation, and is valid for 
highly reactive intermediates. We then write from the second step Equation 2.40 

^1 = * a [B] (2.40) 


for the rate of product formation. But because B is a reactive intermediate, its 
concentration will be difficult to measure; we require a rate equation expressed 
in terms of measurable concentrations. We therefore write, from Equations 2.37 
and 2.38, 

^ = Ax [A] - A a [B] (2.41) 


and, from Equation 2.39, 


-^ = k,[A] - * 2 [B] = (2.42) 


The stationary-state approximation thus allows us to equate ^[A] with A; 2 [B]. 
The rates of formation and of disappearance of the reactive intermediate B are 
equal. We can therefore write instead of 2.40 the final rate equation 2.43: 

^1 = AJA] (2.43) 


Note that overall kinetic behavior is unaffected by events following a true rate- 
determining step. 

Suppose now that B is still a reactive intermediate, but the reverse of the first 
step must be considered (Equations 2.44 and 2.45). There is now a competition 

A ■ 

*■ B 



>■ G 


between two pathways: B may go on to C or return to A. Even though B still 
does not accumulate, it is no longer true that every A reacting leads directly to C. 
The first step is not strictly rate-determining, and the rate constant for the second 
step enters into the rate equation (Problem 2). 

94 Some Fundamentals of Physical Organic Chemistry 

If, in the two-step mechanism in Equations 2.37-2.38, it is not justifiable to 
assume that B is consumed as fast as formed, [B] will increase and then decrease; 
the rate of disappearance of A will not equal the rate of appearance of C, and the 
stationary-state approximation is not valid. This situation requires a more general 
approach. 35 

Preliminary equilibrium In a second common limiting case of the 
two-step mechanism, the second step is slow. Then ordinarily the reverse of the 
first step will be important, so we need to use Equations 2.44-2.45. With the first 
step and its reverse much faster than the second step, nearly all B formed returns 
to A. Now there is an equilibrium always maintained between A and B and the 
second step is rate-determining. We can therefore write an equilibrium constant 
for Equation 2.44, 

[Bl k x 

.RT = -t — i = — ^— (2.46) 

[A] k. x 

Then since 


= * a [B] (2.47) 

we can at once write the rate equation 2.48 for rate of formation of C in terms of 
starting material A. 

^1 = k 2 K[A] (2.48) 


The mechanism thus predicts first-order behavior, with an observed rate constant 

k obs = k 2 K (2.49) 

If the equilibrium constant K can be measured independently, k 2 can be recovered. 
A judicious combination of the stationary-state, preliminary-equilibrium, 
and rate-determining step concepts will often yield the rate equation for more 
complex reaction schemes. An example is given in Problem 6. 


The utility of rate constants for understanding reaction mechanisms depends 
largely on interpreting them in terms of energies. Energy information is ordinarily 
obtained from rate data by either of two methods, one empirical and the other 
more theoretical. 

The Arrhenius Equation 

The temperature dependence of observed rate constants follows the Arrhenius 
equation (2.50) with good accuracy for most reactions. A and E a are parameters 
determined experimentally, R is the gas constant, 1 .986 cal °K "" 1 mole ~ 1 , and 

* ob9 = ^« P (-AJ (2.50) 

35 See note 34. 

Interpretation of Rate Constants 95 

T is the temperature in degrees Kelvin. The units of A, called the pre-exponential 
factor, are the same as those of A; obs : for a first-order rate constant, time -1 ; for a 
second-order rate constant, / mole -1 time -1 . We use the notation k obs to empha- 
size that the equation applies to the observed rate constant, which may or may 
not be simply related to the microscopic k's characterizing the individual steps 
of a reaction sequence. 

If we write Equation 2.50 in the form of Equation 2.51, we see at once a 
resemblance to the familiar relation 2.52 between the equilibrium constant of a 

-E a = RTln(^j (2.51) 

-AG° = RT\nK (2.52) 

reaction and its free-energy change. Hence it is natural to interpret E a as an 
energy. This energy is called the Arrhenius activation energy, or simply activation 
energy, and may be crudely interpreted as the height of an energy barrier over 
which reactants must pass on their way to products. Yet because k ohs will not in 
general correspond to the microscopic constant for a single step, the origin of the 
activation energy on the molecular level is not well defined. To obtain a more 
precise idea of the dynamic behavior of molecules during a reaction, we turn to 
the transition-state theory. 

Transition State Theory 36 

The transition state theory is confined to consideration of single elementary re- 
action steps, and is meaningful only when applied to a single microscopic rate 
constant. The theory postulates that when two molecules come together in a 
collision that leads to products (or when a single molecule in a unimolecular step 
follows the motions that cause the chemical change), they pass through a con- 
figuration of maximum potential energy called the transition state. In order to 
understand this concept fully, we must first digress to consider some ideas about 
potential energy surfaces. 

Potential energy surfaces Because each of the N atoms in a molecule can 
move in three mutually perpendicular and therefore independent directions, a 
molecule has a total of 3 N degrees of freedom. But since we think of a molecule 
as a unit, it is useful to divide these degrees of freedom into three categories. If 
the atoms were fixed relative to each other, the position of the rigid molecule in 
space would be defined by specifying six quantities: the three cartesian coordi- 
nates of its center of mass and three rotational angles to indicate its orientation 
in space. Hence there remain 3JV — 6 degrees of freedom which are internal 
vibrational motions of the atoms with respect to each other. (A linear molecule 

36 Transition state theory is discussed in standard texts on physical chemistry, kinetics, and physical 
organic chemistry. See, for example, (a) W. J. Moore, Physical Chemistry, 3rd ed., Prentice-Hall, 
Englewood Cliffs, N.J., 1962, p. 296; (b) S. W. Benson, Thermochemical Kinetics, Wiley, New York, 
1968; (c) K.J. Laidler, Chemical Kinetics, 2nd ed., McGraw-Hill, New York, 1965; (d) K. B. Wiberg, 
Physical Organic Chemistry, Wiley, New York, 1964; (e) L. P. Hammett, Physical Organic Chemistry, 
2nd ed., McGraw-Hill, New York, 1970. For a different approach to chemical dynamics, see 
(f) D. L. Bunker, Accts. Chem. Res., 7, 195 (1974). 

96 Some Fundamentals of Physical Organic Chemistry 


Figure 2.6 Potential energy of a diatomic molecule as a function of internuclear separation 
r. The equilibrium separation is r e . A normal mode in a polyatomic molecule 
would have a similar potential curve, with a parameter characterizing the phase 
of the motion replacing r. 

has only two rotational coordinates, hence 3N — 5 vibrational degrees of free- 
dom. We shall continue to say 3N — 6, with the understanding that 3N — 5 is 
to be substituted if the molecule is linear.) 

The total molecular vibration is complex, but to a good approximation the 
vibration may be divided into 3JV — 6 independent normal modes, with the entire 
vibration being a superposition of these. 37 Each normal mode will in general 
involve many atoms, and may include bond stretching or bending or both, but 
as all motions are in phase with each other, just one parameter suffices to follow 
the vibration of a single mode, and each mode can be thought of as being essenti- 
ally equivalent to the stretching vibration of a diatomic molecule. The appro- 
priate model for vibration of a diatomic is two masses joined by a spring, with 
restoring force proportional to the displacement from the equilibrium separation. 

The potential energy of such an oscillator can be plotted as a function of the 
separation r, or, for a normal mode in a polyatomic molecule, as a function of a 
parameter characterizing the phase of the oscillation. For a simple harmonic 
oscillator, the potential energy function is parabolic, but for a molecule its shape 
is that indicated in Figure 2.6. The true curve is close to a parabola at the bottom, 
and it is for this reason that the assumption of simple harmonic motion is justified 
for vibrations of low amplitude. 

For a polyatomic molecule there will be a potential energy curve like that of 
Figure 2.6 for each of the 3N — 6 vibrational modes. The potential energy is 
therefore characterized by a surface in 3N — 6 + 1 -dimensional space. To plot 
such a surface is clearly impossible; we must be content with slices through it 
along the coordinates of the various normal modes, each of which will resemble 
Figure 2.6. 

37 The vibrations are separable if they follow simple harmonic motion. Molecular vibrations are not 
quite harmonic, but are nearly so. Everything that follows will assume harmonic vibration. 

Interpretation of Rate Constants 97 


A+ B C + D 


x = x = x t x = 1 

Reaction coordinate 
Figure 2.7 The reaction coordinate diagram for the reaction A + B . . "* C+D. 

The reaction coordinate When two molecules come together and react, 
it is the potential energy surface for the whole process that is of interest. Let us 
imagine a reaction in which A and B come together and the constituent atoms 
move over the potential energy surface of the combined system to produce C and 
D. We shall suppose that we have identified the particular set of atomic motions 
that has to occur to accomplish this change, and we make a slice through the 
surface along the dimension of this particular motion. We shall find that the 
shape of the surface along the line of the slice is something like that shown in 
Figure 2.7. The motion of atoms characterizing the change is called the reaction 
coordinate. It is convenient to define a parameter x that characterizes progress of 
the system along the reaction coordinate. The graph of potential energy as a 
function of x is the reaction coordinate diagram?® 

When A and B are separate and not yet interacting, we are at the left-hand 
side of the diagram, x = 0; as they come together in a reactive collision, the 
potential energy rises as the atoms begin to execute the motion that will carry 

38 We shall have occasion to use reaction coordinate diagrams frequently throughout this book. While 
we shall sometimes, as here, be plotting potential energy as a function of reaction coordinate, we shall 
often want to use a more comprehensive quantity such as enthalpy or free energy. The internal 
energy £ of a system is the sum of the potential and kinetic energies of its constituent parts : 

E = k.e. + p.e. (1) 

Its enthalpy is a function of its internal energy, pressure, and volume: 

H = E + PV (2) 

Its free energy depends on both its enthalpy and its entropy: 

G = H - TS (3) 

The free energy includes all the other energy terms, and any changes in the individual terms will be 
reflected in it. Thus free energy can always be used as the y coordinate in a reaction coordinate 
diagram. When the changes being considered chiefly affect one of the less comprehensive terms, it 
may be more meaningful to plot that energy term against the reaction coordinate. 

98 Some Fundamentals of Physical Organic Chemistry 

Figure 2.8 A three-dimensional reaction coordinate diagram. The reaction coordinate is a 
path following the lowest altitude line up one valley, over the pass, and down the 

over to products. At some configuration the potential passes through a maximum, 
and then falls as we proceed to the right, finally reaching a minimum again with 
separated products C and D, x = 1 . An entirely similar process can be imagined 
for a unimolecular reaction. The configuration of atoms corresponding to the 
maximum in the reaction coordinate diagram is the transition state, symbolized 
by X- It occurs at x = x$. 

There are two perhaps obvious but easily overlooked points about the re- 
action coordinate diagram that must be stressed. First, it is only a one-dimensional 
slice of a 3N — 6 + 1-dimensional surface. (iV is the total number of atoms in 
A and B.) We can imagine, at each point of the line, motions off the line corre- 
sponding to vibrations other than the single one that is carrying the molecules 
over to products. These motions are all ordinary vibrations, having nothing to 
do (in a first approximation at least) with the reaction, and proceeding quite 
independently of it. If we assume that the reaction coordinate corresponds to a 
normal mode of the reacting system, 39 the reaction coordinate is "perpendicular" 
(in 3N — 6-dimensional space) to each of these other normal modes. Our 
curve passes along the equilibrium position of each of the other vibrations, so that 
if we were to leave the reaction coordinate line and follow the potential energy 
surface in the direction of some other mode, the energy would always go up. 

39 This assumption is implicit in the transition state theory, although it may not be entirely correct. 

Interpretation of Rate Constants 99 

The situation can be visualized if only one vibrational degree of freedom 
besides the reaction coordinate is included. Then we have the three-dimensional 
potential energy surface of Figure 2.8, two valleys meeting over a mountain pass. 40 
If we climb along the reaction coordinate out of one valley over the pass into the 
other, we go over an energy maximum along the reaction coordinate, but the 
surface rises in the perpendicular direction and we are therefore following a 
potential energy minimum with respect to the motion perpendicular to the 
reaction coordinate. 

The second point about the surface is that it shows only the potential energy. 
The total energy of the molecular system is the sum of its kinetic and potential 
energies. The molecules exchange kinetic energy by collisions, and are distributed 
over a range of total energies, with many at low energies and fewer at higher 
energies. It is tempting to think of a reaction as following the path of a pack horse 
up out of the left-hand valley and over the pass into the right-hand one. This 
model is quite inappropriate; a much better way to think of the situation is to 
imagine many birds flying in the valleys at various levels, the levels representing 
the various possible total energies. The individual birds can go up or down by 
receiving or giving up some energy to their surroundings, but the vertical 
distribution of birds is in equilibrium and remains unchanged. The birds are 
flying around at random, and those that are high enough may in their wanderings 
happen to sail over the pass and join the population in the other valley. The rate 
of passage of the birds from one side to the other depends on the height of the pass 
and on the vertical distribution of the birds. In the molecular system the vertical 
distribution is determined by the temperature. 41 

Thermodynamics of the Transition State 

In developing the transition state theory, we shall take advantage of the fact that 
most of the motions in a reacting molecular system are ordinary vibrations, 
rotations, and translations. Only the one normal mode corresponding to the 
reaction coordinate is doing something peculiar by coming apart to form new 
molecules. We shall postulate therefore that the molecules going over the barrier 
are in equilibrium with all the other reactant molecules, just as in our bird analogy 
we said that the birds that can get over the pass are just those that happen to be 
high enough up and headed in the right direction. 

We assume that in Reaction 2.53 there are at any instant some molecules 

B (2.53) 

40 This surface could never be the complete one in a molecular system, as it would require that 
3N — 6 + 1=3 (nonlinear) or 3N —5+1=3 (linear), neither of which have solutions for jV 
an integer. A three-dimensional reaction coordinate diagram like Figure 2.8 is thus always only a 
projection of a surface of higher dimensionality, just as the two-dimensional one is. 

41 We must also remember that, although we tend to think of the atoms as classical particles, their 
motions are actually determined by the rules of quantum mechanics. If we tried to follow in detail 
the motions of the atoms in a molecule crossing the barrier with just enough total energy to get over, 
we would come up against the uncertainty principle just as we do in trying to follow electron 
motions, and would be unable to say just how the atoms got from one place to the other. For further 
discussion see W. F. Sheehan, J. Chem. Educ, 47, 254 (1970). 

100 Some Fundamentals of Physical Organic Chemistry 

at the transition state going in each direction over the barrier, and we shall con- 
centrate on one direction only, A — > B. We are therefore dealing with rate 
constant A^ ; exactly the same arguments will apply to the A <- B reaction and k_ 1# 
We suppose that the transition state molecules moving from left to right, At, are 
at equilibrium with the bulk of the A molecules in the restricted sense specified 
above. The concentration [A*] can therefore be written in terms of an equilibrium 
constant, Kx (Equation (2.54)). The rate of the reaction from left to right is 

[A*] = K t [A] (2.54) 

A;* [A*], the concentration of molecules at the transition state multiplied by a rate 
constant characterizing their rate of passage over the barrier. Then since A^fA] 
is the conventional reaction rate, 

yti[A] = A*[A*] (2.55) 

and, substituting for [A+] from Equation 2.54, and cancelling [A] from both sides, 
we find Equation 2.56 relating the first-order rate constant to properties of the 
transition state. 

*i = k*K t (2.56) 

The equilibrium constant K^ is then analyzed by the methods of statistical 
thermodynamics to separate out the contribution of the reaction coordinate from 
other contributions. The rate constant k* is also calculated by statistical thermo- 
dynamic methods. These calculations are given in Appendix 1 to this chapter. 
The results of the analysis are expressed by Equation 2.57, where k is the Boltz- 


k, = —K* (2.57) 

mann constant, h is Planck's constant, T is the Kelvin temperature, and K* 
is a new equilibrium constant that excludes the contributions from the reaction 
coordinate. The new equilibrium constant K* can be written in terms of a free 
energy of activation, AG* (Equation 2.58), and AG* can in turn be divided into 

AG* = -RTlnKt (2.58) 

AG* = AW - TAS* (2.59) 

kT I AGt\ 
k > = -~>\-RT) (2 - 60) 

kT I AHt\ /AS*\ 

* i = - exp (-^) exp hr) (2 - 61) 

contributions from enthalpy of activation, AH*, and entropy of activation, AS* 
(Equation 2.59). Equations 2.60 and 2.61 then follow. Equation 2.60 is called 
the Eyring equation, after Henry Eyring, who was instrumental in the develop- 
ment of the transition state theory. 

Interpretation of Rate Constants 101 

Table 2.12 Differences in AH* or E a and in AS* Corresponding 

to Various Rate Constant Ratios for Two Elementary 
Reaction Steps, a and b 

AH* - AH*, or E ab - E aa 
(kcal mole -1 , 300°K, constant 
kjh AS*otA) 

2 0.41 

10 1.37 

10 2 2.74 
10* 5.49 
10 6 8.23 

AS* - AS* 
(entropy units, e.u., cal mole x °K 1 
kjk b constant AH*) 

2 1.38 

10 4.57 

10 3 9.15 
10* 18.29 
10 a 27.44 

Comparison between the transition state expression (2.61) and the Ar- 
rhenius equation (2.50) may be made if both are applied to the microscopic rate 
constant for a single reaction step. 42 The correspondence is as follows: 43 

ekT MS*' 

— exp hr, 


E a = A.W + RT (2.63) 

The term RT is small at ordinary temperatures; in the neighborhood of 300° K 
the difference between E a and A//t is only about 0.6 kcal mole" 1 . The factor 
kT\h is equal to 10 128 sec" 1 at 300°K, and ekTjh is 10 13 2 sec" 1 at this tempera- 
ture. These figures should thus represent roughly the rate to be expected for a 
gas-phase reaction step of zero enthalpy and entropy of activation. 

Magnitudes of kinetic quantities Because rates of different reactions 
are often compared, it is well to have an idea of the relationship between a given 
rate ratio and the difference in activation parameters. Table 2.12 gives some 
values. Note particularly the relatively small differences in activation energy or 
enthalpy that correspond to even rather large ratios of rates. The following rela- 
tion may sometimes by useful: 

AE a x 1.37 log (^j (2.64) 

where A-£ a is the activation energy difference between reactions a and b in 
kcal mole -1 . 

42 Recall that the Arrhenius equation applies to any rate constant, but the transition state theory 
treats only rate constants for individual steps. 

43 See note 36(b), p. 95. 

102 Some Fundamentals of Physical Organic Chemistry 




Reaction coordinate 



Reaction coordinate 

Figure 2.9 In an exothermic reaction (a), the Hammond postulate assumes that the 
transition state should resemble the starting material, whereas in an endothermic 
process (b), it should resemble the product. 

The Hammond Postulate 

Consider a reaction in which starting materials and products lie at significantly 
different energies. We have no a priori way of predicting, short of carrying out 
time-consuming and expensive calculations, where along the reaction coordinate 
the transition state will occur. But it seems intuitively reasonable that if the 
starting materials are of high energy (exothermic reaction) , relatively little change 

Interpretation of Rate Constants 103 


Reaction coordinate 

Figure 2.10 Addition to the reaction coordinate potential (solid curve) of a perturbation of 
positive slope makes the reaction toward the right more difficult and shifts the 
transition state to the right (dashed curve). Reprinted with permission from , 
E. R. Thornton, J. Amer. Chem. Soc, 89, 2915 (1967). Copyright by the American 
Chemical Society. 

of geometry will be required to reach the transition state, whereas if the reaction 
is endothermic, the reorganization required will be considerable and the transi- 
tion state will not be reached until the geometry already closely resembles the 
high-energy products. This idea, illustrated in Figure 2.9, is known as the 
Hammond postulated 

A reaction that is highly exothermic is expected on the basis of the Hammond 
postulate to have a small activation energy and therefore a high rate. Chemists 
therefore sometimes speak of a feature of a structure that makes a large exo- 
thermic contribution to the equilibrium free-energy change as a driving force for 
the reaction. The formation of a particularly strong bond, or relief of an un- 
favorable steric interaction, might constitute a driving force. It is well to remem- 
ber that there is no direct connection between equilibrium thermodynamics and 
rate ; the driving force idea is therefore only a rough qualitative one and must be 
used cautiously. 

Reacting Bond Rules 

It is often useful to have the Hammond postulate stated in the context of a small 
change in structure or perturbation, brought about, for example, by changing a 
substituent. Thornton has given an analysis that we follow here. 45 We approxi- 
mate our potential energy curve in the region of the transition state by a parabola, 
opening downward as shown in Figure 2.10. We then suppose that we make 
some small change in structure that makes it more difficult to proceed to the right. 
This change is equivalent to raising the right-hand side of the reaction coordinate 

1 G. S. Hammond, J. Amer. Chem. Soc, 77, 334 (1955). 
'< E. R. Thornton, J. Amer. Chem. Soc, 89, 2915 (1967). 

104 Some Fundamentals of Physical Organic Chemistry 

curve more than the left-hand side, and can be accomplished by adding to the 
free energy at each point along the curve an increment SAG that increases to the 
right. Here the symbol S signifies the effect on the quantity AG° of the structural 
change. 46 The simplest approach is to make the increment increase linearly with 
x, that is, 

S AG° = mx (2.65) 

where x is the reaction parameter defined earlier (Figure 2.7), and m is the slope, 
positive in the present example. In Figure 2.10 the straight line superimposed on 
the reaction coordinate potential curve represents the perturbation SAG . If we 
place the origin at the vertex of the parabola, it is easy to verify by inspection 
that the result of adding the perturbation to the potential energy curve will be to 
shift its maximum, and thus the transition state, to the right (dashed curve). A 
perturbation with a negative slope, that is, a structural change making motion 
from left to right easier, will shift the curve to the left. 

It may in some instances be of interest to know how structural changes affect 
the position of the transition state on the potential energy surface with respect to 
degrees of freedom other than the reaction coordinate. Recall that these other 
degrees of freedom correspond to ordinary vibrations. They cut across the surface 
perpendicular to the reaction coordinate and are valleys rather than hills. Sup- 
pose that we make a change in structure that will make a certain bond, not 
corresponding to the one breaking, more difficult to stretch. We show in Figure 
2. 1 1 the potential surface cut along the stretching degree of freedom, with a 

8 AG° = mz (2.66) 

where m is positive. Now the perturbed potential (dashed curve) is shifted to the 
left. Making the bond more difficult to stretch has changed the structure of the 
transition state so that the equilibrium bond distance is shorter. 
These arguments are summarized as the reacting bond rules : 47 

1. For an internal motion of a molecule that corresponds to progress over a 
transition state (energy maximum), any change that makes the motion more 
difficult will lead to a new molecular geometry at the energy maximum in which 
the motion has proceeded farther. Changes that make the motion less difficult 
have the opposite effect. (This rule corresponds to the Hammond postulate.) 

2. For an internal motion of a molecule that corresponds to a vibration, 
any change that tends to force a change in the equilibrium point of the vibration 
in a particular direction will do so. 

3. Effects on reacting bonds (bonds made or broken in the reaction) are the 
most significant; most strongly influenced are reacting bonds nearest the site of 
structural change. 

These rules will be useful when we wish to analyze reaction paths in terms of 
motion along more than one dimension of a potential energy surface. The need 

48 8 is known as a Leffler-Grunwald operator, and is used to designate the change in any quantity re- 
sulting from a structural change. See J. E. Leffler and E. Grunwald, Rates and Equilibria of Organic 
Reactions, Wiley, New York, 1963, p. 26. 
47 See note 45, p. 103. 

Isotope Effects 105 


Vibration coordinate 

Figure 2.11 Addition to a vibration potential (solid curve) of a perturbation of positive 
slope makes bond stretching more difficult and decreases the equilibrium 
separation (dashed curve). Reprinted with permission from E. R. Thornton, 
J. Amer. Chem. Soc, 89, 2915 (1967). Copyright by the American Chemical 

for such analysis arises in the study of reactions such as nucleophilic substitution, 
elimination, and acid-catalyzed addition to carbonyl, where a process can occur 
either by a stepwise route (S N 1 substitution, E x elimination) or by a concerted 
route (S w 2 substitution, E 2 elimination). Applications are discussed in Sections 
5.4, 7.2, and 8.1. 


The kinetic isotope effect, a change of rate that occurs upon isotopic substitution, 
is a widely used tool for elucidating reaction mechanism. 48 The most common 
isotopic substitution is D for H, although isotope effects for heavier atoms have 
been measured. Our discussion will be in terms of hydrogen isotope effects ; the 
same principles apply to other atoms. 

To a good approximation, substitution of one isotope for another does not 
alter the potential energy surface. The electronic structure, and thus all binding 
forces, remain the same. All differences are attributable solely to the change in 
mass, which manifests itself primarily in the frequencies of vibrational modes. 
For a hypothetical model of a small mass m attached to a much larger mass by a 
spring of force constant k, the classical vibrational frequency is given by: 49 

1 fk 
v=— - (2.67) 

l-n \ m 

48 For general treatments of the isotope effect, see (a) K. B. Wiberg, Physical Organic Chemistry, Wiley, 
New York, 1964, p. 273 and p. 351; (b) L. Melander, Isotope Effects on Reaction RatesJTt.cma\d Press, 
New York, 1960; (c) F. H. Westheimer, Chem. Rev., 61, 265 (1961); (d) J. Bigeleisen and M. Wolfs- 
berg, Advan. Chem. Phys., 1, 15 (1958), (e) C. J. Collins and N. S. Bowman, Eds., Isotope Effects in 
Chemical Reactions, ACS Monograph 167, Van Nostrand Reinhold, New York, 1970. 

49 If the two masses joined by the spring are comparable, m in Equation 2.67 must be replaced by the 

106 Some Fundamentals of Physical Organic Chemistry 


Vibration coordinate 

Figure 2.12 The zero-point energy is proportional to v and thus to vl/m; the C — D bond 
therefore has a lower zero-point energy than the C — H bond. 

The quantum mechanical treatment of the same model leads to energy levels 

e n = (n + i)h v n = 0, 1, 2, . . . (2.68) 

and thus to energy-level separations Ae = hv, where v is the classical frequency 
given by Equation 2.67. Energies are measured from the lowest point on the 
potential energy curve. 

An important feature of the vibrational energy levels is that the energy of 
the lowest possible level lies \hv above the minimum of the potential curve. This 
zero-point energy, is by Equation 2.67, inversely proportional to the square root 
of the mass. 

Primary Isotope Effects 

Figure 2.12 illustrates the zero-point energy level for a C — H stretching vibration 
and compares it with the zero-point energy of the same stretch for a C — D bond. 
In a reaction in which the C — H (G — D) bond breaks, there will be a primary 
isotope effect. The stretching vibration of the reactants is converted to the trans- 
lational motion over the barrier, and the zero-point energy disappears for that 
particular degree of freedom. Since the C — H molecule starts out at a higher 
energy, its activation energy is lower, and £ H /£ D will be greater than 1 . 

We can easily calculate the isotope effect to be expected were this loss of 
zero-point energy the sole contributor. The C — D frequency should be smaller 
than the C — H frequency by a factor of roughly 1/V2 = 1/1.41 according to 
Equation 2.67; the observed ratio is closer to 1/1.35. 50 The zero-point energy 

reduced mass, 

m 1 m a 

fi - 

m l + m 2 

When one of the masses is much larger than the other, as would be the case for a hydrogen attached 

to a large molecule ft is approximately equal to the smaller mass. 

50 A. Streitwieser, Jr., R. H. Jagow, R. C. Fahey, and S. Suzuki, J. Amer. Chem. Soc, 80, 2326 (1958). 

Isotope Effects 107 

difference is therefore 51 

Ae = ihc(v H - v D ) = Vu(l- j^j v H (2.69) 

The resulting isotope effect would be approximately 52 

k K [ he / 1 \ 1 / 0.1865 \ 

Since the C — H stretching vibration appears in the infrared spectrum around 
3000 cm" 1 , the isotope effect at T = 300°K would be 


exp[-^^(30ee}] = 6.4 (2.71) 

This model is, however, too crude to account for the observed range of isotope 
effects. There are other changes occurring in the vibrations, and a more careful 
treatment must take them into account. 

Appendix 2 to this chapter gives a derivation that shows that the isotope 
effect is more closely approximated by Equation 2.72. The II symbols signify a 

k x 

-£- sn«p[-i(% - «,D)j]n ex p[ + ^"'H - "«>),] ( 2 - 72 ) 

product of terms ; the first is a product over normal modes of vibration of the 
transition state, and the second over normal modes of the reactants. The quantity 
«j is defined as hv^kT, where v t is the frequency of normal mode i; each of the 
exponential terms thus contains a difference in vibrational frequency between 
the hydrogen and the deuterium compound. The products are over bound vibra- 
tions only. In other words, the reaction coordinate itself, which is a vibration in 
the reactants but not in the transition state, contributes only to the reactant part 
of Equation 2.72. It is necessary to include in Equation 2.72 only those vibrations 
that involve changes of force constants at isotopically substituted positions. An 
expression for the isotope effect on an equilibrium is given in Appendix 2. 

The following qualitative statement of the direction of an isotope effect is 
sometimes useful. The heavy isotope will concentrate at that site where it is bound 
more strongly, that is, has the larger force constant and frequency. For a kinetic 
effect, this statement means that deuterium will prefer the reactant, where the 
force constant is higher, and the hydrogen will prefer the transition state, where 
the force constant is lower; the hydrogen compound will react faster. For an 

AH + BD , "'"' AD + BH (2.73) 

if the force constant is higher in AH(D) than in BH(D), the deuterium will prefer 
to be in A and the hydrogen will prefer to be in B ; K WIU will be greater than 1 . 

51 Multiplication by the speed of light, c, converts frequency expressed in cm" 1 to sec -1 . 

52 The units of hcv are erg molecule -1 . To convert to cal mole" 1 , multiply by 1.439 x 10 16 ; then 
the gas constant R = 1.987 cal mole -1 °K -1 must be used in place of A:. 

108 Some Fundamentals of Physical Organic Chemistry 

Isotope effects in linear transition states Let us now analyze the 
kinetic isotope effect in a simple system, a transfer of hydrogen from AH to B 
through a linear transition state (Equation 2.74). 53 We assume that A and B are 
polyatomic fragments. In the reactants we have to consider the A— H stretching 

AH + B-.-A--H--B-..A + HB (2.74) 

and A — H bending modes. In the transition state, the A — H stretch has become 
the reaction coordinate (28), 

-O O > 4 — o 



and contributes nothing to the transition state term in Equation 2.72, leaving 
exp[ + ^(« iH — « jD )] for this mode to contribute to the reactant term. It is this 
factor that we evaluated earlier as being about 6.4. But there are also in the 
transition state other vibrations to be considered. There will be two degenerate 
bends, 29 and 30, which are identical but occur in mutually perpendicular 

o o o © e © 

A H B 

A H B 30 


planes. These motions are not present in the reactants, and it is difficult to know 
how to deal with them. They are, however, roughly comparable to the reactant 
A — H bending; and since bending frequencies are lower than stretching and 
therefore contribute less to the isotope effect in any event, bending frequencies 
are usually considered to cancel approximately between reactant and transition 
state when a primary isotope effect is being evaluated. 54 

We are then left with one final transition state vibration, a symmetric 
stretch (31), which has no counterpart in the reactants. If the transition state is 

■* — 

— o 



— >■ 




highly symmetric, so that the A •••• H and the H •■■• B force constants are equal, this 
stretch will involve only A and B moving in and out together, with no motion of 
the H (or D) . The frequency will then be the same for H and D, and its contribu- 
tion to the transition state term in Equation 2.72 will cancel. We shall then be left 
with only the reaction coordinate mode, and an isotope effect around 6.4. If the 
transition state is not symmetric, the H (D) will be closer to A or to B ; then the 
H (D) will move in the symmetric stretch and since v H > v D , exp[ — -j(« H — « D )] 

63 See (a) note 48(b, c), p. 105. 
V 54 See Wiberg, Physical Organic Chemistry, pp. 332-361, for calculations that roughly justify this 
assumption for a specific example. 

Isotope Effects 109 

for this mode will be less than 1 . Part of the contribution from the reactant zero- 
point energy of the reaction coordinate mode will be canceled and the isotope 
effect will be lowered. In the limit that the transition state is nearly the same as 
reactant, the symmetric stretch (32) will involve nearly as much motion of H or 

* — o «-o o — >■ 


D as the reactant stretch, and its zero-point difference will largely cancel the 
contribution from the reactant stretch zero-point energy. The isotope effect, in 
this simple model at least, thus becomes a rough measure of the position of the 
transition state along the reaction coordinate. The isotope effect is expected to be 
largest for the most symmetrical location of the transition state, and smaller the 
closer the transition state is to either reactant or product. 

Primary isotope effects in non-linear transition states If the transi- 
tion state is nonlinear, the vibration corresponding to the symmetric stretch looks 
like 33. Now even for the symmetrical case, the H (D) moves with relatively high 




frequency, and this mode cancels most of the zero-point contribution from the 
reaction coordinate mode of the reactants. Hence a bent transition state should 
show a small isotope effect. This mode is furthermore little affected by dissym- 
metry, and so the isotope effect for a nonlinear transition state will not be a 
sensitive indicator of position of the transition state along the reaction coordinate. 55 

Secondary Isotope Effects 56 

A secondary isotope effect is one that results from isotopic substitution at a bond not 
being broken in the reaction. As the reaction cordinate, not being affected by the 
substitution, does not make any contribution, the secondary effects must arise 
solely from changes of zero-point energies of ordinary vibrations. Thus if an 
isotopically substituted C — H bond experiences a change of force constant on 
going from reactant to transition state, the effect is approximately 

— = exp{--j-[u iH - kj d - (u rii - u rD )]} (2.75) 

or, using the approximation that v D = v H /1.35, 

k s r 0.1865 1 

— = exp ^- __(„,„ - „ rH )J (2.76) 

5 R. A. More O'Ferrall, J. Chem. Soc. B, 785 (1970). 

' For a review of secondary isotope effects, see E. A. Halevi, Prog. Phys. Org. Chem., 1, 109 (1963). 

110 Some Fundamentals of Physical Organic Chemistry 

Any vibration for which the frequency decreases on going to the transition state 
contributes a factor greater than 1 to £ H /A; D , and any vibration for which the 
frequency increases contributes a factor less than 1. A commonly observed 
secondary isotope effect occurs when deuterium substitution is made at a carbon 
that changes hybridization, as in Equations 2.77 and 2.78. 

R R 

^C^H(D) > )c + -H(D) + X- (2.77) 

R' R 

/ v, 


H (D) > / \/ (2.78) 

Streitwieser and collaborators have analyzed this process and concluded 
that, in going from sp 3 to sp 2 (Equation 2.77) the three C — H vibrations, one 
stretch and two bends, change as indicated below: 57 

C-< — H— ► > £-<— H-* 

stretch stretch 

2900 cm- 1 2800 cm- 1 

\ ^ \ ^ 

^C— H > C— H 

/•' J 'J 

bend in-plane bend 

1350 cm" 1 1350 cm- 1 

C~ H ► C— H 

/' ^ / ^ 

bend out-of-plane bend 

1350 cm" 1 800 cm- 1 

The first change is small and the second nearly zero ; the last one is significant and 
would contribute a factor of approximately 

k H T 0.1865 I 

— = exp (800 - 1350) = 1.41 

*D L •■ J 

at 300°K if the transition state were very close to sp 2 hybridized product. The 
isotope effect will be smaller if the transition state comes earlier; it is typically 
around 1.15 to 1.25 for reactions of the type of Equation 2.77. (See Section 5.2 
for further discussion.) For a reaction in which hybridization changes from sp 2 
to sp 3 , as in 2.78, the effect will be inverse, k H jk D less than 1, with a minimum of 
roughly 1/1.41 = 0.71 for a transition state closely resembling sp 3 hybridized 
product, but typical values being between 0.8 and 0.9. 

67 See note 50, p. 106. 

Problems 111 

Substitution of deuterium at the /3 position leads to the /3 deuterium isotope 
effect in reactions like 2.79. 

(D)H X X (D)H + 

,-C— C-. > ,C— C-^ (2.79) 

-/ \ 4 

Here the C — H bond is weakened and the frequencies lowered by derealization 
of electron density toward the positively charged center (hyperconjugation ; see 
Section 10.2 for further discussion). A bending mode is probably again the most 
important one; 58 k n lk D is greater than 1, values ranging up to about 1.4 for 
favorably situated hydrogens, 59 but more typically on the order of 1.1. 

Solvent Isotope Effects 

Isotope effects are frequently observed when reactions are carried out in solvents 
with O — H (O — D) groups. The reader is referred to the literature for further 
information. 60 


1. Cyanohydrin formation, shown below, may involve rate-determining attack of 
either H + or ~ CN. From the p value for the formation of cyanohydrins from substituted 
benzaldehydes (Table 2.3), which step do you think is rate-determining? 


RC— H + HCN > RC— H 


2. Derive a rate equation for formation of C in the following mechanism, assuming 
the stationary state for B : 

-* c 

3. Derive a rate equation for formation of C in the following mechanism, assuming 
the stationary state for B and constant concentrations of D and E : 

A ; B + D 

E + B > C 

4. Derive the rate equation for rate of formation of E in terms of concentrations of 
reactants A and B in the following mechanism, assuming that the rates of steps k x and 

68 See note 50, p. 106. 

69 V.J. Shiner, Jr. and J. G. Jewett, J. Amer. Chem. Soc, 86, 945 (1964). 

80 (a) R. L. Schowen, Prog. Phys. Org. Chem., 9, 275 (1972); see also (b) P. M. Laughton and R. E. 
Robertson, in Solute-Solvent Interactions, J. F. Coetzee and C. D. Ritchie, Eds., Marcel Dekker, New 
York, 1969, p. 399. 

112 Some Fundamentals of Physical Organic Chemistry 

£_! are both fast compared with the rate of step k 2 . What is the kinetic order? 

2A + B , C + D 



C + D > E 

5. Define the terms microscopic rate constant and observed rate constant. 

6. Derive the rate equation for formation of F in terms of concentrations of A, B, 
and D in the following mechanisms, assuming that A, B, and C are in equilibrium and 
E is a highly reactive intermediate. 


A + B " C 


C + D -^-> E 

2E > F 

7. Estimate the heat of hydrogenation of benzene and of a hypothetical benzene 
with three fixed double bonds, each reacting with three moles of H 2 to yield cyclohexane. 

8. Verify analytically that the effect of adding a linear perturbation of the form 
y = mx to a parabola is to maintain its curvature but to shift it in the sense concluded 
in the text, p. 104. The general formula for a parabola is 

Ax 2 + Dx + Ey + F = 

(* - hy = 4p(y - k) 

where 4/> = -El A, h = -D/2A, k = D 2 \A-AE - FjE. The parabola opens upward if/) 
is positive and downward if/) is negative; the vertex is at x = h, y = k. 

9. Verify the expression for the equilibrium isotope effect, K HID (Equation A2. 1 5 
in Appendix 2). 

10. Verify by reference to the equilibrium isotope effect equation, A2.15 in 
Appendix 2, the statement that the heavy isotope will concentrate, relative to the light, 
at that site where it is more strongly bound. 

11. Rationalize the observation that D 3 + is a stronger acid than H 3 + . 

12. Verify that a decrease in H — C (D — C) vibrational frequency on dissociation 
will cause the observed secondary equilibrium isotope effect K^jK^ > 1 for dissociation 

13. Estimate (a) AH r ° for triethylamine ; (b) S° for 1,1-dimethylhydrazine. 


8. G. B. Thomas, Jr., Calculus and Analytic Geometry, Addison-Wesley, Reading, Mass., 

1953, p. 237. 

9. K. B. Wiberg, Physical Organic Chemistry, Wiley, New York, 1964, p. 273. 

13. S. W. Benson, F. R. Cruickshank, D. M. Golden, G. R. Haugen, H. E. O'Neal, 
A. S. Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69, 279 (1969). 

Appendix 1 




In order to analyze the transition state equilibrium, we need to know how a 
collection of molecules divides up the available energy. 


Molecules distribute their total energy among translational, rotational, vibra- 
tional, and electronic motions. These motions are all quantized, with energy-level 
separations very small for translation, larger for rotation, still larger for vibration, 
and very large for electronic motion. There are therefore many discrete energy 
states available. At very low temperature, approaching absolute zero, nearly all 
the molecules are in their lowest energy state ; but as the temperature is raised, 
the molecules acquire more energy and begin to populate higher states. The ratio 
of numbers of molecules in any two states depends on the energy difference be- 
tween the states and on the temperature, and is given by the Boltzmann distribu- 
tion law, 

Here n± is the number of molecules in state 1, energy e x , n 2 is the number of 
molecules in state 2, energy e 2 , k is the Boltzmann constant, 1.3806 x 10~ 16 
erg °K _1 , and T'\% the absolute temperature in degrees Kelvin." 

Derivations may be found in the sources cited in note 36 of Chapter 2. 

6 For a derivation see K. B. Wiberg, Physical Organic Chemistry, Wiley, New York, 1964, p. 211, or 

W.J. Moore, Physical Chemistry, 3rd ed., Prentice-Hall, Englewood Cliffs, N.J., 1962, p. 619. 


114 Appendix 1 

Let us assume that we have two isomeric substances A and B in equilibrium 
at very low temperature, so that we can say that for practical purposes all mole- 
cules are in their lowest energy states. Then we could regard A and B as two 
energy states of a system, and since there are only two populated states, the 
equilibrium constant K, the ratio of the number of B molecules to the number of A 
molecules, would be given by Equation A1.2, 

* = ^ =eXP [ kf J (A12) 

The quantity € 0B is the energy of the lowest state of B, and e 0A is the energy of the 
lowest state of A. As it is more convenient to have energies on a molar basis, we 
multiply the energies and the Boltzmann constant by Avagadro's number, N , 
and since kN is equal to the gas constant R, 1.986 cal °K mole -1 , we obtain 
Equation A 1.3: 

XP [ RT J ( } 

Eq is the standard state energy at 0°K. Equation A1.3 may be written in the 
form A 1.4, and since at absolute zero A.E% = A//q = AGq, this equation is 

-A£o = RTlnK (A1.4) 

indeed the familiar thermodynamic expression for the equilibrium constant. 

The Partition Function 

The example we have used is of course unrealistic; we are interested in what goes 
on at temperatures above absolute zero, where many energy levels of the mole- 
cules are populated. All we need do to correct our equilibrium constant A1.3 is 
to find out how many molecules of A and of B are in each energy level at the 
temperature of interest. The total number of molecules of A, N A , is the sum of 
numbers of molecules in each energy state, 

^A = «0A + "lA + «2A + ■ • • (A1.5) 

So far we have assumed that each state has a different energy, but this will not 
always be true. We have to allow for degeneracies, that is, groups of more than one 
state at the same energy. When two states have the same energy, their populations 
must be identical; we therefore modify Equation A1.5 to A1.6, where g iA is the 

N A = £oa«OA + £lA«lA + «2A"2A + ' ' • (A 1.6) 

number of states that have energy € iA , and n iA is the number of molecules occupy- 
ing a single state of energy e jA . Since the Boltzmann distribution deals with ratios 
of numbers in various states, we divide both sides of Equation A1.6 by n 0A and 
obtain Equation A 1.7, which gives the ratio of the total number of molecules to 

N A «1A «2A ,»,-■> 

= gOA + glA + g2A + • • ■ (A1.7) 

ftOA n 0A "OA 

Derivation of Transition State Theory Expression for a Rate Constant 115 
the number in the lowest energy state. Then, using Equation Al.l, we obtain 

N A I"- («ia - e 0A ) 
= £oa + £ia exp 

"OA L *J 


f— (f2A — £oa)1 , . . -. 

+ g2A expl — 1 + • • • (A 1.8) 

The ratio N A ln 0A is defined as the partition function for A, Q A , 

„ #A V- r~ («IA - Coa)' 

Qa = — = > ft A exp - 

«0A j L 




If we want to know the equilibrium constant for the isomerization A ^ B, 
we need again K = N B jN A . But we have N A and N B summed up over all the 
energy states in the partition functions, 

#a = "oaQa (ALU) 

N B = n 03 Q 3 (A1.12) 

and the equilibrium constant is given by Equation A1.13: 

K= N R = no»Q 1 (All3) 

"a i aQa 

The ratio n 0B /n 0A , the numbers in the lowest states, is, as we have already seen, 
just exp[- (Eqb — El A )/RT], so our equilibrium constant is 

A = — exp 

<?A L R 

- E° A j 




RTlnK = -A£ ° + RT In Hr (A1.15) 

For an isomerization, in which there is no change in the number of molecules, 
the expression A1.15 is equal to — AG£. When the number of molecules changes, 
Equation A1.15 must be modified to Equation A1.16. c 

RTln K = - AG? = - A£o + A(PK) + RTln (— \ (A1.16) 


The Components of the Partition Function 

For thinking about transition states, it is useful to divide the energy levels into 
categories, and to associate a fraction of the partition function with each category. 

c The other thermodynamic functions are readily derived from Equation A1.16. See, for example, 
Wiberg, Physical Organic Chemistry, p. 2 1 6. 

116 Appendix 1 

Each energy level has contributions from translational, rotational, vibrational, 
and electronic substates, 

f, = € (( + €, r + C iv + € ie (A1.17) 

If the state multiplicity g t is the product of the multiplicities of the substates, each 
term in the partition function sum can be written in terms of these energies as in 
Equation A 1.1 8, 

r-fo-eo)l r-(e«-eoi)l I"- for - «or)l I"- fo» - «ov)l 

gt CXP [ kT \ = gu CXP [ kT \ g » CXP [ kT \ g >" CXP [ kT \ 

There is a term like Equation A 1.18 for each energy level, and there is an energy 
level for every combination of each e it , e ir , e iv , e jc with every other, so the whole 
partition function is a multiple sum over all combinations, 

„ ^- [-fot - eot)l ^, [-for - for)] ^, T-fol) - «Oll)l 

Q = 2 '« CXP [ kT \ 2 *' CXP [ kT J I g '» CXP [ kT J 

x 2^ ex p[ ~ fa ;~ £oe) ] ( ai - 19 ) 


Q =ftfrfvf. (Al-20) 

where them's are separated partition functions for the different kinds of motion. 
We shall need to know how to evaluate these separated partition functions. 
The translational energy levels can be derived from the quantum mechanical 
solution for a particle in a box; they are so closely spaced that the partition 
function can be evaluated in closed form by integration, and has the value 

/t = hH a (AL2I) 

for each dimension, where M is the mass, h is Planck's constant, and a is the 
length of the box. For three dimensions/ 

/2t7 MkT\ 312 
/<=HH y (M.22) 

where V is the volume. 

The rotational partition function, found in a similar way, is e 

/877A7V' 2 (IJJz) 112 
where I x , I y , I z are the moments of inertia about three mutually perpendicular 

" This value is, strictly speaking, correct only for the gas phase. See, for example, Moore, Physical 

Chemistry, p. 627. 

' Moore, Physical Chemistry, p. 630; Wiberg, Physical Organic Chemistry, p. 221. 

Derivation of Transition State Theory Expression for a Rate Constant 117 

axes and a is the symmetry number, the number of equivalent ways of orienting 
the molecule. 

The vibrational part: 1 function, which is t )ne of most concern for our 
purposes, is found by sum: ^ i*—^.--. -~rgy levels for each vibra- 
tional mode and multiplying together the results for all the modes. Assuming 
simDle harmonic motion, the lowest energy level for a normal mode, the zero- 
pox as energy e = \hv, measured from the minimum of the potential 
en :. Here v is the excitation frequency for the vibration (equal to the 

fre u J served for that mode in the infrared or Raman spectrum) . The other 

levels are spaced upwards from this one at intervals of hv. The levels thus fall at 
integral multiples of hv above the lowest and, since there are no degeneracies, the 
vibrational partition function for each normal mode is 

fr de ' = 2 ex p —tf < A1 - 24 ) 

n = o hl 

Since an infinite sum of terms of the form e~ ax converges to 1/(1 — e~ ax ), the 
partition function A 1.24 is more simply written 

/»<*•' = [1 - exp (-«,)] - 1 (A1.25) 

where m, = hvJkT. The total vibrational partition function is then a product of 
terms for the 3^—6 modes, 


/. = EI [1 - exp (-aO]- 1 (A1.26) 

1 = 1 

• The electronic partition function can be evaluated by summing over 
spectroscopically determined electronic states, but as the electronic energy-level 
separations are large, the number of molecules in excited electronic states is 
negligibly small at ordinary temperatures and the electronic partition function is 
unity and will be ignored henceforth. 


Now consider Reaction A 1.2 7 in the k 1 direction. 

A , B (A1.27) 

We have from Section 2.6 the following relations: 

[A*] = K t [A] (A1.28) 

*i[A] = A*[A*] (A 1. 29) 

k t = k*K t (A1.30) 

We express the equilibrium constant A'j in terms of the partition function ratio 
QxIQa to yield Equation A1.31, where A.E% is the difference between the lowest 

Qx &El 

k 1 =kt—exp (A1.31) 

Qa RT y 

energy level of A and the lowest energy level of the transition state. 

118 Appendix 1 

Now we must analyze Qj. It contains the usual translational and rotational 
functions,/* and/*: ; the electronic contribution/* is unity. It is in the vibrational 
part that the difference from the ordinary stable molecule appears. Since one 
degree of freedom (that corresponding to the reaction coordinate) is no longer a 
vibration, there are only 3N — 7 vibrations in Qj, and these contribute in the usual 
way according to Equation A1.32. The motion along the reaction coordinate is 


ft = fl [1 - cxp(- ii,,)]- 1 (AI.32) 

much more like a translation than a vibration and its contribution,^ c , is there- 
fore written as a one-dimensional translational function (p. 116), 

/rc = (2^ 8 (A[ 33) 


where 8 is an arbitrary interval measured along the reaction coordinate at the 

top of the barrier. (We shall see later that the exact value of 8 is immaterial.) 

The expression for k x can now be written in terms of a reduced partition 

function, Q*, which contains only the translational, rotational, and vibrational 

contributions an ordinary molecule would have, and the special contribution 

/r.c. : 

(2m t kT)^ Qt AEl 

k, = kt S — exp — (A1.34) 

h Q A F RT 

Next we examine ki. At the top of the barrier, in the interval 8, there will 
be transition state molecules moving both to the right, in the direction A — >- B, 
and to the left, in the direction A <- B. We want to know the average velocity of 
motion of those that are moving from left to right. The energy of motion of one 
of the transition state molecules is \m%v 2 , where v is its velocity. Positive v corre- 
sponds to motion from left to right, negative from right to left. The average we 
shall find with the aid of a velocity distribution function, that is, a function that 
for each velocity is proportional to the probability of finding that velocity. When 
the velocity is v, the energy of motion is \mv i . The Boltzmann distribution gives 
the ratio of the number of transition states with velocity v to the number with zero 
velocity as 

N " i™*" 2 /A I CRN 

A^ =eXp -^ (AL35) 

A plot of this function against velocity is the required distribution, and the area 
under the curve between v and v + d v is, in the limit as dv — > 0, proportional to 
the probability of finding a transition state with velocity v. The average is found 
by summing over all velocities the product of velocity times the probability of 
finding that velocity. Since the total probability of finding some velocity should be 
unity, the result must be divided by the total area under the curve to correct for 
the lack of normalization. The desired average, v is then given by Equation A1.36, 


I v exp ( — ^mv 2 fk T) dv 
v = i (A 1.36) 

f ex.p( — ^mv 2 /kT) dv 

Derivation of Transition State Theory Expression for a Rate Constant 119 

where the limits of integration in the numerator are set at to +00 because we are 
interested only in positive v. Evaluation of the integrals yields Equation A 1.37: 

kT/m t _ / kT \ 1/2 
{2nkT/m t ) 112 ~~ \2nm t ) 


The rate at which transition states pass over the barrier from left to right is 
just their velocity, v, divided by the distance they must go, which we called 8 
above in the partition function. Therefore 

1/ kT y 2 

*' = ate) (AL38) 

and, from Equation A1.34, 

il = ste) a 8 o: exp {-T¥) (A1 ' 39) 

Equation A1.39 reduces to Equation A1.40: 

kT Qt I A£!\ 

kx = 7T exp ^ (A1.40) 

h Q A ^\ RT J 

Another way to express this result is to define a new equilibrium constant, K*, 
which includes all features of the transition state except the reaction coordinate, 
and write 


*! = Kt (A1.41) 


We then define free energy of activation as the free energy of the transition state 
excluding the reaction coordinate mode, so that Equations A1.42 and A1.43 hold. 

AG* = -RT\nK* (A1.42) 

K* = exp(=£p) (A1.43) 

A factor k, called the transmission coefficient, is sometimes included in the expression 
for k x to allow for the possibility that some transition states may be refl ected back 
at the barrier, or that some may tunnel through it even though classically they 
do not have the requisite energy. These corrections are usually considered to be 
small, and we shall simply disregard them. We leave it as an exercise to the reader 
to extend the transition state treatment to bimolecular reactions. 

Appendix 2 




We begin with the transition state theory result for the rate constant, Equation 

A 1.40. We shall need to consider bimolecular processes, A + B-^ C, for which 

the proper adaptation of Equation A1.40 is Equation A2.1. The quantity AEq is 

kT Qt I AE\\ 

A = — exp ° (A2.1) 

h Q A Q B \ RT] 

the energy difference from the lowest level of the reactants up to the lowest energy 
level of the transition state. But each of these lowest levels is above the potential 
energy curve by the sum of the zero-point vibrational energies of all the modes. 
It is in these zero-point energies that the differences between the H and D com- 
pounds lie ; we must therefore measure energies instead from the potential energy 
surface, which is the same for both. The quantity AE%\R T is given by 

AE* (e ot - <r or ) 

o. = LEI °.LL (A2.2) 

RT kT K ' 

where e 0i is the zero-point energy of the transition state and e 0r is the zero-point 
energy of reactants. Also, 






3NJ -7 

= I 

kT RT 

3N r -6 

ihVir E, 

kT RT 



The Transition State Theory of Isotope Effects 121 

The transition state sum omits the reaction coordinate degree of freedom since 
it is not a bound vibration and does not contribute to the zero-point energy in the 
transition state. E t and E r are respectively the energy of the potential energy 
surface at transition state and reactants. Then, 

AEt 1 r 3N t^ 7 1. 2N l^ 6 1.1 AE 

RT kT 

[ 2 t V « ~ ? 2"H + RT (A2 - 5) 


/ AEl\ f 1 / 3 "t- 7 1 3 V 6 1 \ AE~\ 

ex P (-^)=exp[-_( J ^- 2 2^)-Rf\ (A2 " 6) 


/ A£*\ 3I ^: 7 / 1 \ 3 "lz 6 /l \ / A£\ 

exp r *r7 = n ex p^-2 B '*j n exp (,2" tr J exp \~^rj (A2-7) 

where «j = hvJkT, and A£ is the energy difference along the potential surface 
from reactants to transition state. The expression for k is now given by Equation 

kT Q* 3 "t- 7 / 1 \ 3 "'" 6 /l \ / AE\ 

k = -Qjf B n ex P (-- M(t ) n ^H exp (-^) (A2 - 8) 

The isotope effect is now found by taking the ratio of rate constants for the 
two isotopic systems (Equation A2.9). 

k H Q AD Q t H 3 ^l; 7 ____r K ,1 3W ^ 6 .. r. K .. ,1 ,.„ 9) 

ko VahVId 

3Nj-7 r 1 -I 3 jr r -6 r l "| 

n exp i 2^" ih ~ " id m n ex p + 2 ^ K,H _ "* D ) ( a2 -- 

The energy difference Ais is independent of isotopic substitution and cancels. We 
have assumed that the isotopic substitution is in A, so Q B cancels also. 

We now refer to Appendix 1 to write the partition functions in terms of 
their translational, rotational, and vibrational components. Of the quantities 
appearing in the expressions for these components, only the molecular mass M, 
the moments of inertia /, the vibrational frequencies u { , and the symmetry num- 
bers a are different for the isotopic molecules; all other factors cancel, leaving 
Equation A2.10. 

* H ■■■*h(JM*Y* / / ^ / vD / 3D \ 1,a /am 3 ' 2 li**W**\ in 3N K 7 \ K J 


1 - exp(- M , Dt ) 3^6 ^ £^ ^ -| 1 - exp(-a 1Hr ) 

1 - exp(-a, H} ) 

^ 6 r 1 1 1 - exp (-a, Hr ) 

fl exp + -(«, H - "<D) r —. ^ (A2.10) 

, L *■ • J 1 - exp (-UtOr) 

This expression can fortunately be simplified by use of a theorem known as 
the Teller-Redlich rule, which expresses the molecular mass and moment of 
inertia ratios in terms of a ratio of a product of all the atomic masses rrij and the 
vibrational frequencies : a 

" (a) K. B, Wiberg, Physical Organic Chemistry, Wiley, New York, 1964, p. 275; (b) J. Bigeleisen and 
M. Wolfsberg, Advan. Chem. Phys., 1, 15 (1958). 

122 Appendix 2 

/AM 3 ' 2 /WvhM 1 ' 2 = * /m«\ 3 ' 2 8 f;"/^H\ 
Wd/ \W,dW V UJ V Ud/ 


For the transition state, of course, one of the 3N — 6 vibrations is really a transla- 
tion; for the moment we single it out and write for its frequency ratio vlh/"^' 
When Equation A2.ll is substituted into Equation A2.10, the products of atomic 
masses will cancel, leaving Equation A2.12: 

*h oh vl H 3I ^ 7 v in [ 1, si 1- ex P(- a <Dj) 
— = — —j— I I exnl (u,ti — u,r.)t I *- 

— n — ex p -,( u 'h - »iD)» — ^ n — 

"L.D V "ID L 2 J 1 - eXp(-U lH{ ) V K 1H 

xexp + -(b, h - u iD ) r 

1 — exp( — u lH ) 

^ ' (A2.12) 

1 - exp(-a, Dr ) 

This expression gives the isotope effect in terms of vibrational frequencies 
only ; if the molecules are simple enough, a complete vibrational analysis and 
direct calculation of the isotope effect will be possible. But for most purposes we 
want an expression that will be easier to apply. Some simplification can be 
achieved by noting that for all those vibrational modes that involve no substantial 
motion at the isotopically substituted position, v iH = v iD (and therefore also 
u ih = "(d) i n b otn reactant and transition state. These modes will therefore 
cancel and need not be considered further. Moreover, any mode that does involve 
motion at the isotopically substituted position but that has the same force constant 
in reactant and transition state will have v H in the reactant equal to v H in the 
transition state and likewise for v D , and will also cancel. We therefore need con- 
sider only those modes for which force constants of vibrations involving the 
isotopically substituted position change on going from reactant to transition 
state. For vibrations involving hydrogen, most of which have frequencies above 
1000 cm -1 , the factor 1 — e~ u is approximately unity. Furthermore, since all the 
ratios v H /v D should be about -\/2, they will approximately cancel. b If we ignore 
for the moment the symmetry number ratio, which can always be put in later if 
needed, we then have 

k * r l 1 r r l 1 

-2 ~ Y\ exp --(U, H - U lD ) X Y[ eX P +2('»tH - «<D)r (A2.13) 

where the products are over only those vibrations that involve force constant 
changes at isotopically substituted positions. 

It is frequently also necessary to assess isotope effects on equilibria. For an 

AH + BD ^ AD + BH (A2.14) 

the appropriate expression is c 

„ '"^Z" '.AD I" 1 .1 1 - eX P (-a, AH ) 3*b-B * ( BH ' 

#h/d = M exp +-(a iAH - «(ad) ; r Y\ 

, " iAH L 2 J 1 - exp(-u iAD ) ■*■/ v (BD 

T l i ] 1 - exp(-M, BD ) ,.„,,, 

x exp - - (a, BH - m ( bd) 1 : : (A2. 1 5) 

L 2 J 1 - exp(-u iBH ) 

" See (a) L. Melander, Isotope Effects on Reaction Rates, Ronald Press, New York, 1960, p. 38; (b) J. 
Bigeleisen, Pure Appl. Chem., 8, 217 (1964), for further discussion. 
c Wiberg, Physical Organic Chemistry, p. 275. 

The Transition State Theory of Isotope Effects 123 

Again the terms 1 — e~ u will all be close to unity and the ratios v H /v D should all 
be close to \/2, leaving 

3WA-8 3Wb-« 

•Kh/d X "[J exp [ + i(Uf AH - « ( ad)] E[ exp[-i(«, BH - «ibd)] (A2.16) 

1 I 

Chapter 3 




Of the concepts that chemists use to make sense of chemical transformations, 
ideas about acids and bases are among the most fruitful. Nearly all of the hetero- 
lytic reactions that we shall be considering can be thought of as acid-base pro- 
cesses ; it is therefore appropriate to begin our discussion of the chemical proper- 
ties of organic compounds with a review of these ideas and of their applications in 
organic chemistry. 

Definition of Bronsted Acids and Bases 

Acids and bases have been known for centuries, but the definitions in common use 
today are of comparatively recent origin. In 1923 J. N. Bronsted proposed the 
following definitions: 1 

An ac id~is~a proton donor. 
A base is a proton acceptor. 

An acid HA is thus any substance that reacts according to Equation 3.1, and 
a base B is any substance that reacts according to Equation 3.2 : 

HA — > H + + A- (3.1) 

B + H + > BH + (3.2) 

If one confines one's attention to the liquid phase, however, these idealized re- 
actions apparently never occur. The proton, H + , does not exist free in solution, 

1 J. N. Bronsted, Rec. Trav. Chim., 42, 718 (1923). 


Bransted Acids and Bases 125 

but rather is always solvated by at least one molecule of some other species. Thus 
in water protons exist as hydronium ions, H 3 + ; in ammonia as ammonium, 
NH 4 + ; in alcohols as ROH 2 + . 2,3 Clearly, in each of these cases the solvating 
molecule has acted as a base according to the Bransted definition. The small size 
and consequent large electrostatic field of the proton makes it seem very likely 
that in solution association of H + with a base is a general phenomenon. 4 It is 
therefore more reasonable to represent the actual process of dissociation of an 
acid (acetic acid, for example) in a solvent such as water as shown in Equation 3.3. 
Here the acid donates a proton and the, base accepts it; this chemical change 
constitutes an acid-base reaction in the Bransted sense. 

O O 


H 3 C— C— OH + H 2 . H 3 + + H 3 C— C— O" (3.3) 

If we look again at Equation 3.3, we can see that we should consider the 
reverse process as an acid-base reaction just as the forward process is. The acetate 
ion is a base that can accept a proton from the acid H 3 + . This reciprocal rela- 
tionship is emphasized by the terminology applied to processes like that in 
Equation 3.3 : Acetate ion is called the mnjuonte. hnw, of the ari d CH 3 CQOH. and 
H 3 Q ^ + is called the conjugate acid of the base H,Q. 

? ? 

H 3 C— C— OH + H 2 T " H 3 0+ + H 3 C— C— O- (3.4) 

acid base conjugate conjugate 

acid base 

In considering an acid-base reaction, it is important to realize that the choice o f 
which acid is to he railed the conjugate acid is completely arbitrary. In Equation 
3.4 we could just as well have decided to call H a O the conjugate base of the acid 
H 3 + and CH 3 COOH the conjugate acid of the base CH 3 COO-. It would 
perhaps be better to emphasize the fundamental symmetry of the situation by 
writing Equation 3.5: 

O O 


H3C-C-OH + H 2 7 - H 3 + + H 3 C— C— O- (3.5) 

acidi base! acid 2 base 2 

However, the conjugate acid-conjugate base nomenclature is convenient, and we 
shall continue to use it. 

We now need to generalize our ideas in various ways. First, it is clear that 
it is not always necessary that the molecules and ions involved be of the charge 
types shown in the example that has been used so far. Acids and bases can have 

2 See (a) R. P. Bell, The Proton in Chemistry, 2nd ed., Cornell University Press, Ithaca, N.Y., 1973, 
p. 13; (b) M. Eigen, Agnew. Chem. Int. Ed., 3, 1 (1964). 

3 The exact degree of solvation is not known; we use these designations for convenience, although 
some formula such as H(H 2 0) n + might in fact be more accurate. The symbol H + is also commonly 
used to represent the proton; this notation should be understood as an abbreviation for the solvated 
species that is actually present. 

i G. A. Olah, A. M. White, and D. H. O'Brien, Chem. Rev., 70, 561 (1970), review evidence for co- 
ordination of protons with a large number of substances. 

126 Acids and Bases 

ajiy__oLa^arietY_ofj <...... • . - t ^ e equilibria shown in 

Equations 3.6-3.9. 

tr o u o+ , (35) 

Fe(H 2 0) e 3+ + H 2 ;=± H 3 + + Fe(H 2 0) 5 OH 2+ (3.7) 

HS0 4 - + H z O ;=: H 3 + + S0 4 2 " (3.8) 

HP0 4 2 - + H 2 ;==t H 3 + + P0 4 3 - (3.9) 

In general we might write : 

HA m+ + B n+ ^=^ a*"- 1 ' 4 - + HB<" + 1 > + (3.10) 

where m and n can each be a positive or negative integer or zero. 

Next, we must recognize that many molecules that we ordinarily think of as 
exhibiting neither acidic nor basic behavior are in fact acids or bases, or, fre- 
quently, both. For example, acetone, which is neutral in water solution, reacts as 
a base in sulfuric acid according to the equilibrium 3.11; and in dimethylsulf- 
oxide containing sodium methoxide, acetone is an acid (Equation 3.12). 5 

■O- :OH + 

=t H,C— C- 

H 3 C— C— CH 3 + H 2 S0 4 , H 3 C— C— CH 3 + HS0 4 - (3.11) 

:0: :Or 

H 3 C— C— CH 3 + CH 3 — O:- , H 3 C— C— CH 2 " + CH 3 OH (3.12) 

Logical extension of these ideas leads to the conclusion that acetic acid is a base 
as well as, an acid, and that aniline, a substance ordinarily considered as a base, 
can also act as an acid (Equations 3.13 and 3.14). 

:0: :OH + 

II .. II .. 

H 3 C— C— OH + H 2 S0 4 ; H 3 C— C— OH + HS0 4 - (3.13) 

C e H 5 — NH 2 + NH 2 - ^z=^ C e H 5 NH- + NH 3 (3.14) 

Indeed, one may conclude that any molecule containing hydrogen is a 
potential Bronsted acid, whereas any molecule at all is a potential Bronsted base. 

Acid and Base Strength 

For acids__that_ can be studied in a queous solution, we measure the str ength- 
by the magn itude of the equilibrium constant for dissociation, K „. This quantity 
is denned by first writing the equilibrium constant K' a for Reaction 3.15, using 

HA m+ + H 2 , A (m - 1)+ + H 3 + (3.15) 

K' a = — 3 — (3.16) 

"HA"* fl H 2 + 

Ka= a^-^a a3 o+ (31?) 

a HA ».+ 

5 Later in this chapter we shall consider the experimental methods of detecting reactions like 3.11 
and 3. 12 and the problem of measurement of their equilibrium constants. 

Bronsted Acids and Bases 127 

activities, 6 and then converting to the more usual form given in Equation 3.17 by 
incorporating the water activity, which is essentially constant in dilute solution 
when water is the solvent, into the equilibrium constant. It is often convenient 
to write K a in terms of concentrations and activity coefficients, as indicated in 
Equation 3.18. 7 

K = [A ( "- 1) + ][H3O^ yA cn-i )+yH30 + 

The standard state is defined as the hypothetical state that w ould exist if 
the soufte_were at a con centr ation of fTB T but with t hejr^lecules_exrjer iencing 
the environment of an extremely dilute solution ; with this standard state^ctiyity 
coefficients approach uni ty with increasing dilution. For electrolytes in dilute 
solution in water, the departure of the coefficients from unity can be calculated 
from the Debye-Hiickel relationship. 8 

It is pos sihle to define another equi librium constant. K v (Equat ion 3.19), 
which does not in c lude the activity rnpffinVnts and h ence will not he a true ron - 

r A (m-l) + ][H 3 + ] 
= L JI_J J (319) 

[HA m + ] 

stant ex ce pt in very dilute so lutions, where ^approache s the thermodynamic^^ 
that we have been considering so far. The constant K c is often used for con- 
venience, but it is not satisfactory for careful work, nor where comparisons 
between different solvents must be made. 

Base strengths can be defined similarly by the equilibrium constant for 
Reaction 3.20: 

B m+ + H 2 Q , '. BH (m + 1)+ + OH- (3.20) 

K' b = -^ — (3.21) 

a B m + fl H 2 o 

Or, adopting the same convention as before with respect to the water activity, 

K t = aBH< ^ 1>+a ° H " (3.22) 

However, it is more convenient to consider instead of Reaction 3.20 the acid 
dissociation of the acid BH (m + x) + : 

BH (m + D+ + Ha0 ^ B m+ + H 3 + (3.23) 

K a = " Bm+aH30+ (3.24) 

If K a for equilibrium 3.23 is known, K b , as defined by Equation 3.22, can easily 
be found by use of the constant K w , the ionization constant of pure water. K w is 

6 W. J. Moore, Physical Chemistry, 3rd ed., Prentice-Hall, Englewood Cliffs, N.J., 1962, p. 191. 

7 The activity coefficient y is defined so that a = yc, where a is activity and c is concentration. See 
Moore, Physical Chemistry, p. 198. 

8 See Moore, Physical Chemistry, p. 351. 

128 Acids and Bases 

defined by Equations 3.25 and 3.26, and has been carefully measured at various 

2H z O ^=i H 3 0+ + OH" (3.25) 

It has the value 10" 14 - 00 at 25°C. 9 From Equations 3.22, 3.24, and 3. 
to verify that the relation between K b of a substance and K a of its coi 
is Equation 3.27 : _ r ^ 

K a K b = K w 

In order to avoid proliferation of tables, it isfcustomary to report only one constant 
for each conjugate acid-conjugate base pair. The reader may easily verifx_that4f 
acid A is a stronger acid_than arirl B»_theconjugate base of A w jll_he a weaker 
base than _thg_co njiiga.te has e-of-B — 

The Leveling Effect 

We are now in a position to consider the experimental problems involved in 
measuring equilibrium constants for acids of differing strengths. One may use 
any of a number of methods of determining the concentrations of the various 
species involved in the reaction; the most common procedure for aqueous solu- 
tions is to use the glass electrode, which allows a convenient and accurate deter- 
mination of hydrogen ion activity over a wide range. 10 Other possibilities include 
spectrophotometric determinations of acid and conjugate base, and conducti- 
metric measurement of ion concentrations. 

It generally happens that the range of acidity that can be determined in a 
given solvent is limited by the acid-base reactions of the solvent itself. Consider, 
for example, the hypothetical situation of two acids, HA! and HA 2 , with dis- 
sociation constants of 10 + 2 and 10 + 3 , respectively - {pK a = — 2 and —3, respec- 
tively). 11 If we add enough of each of these acids to water to give solutions 0.1 M 
in total acid, the solutions will be respectively 0.09990 M and 0.09999 M in 
hydrogen ion, a difference of only 0.0004 pH unit. This difference is too small to 
measure ; the most one can say is that both substances, being stronger acids than 
H 3 + , behave as strong acids in water, and are essentially completely dissociated. 
Note that, if the two acids are again separated by one pK unit, but this time have 
dissociation constants of 10 ~ 4 and 10 " 5 (pK a = + 4 and + 5), the pH of the two 
solutions will differ by an easily measurable 0.5 unit. Similar difficulties arise 
with very weak acids ; in this case the amount of H a O + produced by dissociation 
of the acid is less than the amount present by virtue of the ionization of water 
itself (Equation 3.25) and so cannot be determined. As a rough rule we can state 
that m water solntion_|tjsjTos ^ih1e to jtrieasure .st rengths only_of_thosc acids that 
are stronger "tHan water jind weaker thanhydronium ion; by the same token, 

9 H. S. Harned and R. A. Robinson, Trans. Faraday Soc, 36, 973 (1940). 

10 See, for example, H. H. Willard, L. L. Merritt, Jr., and J. A. Dean, Instrumental Methods of Analysis, 
4th ed., Van Nostrand ReinholJ, New York, 1965, p. 589. 

11 pK a is denned by the equation: 

?K a = - log K* 
A pK difference of one unit thus corresponds to a factor of ten difference in K a . 

Strengths of Weak Bronsted Bases 129 

bases can be studied in water only if they are stronger bases than water j.nd 
weaker tl 

The phenomenon described above for water also applies to other amphoteric 
solvents. It is termed the leveling effect, and may be summarized by the following 
statements : 

1. No acid stronger than the conjugate acid of a solvent can exist in 
appreciable concentration in that solvent. 

2. No base stronger than the conjugate base of a solvent can exist in 
appreciable concentration in that solvent. 

Useful correlaries of these statements are the following: 

1. Relative strengths of acids stronger than the conjugate acid of a solvent 
cannot be determined in that solvent. 

2. Relative strengths of bases stronger than the conjugate base of the solvent 
cannot be determined in that solvent. 

The acids in which we are interested span a range of roughly 60 pK units, 
from the strongest acids (HI, HC10 4 ) to the weakest (methane, cyclohexane) , 
and since there is no single solvent that is suitable for the entire range, it is 
necessary to use several different solvents and to try to make connections among 
the results obtained. 

Water is taken as the standard solvent for setting up a scale of acidity. It 
has the advantage, in addition to convenience, of having a high dielectric con- 
stant and being effective in solvating ions. As we noted in Section 2.4 (p. 85), 
the result of these properties is that positive and negative ions separate, and 
complications that result from association of ions in pairs or in larger aggregates 
are avoided. 12 For acids too strong to be investigated in water solution, more 
acidic media such as acetic acid or mixtures of water with sulfuric or perchloric 
acid are commonly used; for very weak acids, solvents such as liquid ammonia, 
dimethylsulfoxide, and cyclohexylamine have been employed. 

The experimental procedures and the results obtained with some of these 
solvents are discussed in Sections 3.2 and 3.3. We note here only that the task of 
relating the results of acidity measurements obtained in different solvents is by no 
means a simple one, and that it has not proved possible to establish a scale that 
provides unambiguously and quantitatively relative acidities of substances 
over the whole range of interest to chemists. Thus the relative acidities of two 
acids may be different in different solvents, and we may have to be content with 
qualitative results if we wish to generalize about acid strengths over wide ranges. 
If, however, we are willing to restrict our attention to acids that can all be in- 
vestigated in the same solvent, it will be possible to obtain quantitative results. 


A variety of organic reactions, including dehydration of alcohols, cleavage of 
ethers, many additions to olefins, a number of nucleophilic substitutions, and 
various rearrangements, are catalyzed by acids. Since the substrates in these 

12 I. M. Kolthoff and S. Bruckenstein, J. Amer. Chem. Soc., 78, 1 (1956). 

130 Acids and Bases 

processes are bases, it is reasonable to postulate that the reactions involve acid- 
base interactions. In order to obtain further information about the detailed 
course of these types of reactions, it is often desirable to be able to make quanti- 
tative measurements of the acid-base properties of the substances involved. 

Acidity Functions 

One solution to the problem of achieving appreciable concentrations of the 
protonated form of very weak bases is to use as a solvent a mixture of water with 
some strong mineral acid. It can be demonstrated by measurement of freezing- 
point depressions 13 that many organic compounds that contain basic atoms such 
as N, O, or S, but that are too weakly basic to be protonated to a significant 
extent in water, are essentially completely converted to their conjugate acids in 
concentrated sulfuric acid. 14 In appropriately chosen mixtures of water and 
sulfuric acid, appreciable concentrations of both base and conjugate acid may be 
expected to be present. In order to study these phenomena, one must have a 
procedure for determining acidity over a very wide range of proton-donating 
capacity, from pure water to pure sulfuric acid. 

Hammett and Deyrup, in 1932, were the first to propose a method of 
determining quantitatively acid-base behavior in water-strong acid mixtures. * 5 ~ 1 7 
In order to understand their contribution, we begin with the general expression 
for the equilibrium constant for the dissociation of an acid (compare Equation 

AH + + S k A + SH + (3.28) 

K a = A (3.29) 

a AH* as 


a SH + [A]y A 

<z g [AH + ]y AH + 

We have chosen to write the reaction in the particular form 3.28 because this form 
corresponds to acids and bases of the same charge type as those on which Ham- 
mett and Deyrup based their original work. AH + corresponds to the protonated 
form of the weak base (for example, (CH 3 ) 2 C=OH + , />-N0 2 — C 6 H 5 NH 3 + , 

13 For a discussion of freezing-point depression, see W.J. Moore, Physical Chemistry, 3rd ed., Prentice- 
Hall, Englewood Cliffs, N.J., 1962, p. 132. 

14 For example, the observation that the freezing point of a 1 molal solution of acetone in sulfuric acid 
is depressed by twice the molal freezing-point depression constant of sulfuric acid is interpreted in 
terms of the reaction 

o + 6h 


H 3 C— C— CH 3 + H 2 S0 4 , H 3 C— C— CH 3 + HS0 4 " 

This equilibrium lies far to the right ; 2 moles of ions are produced for each mole of acetone added 
Similar results are obtained with many other compounds that are neutral in water but contaiik 
unshared electron pairs. 

15 L. P. Hammett and A. J. Deyrup, J. Amer. Chem. Soc, 54, 2721 (1932). 

16 L. P. Hammett, Physical Organic Chemistry, 2nd ed., McGraw-Hill, New York, 1970, chapter 9. 

17 For reviews, see (a) M. A. Paul and F. A. Long, Chem. Rev., 57, 1 (1957); (b) R. H. Boyd, 
Solute-Solvent Interactions, J. F. Coetzee and C. D. Ritchie, Eds., Marcel Dekker, New York, 196 
p. 97; (c) V. A. Palm, tj. L. Haldna, and A.J. Talvik, in The Chemistry of the Carbonyl Group, S.Pat^i, 
Ed., Wiley-Interscience, London, 1966 (applications to carbonyl compounds only). 

Strengths of Weak Bransted Bases 131 

etc.) , A to the free base form, S to some base present in the solvent (H z O mole- 
cules or HS0 4 " ions), and SH + to the conjugate acids of these species (H 3 + , 
H 2 S0 4 ). Note that the nature of S and SH + is not well denned, since in mixed 
solvents each consists of more than one species ; however, the proton-donating 
ability of SH + and the proton-accepting ability of S, whatever they may be, 
together determine the effectiveness of the particular solvent mixture in pro- 
tonating the base A, and so are characteristic of that solvent mixture. It is this 
"protonation effectiveness" that Hammett and Deyrup first set out to measure. 

The next step is to choose a series of bases, A 1} A 2 , A 3 . . . , A n , . . . , each 
weaker than the previous one. We also require that these substances absorb light 
in the visible or ultraviolet region, and that the absorption spectra of the free 
bases differ from the spectra of their respective conjugate acids. The reason for 
this latter requirement is that we must have some means of determining the 
concentrations [A] and [AH + ] for each of the base-conjugate acid pairs; the 
visible-ultraviolet spectrophotometric method is convenient and is the one that 
has been employed most frequently, although there are other methods. Hammett 
and Deyrup picked as their series of bases various substituted anilines with in- 
creasing numbers of electron-withdrawing substituents to provide successively 
weaker bases. It is essential to the method that the first base, A l5 be sufficiently 
strong that the acid dissociation constant of its conjugate acid can be determined 
in pure water. In dilute aqueous solution, SH + in Equation 3.28 is H a O + , S is 
H 2 0, and the activity coefficients approach unity, so the problem reduces to the 
relatively straightforward one discussed in Section 3.1. We next go to a solvent 
containing a small amount of sulfuric acid, for example 1 percent of H 2 S0 4 , in 
which the base A 1 will still give appreciable concentrations of both the conjugate 
acid and conjugate base forms, and that will also allow measurements to be made 
on the weaker base A 2 , which is too weak to give measurable amounts of A 2 H + 
in pure water. 

We may now write two equations of the type 3.30 describing the behavior 
of our two bases in the new solvent : 

1 a s [A 1 H + ]y AlH + 

„ _ asH+[A 2 ]y A|z 

A ^" + -a s [A 2 H + ]yA2H+ {±i ' } 

Note that K aA H+ is known from the measurements in dilute water solution; we 
have denned the quantities in the equations in such a way that the K a 's are truly 
constants (at constant temperature and pressure), and all nonideal behavior 
resulting from changing the solvent is incorporated into the activities. Further- 
more, the concentrations [AJ, [A^H" 1 "], [A 2 ], [A 2 H + ] are directly measurable 
spectrophotometrically. If we divide Equation 3.31 by Equation 3.32, we obtain 
Equation 3.33: 

^a.h> = [A 1 ][A 2 H+] yAl r A2 H+ 

^* sB + [A 2 ][A 1 H + ]y A2 y AlH + 

In Equation 3.33 all quantities are known or measurable except K aA H+ and the 
ratio involving activity coefficients. 

132 Acids and Bases 

If it were possible to obtain the activity coefficients, Equation 3.33 would 
provide a way of obtaining K aA H + . In dilute aqueous solution the Debye-Hiickel 
theory, which is based on calculation of interionic forces in a medium containing 
dissociated ions, provides a method for estimating activity coefficients of ions. 18 
However, <even for ionic strengths as low as 0.01 there are significant deviations 
from the theory. 19 In the strong acid-water mixtures under consideration here, 
the concentration of ionic species (H 3 + , HS0 4 ~) is of necessity high; thus, 
even if the concentrations of the acids and bases under study are kept small (as they 
must in any case be in order for the spectrophotometric measurements to be 
reliable), the Debye-Hiickel theory is of no help. It is possible, however, to make 
the following qualitative argument. The departure of the activity coefficients from 
unity is the result of some nonideal behavior of the species involved. Departures 
from ideality therefore depend on the structure, and probably particularly on the 
charges, of the components. If A x and A 2 (and thus also A X H + and A 2 H + ) are 
sufficiently close in structure, one might guess that in a given solvent the ratio 
y Al /y AlH + would be approximately the same as yA 2 /yA 2 H + - If this were the case, 
the ratio of activity coefficients in Equation 3.33 would equal unity and the 
equation would become 

***** = [Ai][A a H + ] 

An experimental check on this assumption about activity coefficients is 
possible over a limited range of solvent acidity. If the composition of water- 
sulfuric acid mixtures is varied over the range in which all four species, A 1; A 2 , 
A 1 H + , and A 2 H + are present in appreciable concentration, then, since 
A'oa h + /^o a h + 1S (by definition) constant, a constant ratio [A 1 "|[A 2 H + ]/ 
[A 2 "| [A X H + ] implies that the assumption of the ratio of y's being constant is 
correct in this range of solvents. Experimentally, for bases that are substituted 
anilines this test is fairly successful, a result that supports the validity of the 
method. The question of how similar two compounds must be to be "sufficiently 
close in structure" will be considered later. 

Proceeding with our analysis, we find that if we can assume that Equation 
3.34 is valid, we know all quantities necessary to obtain K aA H + , the equilibrium 
constant for the second base. This base is now used in conjunction with a third 
base, A 3 , in a solvent system containing a larger proportion of strong acid, and the 
procedure is continued until equilibrium constants are established for the whole 
range of bases. 

Having found equilibrium constants for the series of bases, we may now use 
them to characterize the proton-donating ability of any mixture of sulfuric acid 
and water. Rearranging Equation 3.30, we have 

[AH + ] a SH+ y A 

K « I-.-, = (3-35) 

[A] a s y AH + 

The quantity on the right side of Equation 3.35 is defined as h ; it gives the 

18 See note 8, p. 127. 

19 Hammett, Physical Organic Chemistry, p. 192. 

Strengths of Weak Brons ted Bases 133 

desired information about proton-donating ability. 20 

u _ v f AH + ] 



Because of the magnitudes of the numbers involved, it is more convenient to use a 
logarithmic scale. A new quantity, H , is therefore defined by Equation 3.37. 

Ho = -log 10 h = -log 10 |jc B I^5p| (3.37) 


H = pK a + log 10 -j§- (3.38) 

[AH + ] 

H Q is known as the Hammett acidity function, and the series of substituted anilines 
used to establish the scale are called Hammett indicators. 

The procedure outlined above serves to define H for mixtures of water and 
various strong acids. Once H has been found for a number of different mixtures, 
one can obtain, by use of Equation 3.38, the pK a for bases other than those used 
in setting up the scale. All that is needed is a method of measuring the ratio 
[A|/[AH + ], together with the assumption that the ratio of the activity coefficients 
of the new base and its conjugate acid is the same as that of the indicator bases. 
Ranges of pK a values that have been found for various types of compounds are 
given in Table 3.2 in Section 3.4. Values for particular compounds may be found 
in the reviews by Arnett 21 and by Paul and Long, 22 where references to the origi- 
nal literature are given. 

Other Acidity Scales 

We return now briefly to the question of uniqueness of the H scale. We have seen 
that for the treatment to be successful, the different bases involved in determining 
the H scale, and also those bases that are to be investigated using the scale, must 
be of sufficiently similar structure that the activity coefficient ratio of Equation 
3.33 will be unity. It has become increasingly evident as data have accumulated 
that this requirement is more restricting than one might have hoped. Arnett 
and Mach, 23 using a set of JV, JV-dialkylnitroanilines and JV-alkylnitroanilines as 

20 The equations are usually written in such a way that Equation 3.35 comes out : 

[AH*] y A _ 

[A] y AH + 

This relationship results if the original acid dissociation is written : 

AH+ - — *- A + H + 

We have chosen the formulation of Equation 3.28 because it seems to be more consistent with our 
discussion in Section 3. 1 about the nature of Bronsted acid-base reactions. Since the quantity h is 
empirically determined and cannot be broken down experimentally into its component parts, it 
makes little difference in practice which derivation is used. For direct measurements of hydrogen 
ion activity coefficients in these solvents, see T. A. Modro, K. Yates, and J. Janata, J. Amer. Chem. 
Soc., 97, 1492 (1975). 

21 E. M. Arnett, Prog. Phys. Org. Chem., 1, 223 (1963). 

22 See note 17 (a), p. 130. 

23 E. M. Arnett and G. W. Mach, J. Amer. Chem. Soc, 86, 2671 (1964). 

134 Acids and Bases 

indicator bases, found an acidity scale, designated H'", which is different from 
H . A group of cyclic amines, indoles of general structure 1, were investigated by 
Hinman and Lang: 24 

these indicators gave still another acidity scale, denoted H„ which differed slightly 
from the H'" scale. Another scale, H A , was established by Yates, Stevens, and 
Katritzky 25 with a series of amides as indicators. Still another function, H R , is 
based on the behavior of triarylcarbinols. These substances, studied by Deno, 
Jaruzelski, and Schriesheim, 26 typically react according to Equation 3.39 to form 
water (which is converted partly to oxonium ion) and a carbocation. The H R 
function thus includes the activity of water in addition to the quantities of 

(C 6 H 5 ) 3 COH + SH + ^=± (C 8 H 5 ) a C + + S + H 2 (3.39) 

Equation 3.38. A slightly different function, H R , is derived from H R by subtrac- 
tion of the logarithm of water activity (Equation 3.40). 

H' R = H R - log a H2 o (3.40) 

Hydrocarbons containing carbon-carbon double bonds can be protonated in 
strong acid media, 27 and a scale designated H c appropriate to these substances 
has been established. 28 

Whereas sulfuric acid has been the most frequently used acid, acidity 
function scales have been set up for other strong acid mixtures. Of particular 
interest have been the superacid media usually prepared from mixtures of fluoro- 
sulfuric acid, HSO a F, with various Lewis acids such as SO a or SbF 5 . These 
media, the most acidic known, have made possible direct observation of highly 
reactive carbocations (see Section 5.4), and the protonation of extremely weak 
bases. 29 Figure 3.1 shows the behavior of some of the different acidity functions 
in sulfuric acid-water mixtures, Figure 3.2 gives the behavior of H in mixtures 
of water with various strong acids, and Figure 3.3 presents data for mixtures of 
HS0 3 FwithSbF 5 . 30 ' 31 

The proliferation of acidity scales, each with an equally sound basis and no 
one of which can claim to be any more fundamental or correct than any other, is 
a rather disappointing development. It nevertheless illustrates the point discussed 

24 R. L. Hinman and J. Lang, J. Amer. Chem. Soc, 86, 3796 (1964). 

25 K. Yates, J. B. Stevens, and A. R. Katritzky, Can. J. Chem., 42, 1957 (1964). 

28 N. C. Deno, J. J. Jaruzelski, and A. Schriesheim, J. Amer. Chem. Soc, 77, 3044 (1955). 

27 (a) H. H. Perkampus, Ado. Phys. Org. Chem., 4, 195 (1966) ; (b) D. M. Brouwer, E. L. Mackor, and 
C. MacLean, in Carbonium Ions, Vol. II, G. A. Olah and P. v. R. Schleyer, Eds., Wiley-Interscience, 
New York, 1970, p. 848. 

28 M. T. Reagan, J. Amer. CheTn. Soc, 91, 5506 (1969). 

29 G. A. Olah and J. Shen, J. Amer. Chem. Soc, 95, 3582 (1973). 

30 Superacid mixtures: R. J. Gillespie and T. E. Peel, J. Amer. Chem. Soc, 95, 5173 (1973). 

31 For a more complete discussion of the various acidity functions, see Hammett, Physical Organic 
Chemistry, chapter 9. 

Strengths of Weak Brans ted Bases 135 

Negative of acidity 
function value 






/ H'" H o 



fflc / J 



/ i 










r /A 


- /fs 









Weight percent H 2 S0 4 

Figure 3.1 Values of various acidity functions in mixtures of water and sulfuric acid. Data 
for H , H", Hj, and H' n are from L. P. Hammett, Physical Organic Chemistry, 2nd 
ed., McGraw-Hill, New York, 1970, p. 271; data for H c are from M. T. 
Reagan, J. Amer. Chem. Soc, 91,5506 (1969). Adapted by permission of McGraw- 

in Section 2.4, that the details of solvent-solute interaction is an area of chemistry 
where much fundamental work remains to be done. 

In principle, the acidity scale concept could be a very useful one in the 
investigation of reaction mechanisms. The logarithm of the rate of a reaction 
suspected of proceeding by way of the conjugate acid of the substrate can be 
measured in media of different acidity and plotted against H Q or some other 
appropriate acidity function. A linear correlation would then be good evidence 
that the conjugate acid was indeed involved. A number of such studies have been 
done, often successfully, but it is becoming increasingly clear that the results of 
such investigations must be interpreted with caution unless the substrate is 
structurally very closely related to the indicator bases used in setting up the 
acidity scale. The generality of the method is thus severely reduced. 

Measurements in Nonaqueous Solvents 

An alternative to the acidity function method for making measurements with 
weak base-strong acid conjugate pairs is to choose a pure solvent that is more 

136 Acids and Bases 


1 1 1 1 

I 1 1 l 



HC10 4 


S\Vr ~~ 

H 6 

/ HNO3 

L^^^ H3PO4- 


l/yViC\ y^^f* 



^T 1 1 1 

1 1 1 1 

H 2 


0.4 0.6 

Mole fraction HA 



Figure 3.2 The H acidity function for mixtures of water with various acids. From G. A. 
Olah, Friedel-Crafts Chemistry, Wiley, New York, 1973, p. 368. Copyright © 1973, 
John Wiley & Sons. Reprinted by permission of John Wiley & Sons, Inc. 


10 12 14 16 1£ 
Weight percent SbF 5 in HSO3F 


Figure 3.3 The H acidity function for mixtures of SbF 5 and HSO3F. Data are from 
R.J. Gillespie and T. E. Peel, J. Amer. Chem. Soc, 95, 5173 (1973). 

Strengths of Weak Bronsted Bases 137 

acidic and less basic than water. The convenient glass electrode and pH meter 
can often be used successfully in nonaqueous media as long as the reference 
solution used for standardization of the meter employs the same solvent. 32 The pH 
values determined, however, will be characteristic of the particular solvent 
system and will not be directly transferable to the water scale. Acetic acid has 
been used as a solvent for determining relative acidities of strong acids. The 
mineral acids HC10 4 , HBr, and HC1, which all behave as strong acids in water, 
are found to differ significantly in acidity. 33 The use of a single solvent avoids 
the difficulties inherent in making comparisons between different solvent systems, 
as is done in work with acid-water mixtures, but at the same time the range of 
acidities that can be considered is more limited. Furthermore, complications arise 
if the dielectric constant is low (acetic acid e = 6.2 compared with e = 78.5 for 
water) ; 34 there is then extensive ion pairing. 35 

Acid-base reactions have been studied in other nonaqueous solvents, such 
as acetonitrile, methanol, ethanol, dimethylformamide, and dimethylsulfoxide. 36 
When acids whose strength can also be measured in water are studied in these 
solvents, the constants obtained are generally quite different, as would be 
expected from the widely different dielectric constants and varying solvating 
power of the different solvents. However, if the relative acidities of two compounds 
in water and another solvent are compared, the difference in pK a between the 
two acids is usually approximately independent of solvent (within about one pK 
unit) as long as the acids being compared are of the same charge type and are very similar 
in structure. 37 For example, two particular substituted carboxylic acids may be 
expected to differ in acidity by roughly the same amount in dimethylformamide 
as they do in water, even though the values of pK a found in the two solvents will 
be quite different; 38 but no such correlation would be expected if the comparison 
were between a carboxylic acid and an anilinium ion (different charge type) or 
between a carboxylic acid and a phenol (same charge type but different structural 
type). It should be noted, however, that there appear to be exceptions even to 
this rough rule-of-thumb. 39 

Other methods of making quantitative measurements on weak bases, less 

32 (a) Hammett, Physical Organic Chemistry, p. 265; (b) J. F. Coetzee, Prog. Phys. Org. Chem., 4, 64 
(1967); (c) I. M. Kolthoff and T. B. Reddy, Inorg. Chem., 1, 189 (1962); (d) C. D. Ritchie and R. E. 
Uschold, J. Am. Chem. Soc, 89, 1721, 2752 (1967). 

33 R. P. Bell, The Proton in Chemistry, 2nd ed., Cornell University Press, Ithaca, N.Y., 1973, p. 46. 
3i See Table 2.1 1 (Section 2.4). 

35 In acetic acid it is possible to measure separately the equilibrium constant of proton transfer to 
form an ion pair and the constant for dissociation of ion pairs to form free ions. [I. M. Kolthoff and 
S. Bruckenstein, J. Amer. Chem. Soc, 78, 1 (1956); S. Bruckenstein and I. M. Kolthoff, J. Amer. 
Chem. Soc, 78, 10 (1956)]. G. W. Ceska and E. Grunwald, J. Amer. Chem. Soc, 89, 1371, 1377 (1967) 
applied this technique to a number of substituted anilines and concluded that the equilibrium 
constant of the ionization step, rather than the overall acid dissociation constant, is the quantity 
that should be considered in discussions of effects of structural changes on acidity. 

36 (a) M. M. Davis, Acid-Base Behavior in Aprotic Organic Solvents, Nat. Bur. Stds. Monograph 105, 
1968; (b) I. M. Kolthoff, M. K. Chantooni, Jr., and S. Bhowmik, J. Amer. Chem. Soc, 90, 23 (1968); 
(c) J. F. Coetzee and G. R. Padmanabhan, J. Amer. Chem. Soc, 87, 5005 (1965); (d) B. W. Clare, 
D. Cook, E. C. F. Ko, Y. C. Mac, and A.J. Parker, J. Amer. Chem. Soc, 88, 1911 (1966); (e) C. D. 
Ritchie and G. H. Megerle, J. Amer. Chem. Soc, 89, 1447, 1452 (1967). 

37 Bell, The Proton in Chemistry, p. 56; see also footnotes 36 (c) and 36 (d). 

38 See note 36 (d). 

39 See notes 36 (c) and 36 (d). 

138 Acids and Bases 

commonly used than those described here, have been reviewed by Arnett. 40 The 
reader is referred to that article for further information. 

Heats of Protonation 

Arnett has summarized the difficulties inherent in the currently available methods 
of dealing with weak bases in solution. 41 He notes, for example, that the pK a 
values given in the literature for ketones, a very important class of compounds 
that undergo a variety of acid-catalyzed reactions, vary over an unacceptably 
wide range. The variations arise not only from the activity coefficient problems 
mentioned above, but also from such practical problems as the effect of differing 
media on position of the absorption peaks in the ultraviolet spectrum. Arnett has 
proposed an alternative to the acidity function method for finding pK a values for 
weak bases. 42 He has measured the heats of protonation of a number of weak 
bases in FS0 3 H, in which most of the bases of interest are known from freezing- 
point depression, electrical conductivity, ultraviolet spectroscopy, and nuclear 
magnetic resonance measurements to be completely protonated. He finds a good 
correlation of these heats of protonation with recorded pK a values for series like 
the original Hammett nitroaniline indicators that are well behaved in acidity 
function experiments. The heat of protonation method has the advantage over 
the acidity function procedure that all measurements are made in the same 
solvent; Arnett proposes that the pK a values obtained for ketones by the heat of 
protonation procedure are more reliable than the older acidity function data. 


The earliest attempts to evaluate quantitatively the acidity of very weak acids 
were contemporaneous with Hammett's pioneering work with weak bases. 
Conant and Wheland 44 published the first investigations in this area in 1932, 
and their results were extended and refined a few years later by McEwen. 45, 46 
Since organometallic compounds of the alkali metals behave chemically like 
carbanions, these investigators reasoned that if an organosodium or organo- 
potassium compound, RiM, were mixed with a hydrocarbon, R 2 H, the equili- 
brium constant for the resulting reaction, Equation 3.41, would be a measure 
of the relative acidities of the two hydrocarbons R^H and R 2 H. 

R X M + R 2 H ^^ R^H + R 2 M (3.41) 

The equilibrium constant for Equation 3.41 does not measure directly the 
pK a difference between RjH and R 2 H, because the pK a is defined in terms ofthlT 

40 See note 21, p. 133. 

41 (a) E. M. Arnett, R. P. Quirk, and J. J. Burke, J. Amer. Chem. Soc, 92, 1260 (1970); (b) E. M. 
Arnett, R. P. Quirk, and J. W. Larsen, ibid., p. 3977. 

42 See note 41. 

43 For reviews see: (a) A. Streitwieser, Jr., and J. H. Hammons, Prog. Phys. Org. Chem., 3, 41 (1965) ; 
(b) H. Fischer and D. Rewicki, Prog, in Org. Chem. (Cook and Carruthers, Eds.), 7, 116 (1968); (c) 
J. R. Jones, The lonisation of Carbon Acids, Academic Press, London, 1973. 

44 J. B. Conant and G. W. Wheland, J. Amer. Chem. Soc, 54, 1212 (1932). 

45 W. K. McEwen, J. Amer. Chem. Soc, 58, 1 124 (1936). 

46 See D. J. Cram, Fundamentals ofCarbanion Chemistry, Academic Press, New York, 1965, for discussion 
of these results. 

Strengths of Weak Bronsted Acids 139 

dissociated ions (Equation 3.42). Ether and benzene were used as solvents, and 
more recent evidence 47 indicates that the organometallics probably exist almost 

Kr + R 2 H ^=± RjH + R 2 " (3.42) 

entirely as ion pairs in nonpolar solvents. Conant and Wheland were aware of 
the dissociation problem; on the basis of some earlier conductivity measure- 
ments, 48 they assumed that the dissociation constants for the various organo- 
metallics would be about the same, and that equilibrium constants for Reaction 
3.41 would give reasonably accurate measures of pK a differences. On the basis 
of this assumption, McEwen determined pK a values for a number of carbon 
acids ; he was also able to relate the acidities of the carbon acids studied with 
those of several weak oxygen acids 49 by studying equilibria such as Equation 3.43. 

RjM + R 2 OH ^=± R^ + RjOM (3.43) 

Further experiments designed to elucidate acid-base relationships among 
weak acids have been carried out more recently by Streitwieser and his co- 
workers. 50 They studied the equilibrium shown in Equation 3.44, with cyclo- 
hexylamine as solvent and lithium or cesium cyclohexylamide as base. Using 
spectrophotometric methods to evaluate the position of the equilibrium, they 
were able to find relative pK a values for a number of hydrocarbons in which the 
conjugate base is, in most cases, a conjugated aromatic anion. In order to attach 

RH + CeHnNH"]^ ^=± R~M + + CeHnNHj - , 

M + = Li + or Cs + { > 

definite pK a values to the results, these authors took as a reference point the 
value of pK a = 18.5 reported by Langford and Burwell 51 for 9-phenylfluorene (2). 
This value was determined in a solvent consisting of a mixture of water and 

O O 

sulfolane (3) using the indicator methods described below. When McEwen's 
results are placed on a scale with 9-phenylfluorene having a pK a of 18.5, the 
agreement with Streitwieser's results is reasonably good up to pK a about 31 
(triphenymethane) . 

47 T. E. Hogen-Esch and J. Smid, J. Amer. Chem. Soc, 87, 669 (1965). 

48 K. Ziegler and H. Wollschitt, Ann., 479, 123 (1930). 

49 We denote acids in which the acidic proton is attached to carbon as carbon acids, those with the 
proton attached to oxygen as oxygen acids, and so forth for acids of other types. 

60 See, for example: (a) A. Streitwieser, Jr., J. I. Brauman, J. H. Hammons, and A. H. Pudjaatmaka, 
J. Amer. Chem. Soc, 87, 384 (1965); (b) A. Streitwieser, Jr., J. H. Hammons, E. Ciuffarin, and J. I. 
Brauman, J. Amer. Chem. Soc, 89, 59 (1967); (c) A. Streitwieser, Jr., E. Ciuffarin, and J. H. Ham- 
mons, J. Amer. Chem. Soc, 89, 63 (1967) ; (d) A. Streitwieser, Jr., and D. M. E. Reuben, J. Amer. Chem. 
Soc, 93, 1794 (1971); (e) A. Streitwieser, Jr., J. R. Murdoch, G. Hafelinger, and C. J. Chang, 
J. Amer. Chem. Soc, 95, 4248 (1973); (f) Acidities found by these methods are ion pair acidities and 
do not represent dissociation to free ions. See A. Streitwieser, Jr., and S. P. Ewing, J. Amer. Chem. 
Soc, 97, 190 (1975). 
51 C. H. Langford and R. L. Burwell, Jr., J. Amer. Chem. Soc, 82, 1503 (1960). 

140 Acids and Bases 

H _ Acidity Functions 

Others have approached the problem from a slightly different viewpoint. This 
alternative method is an extension to basic media of the acidity function tech- 
niques discussed in the previous section. 32 Solvents containing dimethylsulfoxide 
mixed with water, methanol, or ethanol and a base (potassium hydroxide, 
methoxide, or ethoxide) have been most commonly used, although other sub- 
stances, such as sulfolane, have also been employed. Spectrophotpmetric measure- 
ments of concentrations of acid and conjugate base forms of an appropriate 
series of indicators establish an acidity function, called H_ t for mixtures contain- 
ing varying proportions of the solvents. The inidcators are usually substituted 
anilines, the same class of compound as serves to establish the H scale in acidic 
mixtures; here, however, the anilines are acting as acids instead of as bases 
(Equation 3.45). 

ArNH 2 + S- ;=^ ArNH" + SH (3.45) 

Once established, the H_ scale is used to find pK a values for weak acids. A 
number of measurements have been made by various groups. 53-57 The results 
obtained at first appeared to disagree with Streitwieser's, but revision of values 
for some compounds on the basis of further measurements brought the results 
of the two methods into fairly good agreement. At the same time, however, it 
became clear that the problems discussed in the previous sections relating to the 
different behavior of substances of different structural type also apply to the H_ 
scale work. 58 The activity coefficient ratio evidently is not the same for carbon 
acids as for the nitrogen acids used to establish the scale. 59 Thus the pK a values 
found by these methods, while probably internally consistent for similar com- 
pounds, are not on a firm basis with respect to their absolute relationship to the 
water scale. 

Arnett and his collaborators have extended the heat of proto nation concept 
(Section 3.2) to weak acids by measuring heats of deprotonation, Ai/ D , of weak 
acids in dimethylsulfoxide containing the dimethylsulfoxide conjugate base, 
H 3 CSOCH 2 ~. 60 The results correlate well with p^ a values of the amines used 

52 For reviews, see: (a) K. Bowden, Chem. Rev., 66, 119 (1966); (b) C. H. Rochester, Quart. Rev. 
(London), 20, 511 (1966); (c) J. R.Jones, Prog. Phys. Org. Chem., 9, 241 (1972). 

53 (a) See note 51, p. 139; (b) R. Stewart, J. P. O'Donnell, D. J. Cram, and B. Rickborn, Tetra- 
hedron, 18, 917 (1962). 

64 E. C. Steiner and J. M. Gilbert, J. Amer. Chem. Soc., 87, 382 (1965). ___ 

55 E. C. Steiner and J. D. Starkey, J. Amer. Chem. Soc, 89, 2751 (1967). 

56 (a) C. D. Ritchie and R. E. Uschold, J. Amer. Chem. Soc., 89, 2752 (1967); (b) C. D. Ritchie and 
R. E. Uschold, J. Amer. Chem. Soc., 90, 2821 (1968); (c) M. M. Kreevoy and E. H. Baughman, J. 
Amer. Chem. Soc, 95, 8178 (1973). 

57 R. Kuhn and D. Rewicki, Ann., 704, 9 (1967); 706, 250 (1967). 

58 See note 55, 56. 

59 //_ is denned by the equation 


H- = -log la H 

(The derivation is analogous to that given in Section 3.3 for H a .) The method will be successful only 
if the activity coefficient ratio-is the same for all acids investigated as it is for the acids used as 
indicators. Since this requirement is evidently not met, it may not be possible to establish a unique 
solution pK scale for weak acids by using H- . 

60 E. M. Arnett, T. Q.. Moriarity, L. E. Small, J. P. Rudolph, and R. P. Quirk, J. Amer. Chem. Soc, 
95, 1492 (1973). 

Strengths of Weak Brensted Acids 141 

to set up the H_ scale. Furthermore, the slope of the line correlating AH D with 
pK a is nearly the same as the slope of the correlation between heat of protonation 
in HSO3F and pK a for the weak bases. This latter result increases confidence in 
the heat of protonation method as a valid way of measuring acid strength over a 
very wide range. 

The Bronsted Catalysis Law 

The experimental work described up to this point has been limited to those carbon 
acids that are more acidic than pK a about 33. Most of these compounds owe their 
acidity to some structural feature that allows the negative charge of the conjugate 
base to be delocalized. We turn now to a brief discussion of a method by which 
measurements can be extended, at least in a semiquantitative way, into the region 
of still weaker acids. 

In the acid-base reaction 3.46, it would seem reasonable that if the rate 
(k x ) at which a proton is removed by a particular base B n + were compared for 

AH m + + B n+ , a*" 1 - 1 )- 1 - + BH (n + 1 > + (3.46) 

various acids AH m + , the base might remove the proton more rapidly from the 
stronger acids. Relationships between rate of an acid-base reaction and an 
equilibrium have been observed in many cases, and are frequently found to obey 
an equation known as the Bronsted catalysis law: 

k = CK a " (3.47) 


log k = a log K a + log C (3.48) 

where k is the rate constant for the reaction, K a is the acid dissociation constant, 
and C is a constant of proportionality. If such a relationship could be shown to 
hold between acid strength and rate of transfer of the proton to some particular 
base, a means would be available to find equilibrium acidities through kinetic 

An appreciation for the form of the catalysis law may be gained by con- 
sideration of the energy relationships involved. In Figure 3.4 is plotted schematic- 
ally the free energy (AG) vs. reaction coordinate for proton transfer reactions 
between a series of acids, A n H, and a single base, B. The differing pK 9 values 
of the acids are reflected in the different free-energy changes in going from re-^ 
actants to products, AG °, AG2, •••, AG°,..., and are caused by structural 
differences among the acids A n H and among the conjugate bases A n ~ . If one * 
assumes that the factors that cause these free-energy differences also cause the 
differences in the transition-state free energies, it is reasonable to suppose as a 
first approximation that the activation free energy for proton transfer, AG*, 
might be related to the AG° in a linear fashion. This relationship is expressed in 
Equation 3.49, where we have arbitrarily chosen the first acid, AxH, as a reference 
compound for the series. 

AGl - AG* = a(AG° - AG°) (3.49) 

We have from equilibrium thermodynamics Relation 3.50 between standard 
free-energy change, AG , and equilibrium constant, K, and from transition-state 

142 Acids and Bases 


t- AT + BH + 

A 3 ~ + BH + 

A 2 ~ + BH + 

Ar + BH + 

— , — AG 4 

AG* AG^ AG* 3 AG* 4 




x = x = 1 

Reaction coordinate 

Figure 3.4 Hypothetical free energy vs. reaction coordinate curves for proton transfer from 

four different acids, A^, A 2 H, A 3 H, A 4 H, to base B. The Brensted catalysis law 

presumes that the effects of structural change on the transition-state free energies 

will be some constant fraction of their effects on the overall free-energy changes. 

theory Equation 3.51 (compare Equation 2.60, p. 100), where AG* is the free 
energy of activation, k is the rate constant, k is the Boltzmann constant, and h is 
Planck's constant. 

-AG° = 2.303/2 T log K 

-AG* = 2.303(RT\ogk - RT\ogkT/h) 


By substituting Equations 3.50 and 3.51 in Equation 3.49 we obtain Equation 

log k n - log * x = a(log K n - log K,) (3.52) 

The acid A^ serves as our standard for comparison of all the others, so that log k x 
and log K 1 are constants for a series of measurements ; therefore we can write 
Equation 3.53 (where C is a constant), which is equivalent to Equation 3.48 and, 
when written in exponential form, to Equation 3.47. 61 

log k n = a log K n + log C 


61 An alternative way of expressing the argument presented here is to assume that AC is some 
unspecified function of AG", 

AG* =/(AG°) 

and to expand that function in a Taylor series about the reference point AGJ : 

AG* = constant + a(AG° - AG°) + a'(AG° - AG°) 2 + a"(AG° - AG°) 3 + . . . 


Strengths of Weak Bronsted Acids 143 

The Bronsted law is a linear fr ee-energy r elationship,, similar in form to the 
Hammett and Taft correlations discussed in Section 2.2. We emphasize that the 
connection between rate and equilibrium expressed by Equation 3.48 is in no 
sense predicted by or derived from the laws of equilibrium thermodynamics. 
The relationship is an empirical one that must be verified experimentally in each 
particular case, and that is subject to severe limitations. We have assumed in 
drawing Figure 3.4 and in making the arguments we have presented rationalizing 
the catalysis law that the position of the transition state along the reaction co- 
ordinate will not change as the acid strengths change. We have seen in Section 
2.6, where we considered the Hammond postulate, that this assumption is 
unlikely to be true if we make more than a rather small change in the reactant-to- 
product free-energy difference. As a result, we can expect that over a wide range 
of acidities a will not be a constant. It should be close to unity for a very endo- 
thermic process of type 3.46 (the transition state closely resembles A (m_1>+ + 
BH (n + 1)+ and the entire AG° differences show up in AG*), and close to zero for a 
very exothermic process (the transition state closely resembles AH m+ + B n + and 
none of the AG° differences show up in AG*) . For carbon acids, a changes relatively 
slowly with changing equilibrium constant; 62 we must nevertheless proceed 
cautiously if we wish to use the catalysis law to assist us in estimating equilibrium 
acidities, and we expect difficulties if the range of equilibrium constants is large. 
We shall return to consider these points in more detail in Section 8.1. 

Kinetic Acidity 

The Bronsted catalysis law can be applied to the problem of determination of 
acidity of very weak acids in the following way. First, a suitable base is chosen; 
the base must be sufficiently strong to remove protons from the carbon acids in 
question at a measurable rate. The acids to be investigated are then prepared 
with deuterium or tritium substituted for hydrogen, and the rate of exchange of 
the isotopic label out of the carbon acid in the presence of the base is measured. 

Experiments of this type have been carried out with weak acids by various 
workers. 63 " 66 In order to use the kinetic data to obtain information about equili- 
bria, it is clearly necessary to know whether the catalysis law (Equation 3.48) 
holds for the system under study and, if it does, what the value of the constant a is. 

The approximation involved in stating the catalysis law is equivalent to dropping terms of order 
higher than the first in the power-series expansion : 

AG* « constant + a(AG° - AG°) 

This expression leads to Equation 3.53. 

62 M. Eigen, Angew. Chem. Int. Ed., 3, 1 (1964). 

63 R. G. Pearson and R. L. Dillon, J. Amer. Chem. Soc, 75, 2439 (1953). 

64 A. I. Shatenshtein, Adv. Phys. Org. Chem., 1, 155 (1963). 

65 See for example: (a) A. Streitwieser, Jr., R. A. Caldwell, R. G. Lawler, and G. R. Ziegler, J. 
Amer. Chem. Soc, 87, 5399 (1965); (b) A. Streitwieser, Jr., W. B. Hollyhead, G. Sonnichsen, A. H. 
Pudjaatmaka, C. J. Chang, and T. L. Kruger, J. Amer. Chem. Soc., 93, 5096 (1971); (c) A. Streit- 
wieser, Jr., and W. C. Langworthy, J. Amer. Chem. Soc, 85, 1757, (1963); (d) A. Streitwieser, Jr., 
R. A. Caldwell, and M. R. Granger, J. Amer. Chem. Soc, 86, 3578 (1964); (e) A. Streitwieser, Jr., 
and D. Holtz, J. Amer. Chem. Soc, 89, 692 (1967); (f) A. Streitwieser, Jr., A. P. Marchand, and A. H. 
Pudjaatmaka, J. Amer. Chem. Soc, 89, 693 (1967); (g) A. Streitwieser, Jr., and F. Mares, J. Amer. 
Chem. Soc, 90, 644, 2444 (1968). See also references cited in Table 3.1. 

66 R. E. Dessy, Y. Okuzumi, and A. Chen, J. Amer. Chem. Soc, 84, 2899 (1962). 

144 Acids and Bases 

Thus it is not possible to use the method to determine pK's without first making 
measurements on a number of compounds of known acid dissociation constant. 
Pearson and Dillon 67 collected data for exchange rates and equilibrium constants 
of a number of carbon acids in the pK a range 4—20. These compounds all con- 
tained electron-withdrawing groups (carbonyl, nitro, cyano, trinuoromethyl, 
etc.) ; the correlation of rate and pK a was only rough. The problem is presumably 
one of differences in behavior arising from variations in structure. Shatenshtein 
measured exchange rates of a number of carbon acids in liquid ammonia ; 68 his 
work demonstrated clearly the acidic properties of even saturated hydrocarbons, 
and allowed a qualitative measure of relative acidity of various types of carbon- 
hydrogen bonds. 

Streitwieser and co-workers have extended their measurements of equili- 
brium acidities in cyclohexylamine to determination of exchange rates. 69 They 
have made quantitative correlations between exchange rate and the pK a 's 
determined by equilibrium methods for various aromatic compounds and have 
thus been able to verify that the Bronsted relation holds for these substances and 
to find Bronsted coefficients a for various types of compounds. A third method 
for evaluating pK a of weak acids, which has been used by Applequist 70 and by 
Dessy, 71 involves the study of exchange reactions of organometallic compounds 
(Equations 3.54 and 3.55). 

RJ + R 2 Li ^^ RjLi + R 2 I (3.54) 

RiHg + R 2 Li ^^ R x Li + R 2 Hg (3.55) 

The MSAD Scale 

In 1965, Cram established a scale of acidities reaching to the very weak carbon 
acids by combining data from the various methods. 72 The basis of the scale is the 
value of pK a = 18.5 found by Langford and Burwell for 9-phenylfluorene (2), 73 
and it includes the equilibrium measurements of Streitwieser and others up to 
pK a 33. Table 3.1 records some selected equilibrium values in this range. Beyond 
pK a 33, direct equilibrium methods fail and only the kinetic and organometallic 
techniques can be used. Cram compared Streitwieser' s exchange-rate measure- 
ments for triphenylmethane and for cumene (4), 74 

CH 3 


67 See note 63, p. 143. 

68 See note 64, p. 143. 

69 See note 65, p. 143. 

70 D. E. Applequist and D. F. O'Brien, J. Amer. Chem. Soc., 85, 743 (1963). 

71 (a) R. M. Salinger and R. E. Dessy, Tetrahedron Lett., 729 (1963) ; (b) R. E. Dessy, W. Kitching, 
T. Psarras, R. Salinger, A. Chen, and T. Chivers, J. Amer. Chem. Soc, 88, 460 (1966). 

72 D. J. Cram, Fundamentals of Carbanion Chemistry, Academic Press, New York, 1965, p. 19. 

73 See note 51, p. 139. 

74 See note 65 (d), p. 143. 

Strengths of Weak Bronsted Acids 145 

with measurements of McEwen on organometallic equilibria. 75 McE wen's pK a 
values for the two compounds differ by about 4.5 units, while Streitwieser's 
exchange rates differ by about five powers often. The Bronsted a calculated from 
these results is 1.1. Benzene has an exchange rate close to that of cumene, and 
toluene exchanges somewhat more rapidly ; these compounds would fit into the 
scale at about pK a 36 and 34, respectively. Cram then extended the scale to still 
weaker acids for which exchange rates were known from Streitwieser's work, 76 
and concluded that cyclopentane and cyclohexane had pK a 's of about 43 and 44 
(relative to triphenylmethane = 31.5). Cram then noted that the equilibrium 
measurements of Applequist on reaction 3.54 and of Dessy on Reaction 3.55 
correlated well with the scale, and was therefore able to assign pK a 's to several 
other compounds. The final list of acidities Cram named the MSAD scale ; it 
served for a number of years as the best available guide to pK a 's of the very weak 
acids. 77 

The breakdown of the MSAD scale In 1971, Streitwieser and his 
collaborators reported new Bronsted catalysis law correlations for exchange rates 
of substituted fluorenes and of polyarylmethanes in methanol-sodium methoxide. 
These compounds all have pK a 's in the range that can be determined by equili- 
brium methods; the values of a were 0.37 for the fluorenes and 0.58 for the poly- 
arylmethanes. 78 Both correlations are accurately linear over ranges of nearly 
ten pK units, and are clearly not two parts of a single line of varying slope. The 
authors proposed that the difference in slope results from the different position of 
the transition state along the reaction coordinate for proton transfer in the two 
series. The fluorenes, which have the extra anion-stabilizing influence of a 
cyclopentadienide ring (Section 1.5, p. 39), reach the transition state relatively 
early, and the polyarylmethanes, somewhat less effective in anion stabilization, 
reach the transition state only when proton transfer is further advanced. 

Then, in 1973, Streitwieser reported that the polyarylmethane exchange 
rates measured in cyclohexylamine-cyclohexylamide correlate with equilibrium 
pK values with a = 0.31. 79 Apparently, when the proton is removed by cyclo- 
hexylamide, the polyarylmethanes have early transition states, just as the 
fluorenes did for proton removal by the weaker base methoxide. 80 A short extra- 
polation of the Bransted correlation led to a pK a for toluene of 40.9, about seven 
units higher than the value assigned in the MSAD scale. Furthermore, if we 

75 See note 45, p. 138. 

76 (a) See note 65 (d), p. 143; (b) A. Streitwieser, Jr., W. R. Young, and R. A. Caldwell, J. Amer. 
Chem. Soc, 91, 527 (1969); (c) A. Streitwieser, Jr., R. A. Caldwell, and W. R. Young, J. Amer. Chem. 
Soc, 91, 529 (1969). 

77 MSAD stands for McEwen, Streitwieser, Applequist, and Dessy. 

78 (a) See note 65 (b), p. 143; (b) A. Streitwieser, Jr., W. B. Hollyhead, A. H. Pudjaatmaka, P. H. 
Owens, T. L. Kruger, P. A. Rubenstein, R. A. MacQuarrie, M. L. Brokaw, W. K. C. Chu, and 
H. M. Niemeyer, J. Amer. Chem. Soc, 93, 5088 (1971). 

79 A. Streitwieser, Jr., M. R. Granger, F. Mares, and R. A. Wolf,./. Amer. Chem. Soc, 95, 4257 (1973). 

80 The situation is complicated by the finding of a large isotope effect, k K lk D =11, indicating a 
transition state symmetrical with respect to the position of the proton between the acid and the 
base. Streitwieser proposed that at the transition state the inicpient anion is still pyramidal, so that 
little charge can be delocalized onto the aryl rings. At the transition state, most of the negative charge 
therefore still resides on the base, hence a is low even though proton transfer is further advanced. 

146 Acids and Bases 

Table 3.1 Approximate pK a Values of Weak Hydrocarbon Acids 1 


(Acidic H indicated) 


Method 3 


H H 


r ^ ?v - 












L&B, S 2 , 
R&U, S&i 





<f> H 

19.9 eq, H_ S 2 , R&U, 


23.2" eq 

22.7 eq, //_ S 2 , R&U, 


24 c eq 


1,1, 3-Triphenylpropene 


26.6 eq 

</> H 






d 2 , blj 



^ 2 CH 2 











<i> — CH3 



Si, Se 


<j>— H 



s 9 


H 2 G^GH 2 





</>— C— H 
N CH 3 




Strengths of Weak Bronsted Acids 147 

Table 3.1 {Continued) 


(Acidic H indicated) pK a 2 Method 3 References 4 

Tripticene V 49.7 ex S^Ss 

Cyclopropane / \ 46 ex S 4 

Methane CH 4 48 ex Sn 

Triphenylcyclopropene / \ 50 e B&B 


50 ex S 4 

Cyclopentane \ / 51 ex S 4 

Cyclohexane 52 

1 Values up to pK a 33 (diphenylmethane) are those reported for equilibrium methods, and were 
measured either directly using the //_ acidity function or by comparing acidity with 9-phenyl- 
fluorene. Above pK a 33, we assume a = 0.3 for toluene, cumene, and tripticene, and base other 
values on pK a = 43 for benzene and an assumed a of 0.9. The scale is based on the Langford and 
Burwell value of 18.5 for pK a of 9-phenylfluorene. 

2 Rounded to three significant figures. Although four significant figures are given in some of the 
original papers cited, a comprehensive scale of greater precision does not appear justified at this time. 

3 Method code: 

eq = equilibrium methods related to the water pK scale by direct or indirect comparison with 

ex = H— D or H— T exchange rate. 
H - = equilibrium measurement using //_ acidity function. 
* References : 
B&B: R. Breslow and K. Balasubramanian, J. Amer. Chem. Soc, 91, 5182 (1969). 

D: R. E. Dessy, Y. Okazumi, and A. Chen, J. Amer. Chem. Soc, 84, 2899 (1962). 
D&R: H.J. Dauben and M. R. Rifi, J. Amer. Chem. Soc, 85, 3041 (1963). 
L&B: C. H. Langford and R. L. Burwell, Jr., J. Amer. Chem. Soc, 82, 1503 (1960). 
R&U: C. D. Ritchie and R. E. Uschold, J. Amer. Chem. Soc, 89, 2752 (1967). 
S&S: E. C. Steiner and J. D. Starkey, J. Amer. Chem. Soc, 89, 2751 (1967); E. C. Steiner and J. M. 
Gilbert, J. Amer. Chem. Soc, 87, 382 (1965). 
W&H: N. S. Wooding and W. E. C. Higginson, J. Chem. Soc, 774, (1952). 

Si: A. Streitwieser, Jr., R. A. Caldwell, and M. R. Granger, J. Amer. Chem. Soc, 86, 3578 (1964). 
S 2 : A. Streitwieser, Jr., E. Ciuffarin, and J. H. Hammons, J. Amer. Chem. Soc, 89, 63 (1967). 

148 Acids and Bases 

assume that the line continues with slope a = 0.3, we find pK a 48 for cumene, 
over ten units higher than the MSAD value. The MSAD scale, based on what is 
evidently much too high a value for a above pK a 31, is therefore in error above 
that point. 

If we accept Streitwieser's results, we are faced with a dilemma for acids 
weaker than cumene. There is an indication from results of exchange rates in 
fluorobenzenes that when the anion is not delocalized, a will be roughly 0.9; 
these measurements yield pK a = 43 for benzene. 81 If we assume that a will 
continue to be 0.9 for the weaker saturated carbon acids, which also yield non- 
delocalized anions, we can revise the MSAD scale for these substances. In Table 
3.1 we list equilibrium pK a values for some selected compounds. These numbers 
correspond closely to Cram's scale below pK 31, with some modifications to take 
account of more recent data ; they should give reasonably reliable relative acidities 
up to toluene. One must, nevertheless, always remember that they are tied to the 
water pK scale through the value listed for 9-phenylfluorene. This pK is deter- 
mined by acidity function methods and is subject to all the uncertainties attend- 
ant on those measurements. 82 Beyond pK a 41, the scale is based on pK a = 43 
for benzene, assuming a = 0.9. The results of Dessy and of Applequist do not 
correlate as well with the revised scale as they did with MSAD, and no attempt 
has been made to include them. It must be emphasized strongly that the values 
listed in the high pK a range are approximate estimates only, and likely to be 
changed, perhaps drastically, by the results of further experimental work. It is 
also important to realize that even at the low end of the scale, values represent 
dissociation to ion pairs and depend on the cation and on solution phenomena. 
Relative acidities reported in different solvent systems may differ substantially. 83 

81 A. Streitwieser, Jr., P. J. Scannon, and H. M. Niemeyer, J. Amer. Chem. Soc, 94, 7936 (1972). 

82 It should be noted that measurements reported by Ritchie and Uschold (notes 56 (a), 56 (b), 
p. 140) yielded a value of 16.4 for the pK a of 9-phenylfluorene; if this value is used instead of the earlier 
one of Langford and Burwell, the entire scale of Table 3.1 is lowered by two pK units. The revision 
has not been made here, as it seems likely that future work will result in further changes. See also 
note 55, p. 140. 

83 (a) F. G. Bordwell and W. S. Matthews, J. Amer. Chem. Soc, 96, 1214 (1974); (b) F. G. Bordwell, 
W. S. Matthews, and N. R. Vanier, J. Amer. Chem. Soc, 97, 442 (1975). 

S 3 : A. Streitwieser, Jr., W. R. Young, and R. A. Caldwell, J. Amer. Chem. Soc, 91, 527 (1969). 
S 4 : A. Streitwieser, Jr., R. A. Caldwell, and W. R. Young, J. Amer. Chem. Soc, 91, 529 (1969). 
S 5 : A. Streitwieser, Jr., and G. R. Ziegler, J. Amer. Chem. Soc, 91, 5081 (1969). 
S 6 : A. Streitwieser, Jr., W. B. Hollyhead, G. Sonnichsen, A. H. Pudjaatmaka, C. J. Chang,' 

and T. L. Kruger, J. Amer. Chem. Soc, 93, 5096 (1971). 
S 7 : A. Streitwieser, Jr., and D. M. E. Reuben, J. Amer. Chem. Soc, 93, 1794 (1971). 
S 8 : A. Streitwieser, Jr., M. R. Granger, F. Mares, and R. A. Wolf, J. Amer. Chem. Soc, 95, 4257 

S 9 : A. Streitwieser, Jr., P.J. Scannon, and H. M. Niemeyer,./. Amer. Chem. Soc, 94, 7936 (1972). 
S 10 : M.J. Maskornick and A. Streitwieser, Jr., Tetrahedron Lett., 1625 (1972). 
S u : A. Streitwieser, Jr., and D. R. Taylor, J. Chem. Soc D, 1248 (1970). 
° Calculated from data of Ref. D assuming pK of jndene X 20 and of fluorene X 23. 
6 The value given is that found in cyclohexylamine. F. G. Bordwell and W. S. Matthews, J. Amer. 
Chem. Soc, 96, 1214 (1974), report 29 (corrected to the present scale) in dimethylsulfoxide. 
c In liquid NH 3 ; corrected to triphenylmethane = 31. 
d Reported to be between diphenylmethane and toluene. 
e Estimated by B&B from electrochemical data. 

Substituent Effects on Strengths of Bronsted Acids and Bases H9 


Acid-base reactions have long served as a starting point for consideration of the 
effects of changes in a structure on the course of chemical reactions. Table 3.2 
summarizes solution data for a variety of Bronsted acids and bases; because of the 
problems of measurement, any such table necessarily contains a fair amount of 
uncertainty. The pK a values that fall between 2 and 10 may be used with 
considerable confidence, since they are based on accurate measurements in dilute 
aqueous solutions ; the values outside this range must be regarded with a certain 
amount of skepticism. As we have noted in the two previous sections, uncertainties 

Table 3.2° Solution Dissociation Constants of Acids and Bases 

Conjugate Acid 

Conjugate Base 


References 1 ' 

RN0 2 H + 
RC=NH + 

OH + 

R X X G 

ArOH 2 H 
RSH 2 + 
ArOR + 


ROR + 

RN0 2 












-6 to 

(G = H, R, Ar, 








-6 to 







2 to - 4 




ROH 2 + 

OH + 

R X X NH 2 

ArNH 3 + 



H 2 S 



NH 4 + 

RNH 3 + 





R / V NH 2 

ArNH 2 






NH 3 

RNH 2 



-2 to -3 

to -2 

3 to 5 

4 to 5 


10 to 12 
9 to 11 


8, 1 










C C 

R CH 2 R 






150 Acids and Bases 

Table 3.2" (Continued) 

Conjugate Acid 

Conjugate Base 



RCH 2 N0 2 
H 2 

R CH 2 



r /Cn ch / 








17 to 20 



18 to ~28 

19 to 20 


12, 13 

9, 14 




CH 3 S0 2 CH 3 

<f> 3 CH 

CH 3 SOCH 3 

NH 3 

<f>CH 3 


CH 4 

<#c/o-C e H 12 



O' X CH X 



CH 3 S0 2 CH 2 

4> 3 C~ 

CH 3 SOCH 2 - 

NH 2 - 
<^CH 2 ~ 

CH 3 " 
cyclo-CeHu " 











Values less than ~ 3 and greater than ~ 10 are approximate, and values at the extremes of the scale 
probably have only qualitative significance. Complications of pK data may be found in D. D. Perrin, 
Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965; G. Kortum, 
W. Vogel, and K. Andrussow, Dissociation Constants of Organic Acids in Aqueous Solution, Butterworths, 
London, 1961 ; and in Refs. 1, 5, 8, and 9. 
' References. 

1. E. M. Arnett, Prog. Phys. Org. Chem., 1, 223 (1963). 

2. N. C. Deno, R. W. Gaugler, and T.J. Schulze, J. Org. Chem., 31, 1968 (1966). 

3. N. C. Deno, R. W. Gaugler, and M.J. Wisotsky, J. Org. Chem., 31, 1967 (1966). 

4. N. C. Deno and J. O. Turner, J. Org. Chem., 31, 1969 (1966). 

5. D. D. Perrin, Dissociation Constants of Inorganic Acids and Bases in Aqueous Solution, Butterworths, 

London, 1969. 

6. E. M. Arnett and C. Y. Wu, J. Amer. Chem. Soc, 82, 5660 (1960). 

7. E. M. Arnett and C. Y. Wu, J. Amer. Chem. Soc, 82, 4999 (I960). 

8. H. C. Brown, D. H. McDaniel, and O. Haflinger, Determination of Organic Structures by Physical 

Methods, E. A. Braude and F. C. Nachod, Eds., Academic Press, New York, 1955, p. 567. 

9. R. G. Pearson and R. G. Dillon, J. Amer. Chem. Soc, 75, 2439 (1953). 

10. See Table 3.6. 

11. See Table 3.1. 

12. K. Bowden, Chem. Rev., 66, 119 (1966). 

13. Data of D. Dolman and R. Stewart, Can. J. Chem., 45, 91 1 ( 1967) and of T. Birchall and W. L. 
Jolly, J. Amer. Chem. Soc, 88, 5439 (1966) indicate a pK a of roughly 27-28 for aniline and 28-29 
for 4-methylaniline. pK a of 4-nitroaniline is about 18 (Ref. 12). 

14. W. K. McEwen, J. Amer. Chem. Soc, 58, 1124 (1936). 

15. F. G. Bordwell, R. H. Imes, and E. C. Steiner, J. Amer. Chem. Soc, 89, 3905 (1967). 

16. R. Stewart and J. R.Jones, J. Amer. Chem. Soc, 89, 5069 (1967). 

Substituent Effects on Strengths of Bransted Acids and Bases 151 

Table 3.3 Approximate pK a Values for Hydrides 

Group IV Group V Group VI Group VII 

CH. 48 a 

NH 3 33" 

H 2 16" 

HF 3.17" 

PH 3 29 c - d 

H 2 S 7.0" 

HC1 -7" 

H 2 Se 3.9 C 

HBr -8" 

H 2 Te 2.6 C 

HI -9" 

-See Table 3.1. 

» See Table 3.2. 

c D. D. Perrin, Dissociation Constants of Inorganic Acids and Bases in Aqueous Solution, Butterworths, 

London, 1969. 

d The order PH a more acidic than NH 3 also holds in the gas phase. See D. Holtz, J. L. Beauchamp, 

and J. R. Eyler, J. Amer. Chem. Soc, 92, 7045 (1970). 

e See Table 3.6. 

Table 3.4 Electronegativities (Pauling Scale) 

Group IV Group V Group VI Group VII 


N 3.0 

O 3.5 

F 4.0 


S 2.5 

CI 3.0 

Se 2.4 

Br 2.8 

Te 2.1 

I 2.5 

Source: Reprinted from L. Pauling, The Nature of the Chemical Bond, 3rd ed., Cornell University Press, 
Ithaca, N.Y., 1960, p. 93, copyright 1960 by Cornell University Press. Used by permission of Cornell 
University Press. 

become severe for very strong and very weak acids ; the extreme values have only 
qualitative significance. 

In Table 3.2 we follow the convention of giving the strength of a base in 
terms of the pK a of the conjugate acid. It is useful to keep in mind that the weaker 
the base, the stronger is its conjugate acid. Hence the weakest bases and strongest 
acids (those with negative pK a ) appear at the beginning of the table, whereas the 
strongest bases and weakest acids (large positive pK a ) are at the end. Since many 
compounds are both acids and bases, it is worthwhile to note that although there 
is a definite relationship between strength of a base and strength of the conjugate 
acid of that base, there is not any quantitative correlation between the strength of a 
given substance as a base and the strength of the same substance as an acid, although 
it is often true that a strongly acidic molecule will be weakly basic and vice versa. 84 

Acid Strengths of Simple Hydrides 

It is useful to begin the discussion of substituent effects on acidity by examining 
briefly the solution acidities of hydrides of some elements of Groups IV, V, VI, 
and VII, given in Table 3.3. These values span a very wide range and are subject 
to considerable uncertainty, but the trends are clear. In a given jow, the hydrides 
bec ome more acidic as one moves to_ the right . This Jjffiad-pai:allels-the--electro- 
negativity of the atom to which the hydrogen is bonded (Table 3.4). A possible 
i nterpr etation oftEe TtrendjOii^^j^Ej^ucri series the increasing nuclear 
charge holcte tht^vaience electrons, all of which have the same principal quantum 

84 (a) E. M. Arnett, Prog. Phys. Org. Chem., 1, 223 (1963); (b) R. J. Gillespie, in Friedel-Crafls and 
Related Reactions, Vol. 1, G. A. Olah, Ed., Wiley-Interscience, New York, 1963, p. 181. 

152 Acids and Bases 

Table 3.5 Bond Dissociation Energies (kcal mole" 1 )" 

Group IV Group V Group VI Group VII 

CH 3 — H 

NH 2 — H 

HO— H 

H— F 




PH 3 

HS— H 

H— CI 




H 2 Se 

H— Br 



H 2 Te 

H— I 



" T. L. Cottrell, The Strengths of Chemical Bonds, Butterworths, London, 1954. 
b Average bond energy. 

numb er, more and inore_stronglv, so thaLJie^ative_ions .iecome more and 
rnprejavorahle r.ornr>arfd with thej-ovaTeptl y honrifd nnnT onJ7eH_r.ompoiinds. The 
electronegativity analogy, however, clearly fails in comparisons among members 
of a given group. The atoms become less electronegative as one goes down a 
column of the table, but the hydrides become stronger acids. Carbon and 
iodine have the same electronegativity on the Pauling scale, but the acidities of 
CH 4 and HI differ by something approaching 60 powers of ten. The_heginning 
ojlajx-explanation iband m the bond- dissociation- energies «f the Jiyd rides 
(Table 3.5). TJi£_jd£cr£asingjeJ£cJiQn^gati¥ky^ 

sated-by-a-W£aker bond to hydrogen. 85 One may rationalize the observations in a 
rough way by saying triat""on~going to larger atoms with valence electrons in 
higher principal quantum levels and hence farther from the nucleus, the overlap 
with the orbital on the small hydrogen atom becomes less favorable and the bonds 
become weaker. 

(__ Gas-Phase Acidity / 

It can be seen from the foregoing discussion that the interpretations of the ob- 
served acidities leave something to be desired even for such a fundamental series 
of compounds as the simple hydrides. The matter has been reopened in recent— 
years by the development of techniques for measuring acidities in the gas phase. 86 
The available results reemphasize the fact, already well known from previous 
work, that solvation factors have a profound influence on the course of acid— base 
reactions. But the gas-phase experiments do more than this; they call into 
question some of the fundamental assumptions and interpretations that have 
long been used to account for observed acidities in terms of molecular structure. 
As an example, let us consider the effect on acidity of substituting one hydro- 
gen of H a O by various organic groups. Table 3.6 presents the available data for 
relative acidities of the simple alcohols in solution, whereas Table 3.7 shows the 
relationships in the gas phase. On the basis of the solution data alone, one 
would conclude that substitution by successively more bulky groups causes a 
steady lowering of acidity, although the relative positions of water and methanol 

85 For a more complete analysis, see R. P. Bell, The Proton in Chemistry, Cornell University Press, 

Ithaca, N.Y., 1959, p. 90. 

66 J. I. Brauman and L. K. Blair, J. Amer. Chem. Soc, 92, 5986 (1970). 

Substituent Effects on Strengths of Bronsted Acids and Bases 153 

Table 3.6 Solution Acidities of Water and the Simple Alcohols 

Compound pK a K e a 

H z O 


CH 3 CH 2 OH 

(CH 3 ) 2 CHOH 
(CH 3 ) 3 COH 

"J. Hine and M. Hine, J. Amer. Chem. Soc, 74, 5266 (1952). In isopropyl alcohol, 

HA + f-prO- „ A" + «-prOH 




16 c 15.5* 


18 d (16)' 


18 d 


19 d 


K. = 


The value for isopropyl alcohol is determined by the definition of K e 
" Calculated for 

[H3O + HOH-] 
[H 2 0] 

using K w = 10" 14 and [H 2 OJ = 55.5 M. 

c A. Unmack, Z. Phys. Chem., 129, 349 (1927); 131, 371 (1928); 133, 45 (1928). 

" W. K. McEwen, J. Amer. Chem. Soc, 58, 1 124 (1936). Measured in benzene using Unmack's value 

for CH3OH as standard. 

e P. Ballinger and F. A. Long, J. Amer. Chem. Soc, 82, 795 ( 1960). Measured by conductivity in water. 

' Ref. d, by extrapolation of a correlation with Taft's a* parameters (see text). 

Table 3.7 Relative Gas-Phase Acidities of Alcohols 

Acidity Order" dpK a (gas)" 

Strongest acid ^OH» 

(CH 3 ) 3 COH > 

(CH 3 ) 2 CHOH> . 

CH 3 CH 2 OH > /. 

CH3OH > 
Weakest acid H 2 

Determined by J. I. Brauman and L. K. Blair, J. Amer. Chem. Soc, 92, 5986 (1970) using ion cyclo- 
tron resonance spectroscopy. 

6 D. K. Bohme, E. Lee-Ruff, and L. B. Young, J. Amer. Chem. Soc, 93, 4608 (1971). The technique 
for the quantitative measurements was the flowing afterglow method. See D. K. Bohme and L. 
B. Young, J. Amer. Chem. Soc, 92, 3301 (1970). 

are somewhat uncertain. Before the advent of the gas-phase measurements, these 
data were the only ones available and were generally interpreted in terms of the 
inductive effects of the alkyl groups. It is well known, for example, that increasing 
alkyl substitution stabilizes carbocations (see Section 5.3), and so it was presumed 
that an alkyl group, being evidently electron-donating, should destabilize a 
negative charge. Hence it was reasonable that the alcohols with more or larger 
groups should have less tendency to form a negative ion by loss of a proton and 
hence should be less acidic. This interpretation was apparently supported by the 
establishment of a correlation between alcohol acidity and the Taft a* inductive 
parameter (see Section 2.2, p. 67), although it should be pointed out that the 

154 Acids and Bases 

Table 3.8 Order of Acidity in the Gas Phase for Selected Compounds" 

acidic: CH 3 (CH 2 ) 
CH 3 N0 2 

3 SH 

H H 




CH 3 — C- 

CH 3 

CH 3 CN 


CH 3 — S— 

CH 3 


(CH 3 ) 3 COH; 

(CH 3 ) 2 CHOH 

CH 3 CH 2 OH 
^CH 3 
H 2 

H 2 
NH 3 

Least acidic: H 2 C=CH 2 , , / \ , CH 4 

<■ D. K. Bohme, E. Lee-Ruff, and L. B. Young, J. Amer. Chem. Soc, 94, 5153 (1972). 

correlation was made up of alcohols of the structure RCH 2 OH and included 
only one of the substances in Table 3.6, namely methanol. 87 

This interpretation is again one that attributes the observed effects solely 
to the intrinsic properties of the acid and conjugate base and ignores solvation. 
The solvation might in fact be expected to be quite important, since in all likeli- 
hood the bulky (CH 3 ) 3 CO~ ion will be much less well solvated than the OH" 
ion. The intrinsic bacisity of OH ~ will thus be reduced by solvation more than 
will that of (CH 3 ) 3 CO". The gas-phase results of Brauman and Blair (Table 3.7), 
show that in the absence of solvent, water is the weakest acid (OH~ the strongest 
base) and tert-buty\ alcohol the strongest acid [(CH 3 ) 3 CO~ the weakest base]. 
If we assume that the gas-phase order reflects intrinsic molecular properties, we 
must conclude that preferential solvation is indeed reversing the order in solution. 
Brauman and Blair feel that the inductive effects have been misinterpreted in the 
past, and that alkyl groups are better able to stabilize both positive and negative 
charge than is hydrogen. They attribute this ability to the increasing polarizability 
of the alkyl groups as they become larger, and they give the outline of a theoretical 
interpretation of the effect. 

87 P. Ballinger and F. A. Long, J. Amer. Chem. Soc, 82, 795 (I960). 

Substituent Effects on Strengths of Bronsted Acids and Bases 155 

Table 3.8 lists comparative gas-phase acidities for a variety of compounds. 
Comparison of the relative gas-phase acidities with the solution pK a values given 
in Table 3.2 reveals a number of changes in order. The most striking difference 
is the position of water, which, in comparison with other compounds, is a very 
much weaker acid in the gas phase than in the liquid phase. One may conclude 
that the strong propensity for water to solvate ions and polar molecules, parti- 
cularly through hydrogen bonding, influences its acid-base properties so strongly 
as to overshadow other effects arising from the internal structure and bonding. 

The conclusion that should be drawn from this discussion is that there are 
two kinds of acidity that must not be confused : ( 1 ) an intrinsic acidity, which is 
best approximated by gas-phase measurements and which reflects the properties 
of the ions and molecules in isolation, and (2) a practical liquid-phase acidity in 
which solvation effects may play the dominant role. In interpretation of structure- 
reactivity relationships, the liquid-phase acidity will probably be misleading 
unless the structures being compared are very similar; for thinking about chemical 
behavior in solution, however, the liquid-phase acidities are clearly the important 

Acidities of Amines 

Acidities of amines in solution are less well known than those of alcohols. Streit- 
wieser and co-workers report that cyclohexylamine is somewhat less acidic than 
triphenylmethane, 88 but there is little information available about the effects of 
structural variation on acidity. In the gas phase, Brauman and Blair found the 
order (most acidic to least acidic) (C 2 H 5 ) 2 NH > (CHg) 3 CCH 2 NH 2 ^ (CH 3 ) 3 
CNH 2 > (CH 3 ) 2 NH > (CH 3 ) 2 CHNH 2 > CH 3 CH 2 CH 2 NH 2 > C 2 H 5 NH 2 > 
CH 3 NH 2 > NH 3 . 89 Water falls between diethylamine and ammonia. T_he 
obseryedjjrdexjsjgejnerally xgnsislerLt-wit h t h e theory that th e charg ed conjugate 
base is_bj^te£Jlahilized,by_jri^^ In the gas phase the 

amines are apparently of comparable acidity to the alcohols, whereas in solution 
they are much weaker acids. 

Acidities of Carbon Acids 

Another class of acids of interest in organic chemistry is the group of carbon 
acids. Here we may discern three kinds of effects on acidity. The first of these is 
illustrated by the acidity of methane {pK a x 48) compared with that of cyclo- 
hexane (pK a x 52) (Table 3.1). It would appear that the trend is in the direction 
of decreasing acid strength with substitution of hydrogen by alkyl. Note that the 
tendency here is in the direction opposite to the effect in alcohols if we take 
Brauman's gas-phase results to be the more accurate indication of intrinsic acid 
strength. The hydrocarbon data are from solution measurements subject to 
considerable uncertainty, and the differences are small. It seems risky to inter- 
pret the results in terms of intrinsic molecular properties. 

A second effect of structure on acidity is evident from the data in Table 3.9. 
Here the differences are considered to be due primarily to the change in hybrid- 

88 A. Streitwieser, Jr., J. I. Brauman, J. H. Hammons, and A. H. Pudjaatmaka, J. Amur. Chem. Soc, 
87, 384 (1965). 

89 J. I. Brauman and L. K. Blair, J. Amer. Chem. Soc, 91, 2126 (1969). 

156 Acids and Bases 

Table 3.9 Acidities of Selected Hydrocarbons 

Compound Approximate pAV 

C 6 H 5 CfeCH 23 

C 6 H B 43 

H 2 C^CH 2 44 



"See Table 3.1. 

ization of the orbital that bears the negative charge in the conjugate base. The 
large contribut ion of th e s orbital in the jft-hybridizedxarhoja o_f jacety, lene results 
irj_ greater electronegativity than is found i n hybr ids with high j)-orbital con- 
triJjutionSjbecause^ the j-orbital fun ction puts the electrons on the average 
njeargxln the nucleus. A regular trend toward weaker acids is evident from the 
data as the hybridization changes from sp (C 6 H 5 G=CH) to sp 2 (H 2 C=CH 2 and 
C 6 H 6 ) to sp 3 (cyclohexane) . Although we are still dealing with solution values, the 
interpretation in terms of molecular structure may be considered to be more 
reliable in this case than for the alcohols or saturated hydrocarbons, as the 
differences observed are larger. 

The final effect to be noted in the carbon acids, and the most important 
one from the point of view of organic reactions in general, is illustrated by the 
data in Table 3,10. It is a well-known feature of organic molecules that certain 
electron-withdrawing groups increase the acidity of neighboring carbon- 
hydrogen bonds. A few of these groups are represented in Table 3.10, which also 
indicates the cumulative effects observed when more than one such group is 
bonded to the same carbon. The acidifying groups shown have unsaturated 
structures containing nitrogen or oxygen or both, and_the^cjd^s:tr£rigtJiemr)g 
ef fect is attrib utable prim arily t o_the_sta bilization of |_the,_ conjugate base by 
derealization of the negative char ge ont o an electronegative center, as illustrated 
in the alternative formulations 5 and 6. 

6: =6T O 

- c c . !l 

H a C^ V CH 3 * ► H 2 C^ ^CH 3 H 2 C'- > K CH 3 

5 6 

Again, solution acidities are being interpreted in terms of intrinsic properties ; 
however, the differences are large enough (CH 4 to acetone over 20 pK units) 
that we may feel fairly confident of our theory in this case. 

Carboxylic Acids 

Another important class of organic acids are the carboxylic acids. Since the p^ a 's 
of these substances fall in the range 4—5, their acidities can be determined with 

Substituent Effects on Strengths of Brensted Acids and Bases 157 

Table 3.10 Acidities of Carbon Acids Containing 
Electron-Withdrawing Groups 

Compound pK a 

CH 3 N0 2 1 1 

N0 2 — CH 2 — N0 2 4 

CH(N0 2 ) 3 

CH 3 — C— CH 3 20 

O O 


CH 3 — -C— CH 2 — C— CH 3 9 



CH(C— CH 3 ) 3 6 

CH 3 S0 2 CH 3 29° 

CH 2 (S0 2 CH 3 ) 2 14 

CH(S0 2 CH 3 ) 3 

CH 3 C=N 25 

CH 2 (C=N) 2 12 

CH(C=N) 3 

Source: Reprinted with permission from R. G. Pearson and R. L. Dillon, J. Amer. Chetn. Soc, 75, 
2439 (1953). Copyright by the American Chemical Society. 
" See Ref. 15 in Table 3.2. 

precision and compared with considerable confidence, despite the fact that the 
differences are small. 90 The p^ a 's of a very large number of carboxylic acids 
have been determined; we list in Table 3.1 1 only a few representative values to 
illustrate trends. 91 The_d ata indicate that the effect of e lectron -withdrawing 
snh stitnents is to increase acid st reng th, even though dirre t - t r rmjugative de- 
lo calization of ch arge is not possible^ as it is in the substituted carbon acids 
considered above. Again, one must be very careful to keep solvation factors 
constant in making comparisons if interpretations in terms of molecular structure 
are to be made; the most careful and informative studies of the carboxylic acids 
have been carried out in series in which the structural changes occur as far from 
the reaction site as possible, as for example in ring systems such as 7. 92 





90 The greatly increased acidity of the carboxylic acids over water and the alcohols is accounted for 
by derealization of charge in the conjugate base, as indicated by Structures a. 

r— c « > r— a 


91 References to compilations are given in Table 3.2, note a. 

92 (a) H. D. Holtz and L. M. Stock, J. Amer. Chem. Soc, 86, 5188 (1964); (b) R. Golden and L. M. 

158 Acids and Bases 

Table 3.11 Acid Dissociation Constants of Some 
Representative Carboxylic Acids 

Compound p^a a 

HCOOH 3.77 

CH3COOH 4.76 

CH 3 CH 2 COOH 4.88 

CH 3 CH 2 CH 2 COOH 4.82 

CH 3 CH 2 CH 2 CH 2 COOH 4.86 

H 3 N + CH 2 COOH 2.31 

2 NCH 2 COOH 1.68 

ClCH 2 COOH 2.86 

Cl 2 CHCOOH 1.29 

Cl 3 CCOOH 0.65 

-OOCCH 2 COOH 5.69 

(/.COOH 4.20 

/>-(CH 3 ) 3 N(£COOH 3.43 

/>-6oC</>COOH 4.82 

H. G. Brown, D. H. McDaaiel, and O. Haflinger, Determination of Organic Structures by Physical 
Methods, Vol. 1, E. A. Braude and F. G. Nachod, Eds., Academic Press, New York, 1955, p. 567. 


We now turn to a brief consideration of the uncharged Bransted bases. There is 
less quantitative information about solution basicity of the simple hydrides than" 
about their acidities; it is only possible to make semiquantitative comparisons. 
The available data are given in Table 3. 12 ; the only really reliable value is that of 
ammonia. Despite the uncertain nature of the information, we can see repeated 
here the same trend as with the acidities of the hydrides; in a given row in the 
periodic table th e basicity d gcreases_a§__elgctronegativity (and acidity) increases. 
Comparing the data for the hydrides within a group, we find again the lack of 
consistency with electronegativity that appeared in the acid-strength data. 
Phosphorus bases are weaker than the corresponding nitrogen bases, although 
phosphorus is less electronegative than nitrogen; similarly, although there are 
no reliable data for H 2 S itself, in solution the sulfur bases are in general weaker 
than oxygen bases. 93 

Nitrogen and Phosphorus Bases 

The effect in the liquid phase of substituting hydrogen by alkyl grmip g_nn the 
nitrogen and phosphorus bases is illustrated by the solution data presented in 
Table 3.13. TJi g^phflggfaorus basicities are m uch more strongly affected thajLare 
the nitrogen . The tertiary amine (CH 3 ) 3 lSr is in an anomalous position with 
respect to the other amines. We suspect immediately that solvation is the culprit. 
In the gas phase, the amine order is (most basic to least) tertiary > secondary > 

Stock, J. Amer. Chem. Soc, 88, 5928 (1966); (c) F. W. Baker, R. C. Parish, and L. M. Stock, J. 
Amer. Chem. Soc, 89, 5677 (1967). 
93 See note 84 (a), p. 151. 

Substituent Effects on Strengths of Bronsted Acids and Bases 159 

Table 3.12 Approximate pK a Values of Conjugate Acids of 
Some Simple Hydrides 

Group V Group VI Group VII 

NH 3 9.24" H 2 C> -7 C HF(-9) e 

PH 3 d ~14 6 -1.74' 

" See Table 3.2. 

6 Estimated from exchange rate measurements by R. E. Weston and J. Bigeleisen, J. Amer. Chem. 

Soc., 76, 3074 (1954). 

c E. M. Arnett, R. P. Quirk, and J. J. Burke, J. Amer. Chem. Soc, 92, 1260 (1970). 

" Relative basicities in the gas phase are consistent with the solution results: D. Holtz and J. L. 

Beauchamp, J. Amer. Chem. Soc, 91, 5913 (1969); D. Holtz, J. L. Beauchamp, and J. R. Eyler, J. 

Amer. Chem. Soc, 92, 7045 (1970). 

e D. D. Perrin, Dissociation Constants of Inorganic Acids and Bases in Aqueous Solution, Butterworths, 

London, 1969. 

' Calculated from the equilibrium : 

H 3 + + H 2 . H 3 C> + + H 2 
[H 3 + ][H 2 0] 

K' = 1 - 

[H 3 + ][H 2 0] 
[H 3 + ][H 2 0] 


PH 3 

~-13 6 

10.6 C 



10. 7 C 

(«-C 4 H 9 ) 2 PH 


9.8 C 

(n-C 4 H 9 ) 3 P 


K a = 55.5 = 

[H 3 + ] 

pK a = -1.74 

Table 3.13 Solution pK a Values of Conjugate Acids of Some Nitrogen and 
Phosphorus Bases 

Base pK a (BH + ) Base pK a (BH + ) 

NH 3 

CH 3 NH 2 

(CH 3 ) 2 NH 

(CH 3 ) 3 N 

" See Table 3.2. 

6 See Table 3.12. 

c D. D. Perrin, Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965. 

Values at 25°C. 

d C. A. Streuli, Anal. Chem., 32, 985 (1960). Determined by titration in nitromethane and corrected 

to water solution. 

primary > ammonia. 94 The phosphines have the same basicity order in the gas 
phase as in solution, tertiary » phosphine. 95 

Arnett has presented an analysis of the solvation thermochemistry of the 
amines and their conjugate acids. 96 Table 3.14 gives Arnett's data for the four 

64 (a) E. M. Arnett, F. M.Jones, III, M. Taagepera, W. G. Henderson, J. L. Beauchamp, D. Holtz, 
and R. W. Taft, J. Amer. Chem Soc, 94, 4724 (1972) ; (b) D. H. Aue, H. M. Webb, andM. T. Bowers, 
J. Amer. Chem. Soc, 94, 4726 (1972); (c) W. G. Henderson, M. Taagepera, D. Holtz, R. T. Melver, 
Jr., J. L. Beauchamp, and R. W. Taft, J. Amer. Chem. Soc, 94, 4728 (1972). 

95 E. M. Arnett, Accts. Chem. Res., 6, 404 (1973). Gas-phase data are reported for (CH 3 ) 3 P and PH 3 
only, but heat of protonation results indicate that secondary and primary phosphines will fall in that 
order between these two. 

96 See note 94 (a). 













160 Acids and Bases 

Table 3.14 Free Energies of Ionization and Solvation of Amines and Ammonium Ions 
in the Gas and Lio_uid Phases 

Amine SAG i9 hAG iw SAG E (B) 8AG S (BH + ) 

NH 3 

CH 3 NH 2 

(CH 3 ) 2 NH 

(CH 3 ) 3 N 

Source: Reprinted with permission from E. M. Arnett, F. M. Jones, III, M. Taagepera, W. G. 
Henderson,]. L. Beauchamp, D. Holtz, and R. W. Taft, J. Amer. Chem. Soc, 94,4724 (1972). Copy- 
right by the American Chemical Society. Values in kcal mole" 1 at 25°C. See text for explanation of 

Table 3.15 Enthalpy and Entropy Contributions to Relative Free 
Energies of Solution of Ammonium Ions 

Amine SAi/ s (BH + ) - S T&S S (BH + ) 

NH 3 

CH 3 NH 2 6.0 1.3 

(CH 3 ) 2 NH 11.2 2.6 

(CH 3 ) 3 N 18.6 2.1 

Source; Reprinted with permission from E. M. Arnett, F. M. Jones, III, M. Taagepera, W. G. 
Henderson, J. L. Beauchamp, D. Holtz, and R. W. Taft, J. Amer. Chem. Soc, 94, 4724 (1972). Copy- 
right by the American Chemical Society. Values in kcal mole" 1 at 25°C. See text for explanation of 

processes of Equations 3.56 through 3.59. The subscript w refers to water solution, 

BH„ + ^B„ + H„ + AG to (3.56) 

BH 9 + -> B g + H 9 + AG i9 (3.57) 

B«,-+B„ AG S (B) (3.58) 

BH g + -^B u , + AG S (BH + ) (3.59) 

g to gas phase, i to the ionization process, and s to the transfer from gas to solution. 
Values reported in Table 3.14 are SAG, free energies measured relative to the 
value for NH 3 . The more positive SAG f , the smaller the tendency for BH + to 
ionize, hence the stronger the base. The more positive SAG S , the more reluctant is 
that species to enter solution from the gas phase. 

The first column of Table 3.14 reflects the gas-phase order, (GH 3 ) 3 N most 
basic. The second column reflects the solution basicities (compare Tabic 3.13). 
The third column reveals that the differences in free energies of solution among 
the free bases are small. In the fourth column we find large differences among 
solvation free energies of the ions BH + . The more substituted BH + , the less 
favorable is its transfer to solution. Therefore, in solution the more substituted 
amines will be reduced in basicity compared with their gas-phase behavior, 
because the solvation of BH + becomes poorer the more highly substituted it is. 
Note that the solvation free-energy differences very nearly cancel the intrinsic 
basicity differences revealed by the gas-phase ionization free-energy differences 
in the first column. The observed solution order (second column) results from 
the small free-energy variations remaining after combining two large, opposing 
terms [SAG ig and SAG S (BH + )] and one small term [3AG S (B)]. 

Substituent Effects on Strengths of Bronsted Acids and Bases 161 

Table 3.16 Enthalpy and Entropy Contributions to Relative Free 
Energies of Solution of Amines 

Amine 8AH,(B) -8TAS S (1&) 

NH 3 

CH 3 NH 2 -2.57 2.30 

(CH 3 ) 2 NH -4.72 4.72 

(CH 3 ) 3 N -4.67 5.76 

Source: Reprinted with permission from E. M. Arnett, F. M. Jones, III, M. Taagepera, W. G. 
Henderson, J. L. Beauchamp, D. Holtz, and R. W. Taft, J. Amer. Chem. Soc, 94, 4724 (1972). Copy- 
right by the American Chemical Society. Values in kcal mole" 1 at 25°C. See text for explanation of 

Table 3.15 dissects the important 8AG 5 (BH + ) term into enthalpy and 
entropy contributions. Increasing substitution on BH + makes both of these 
quantities less favorable in the gas — >- solution direction. For the bases themselves, 
on the other hand, the solution enthalpies and entropies are in opposition (Table 
3.16), enthalpies being more favorable to the solution process the more substi- 
tuents, but entropies becoming less favorable with more substituents. The 
cancelation of these opposing effects leaves the small 8AG S (B) values shown in 
Table 3.14. As we have noted in Section 2.4, these results are not easily inter- 
preted at the molecular level, although the most important effect, that on solution 
free energy of BH + , is undoubtedly caused by decreasing opportunity for hydro- 
gen bonding as hydrogens are replaced by alkyl groups. 97 

Oxygen and Sulfur Bases 

The oxygen and sulfur bases are weaker than the nitrogen bases, and accurate 
solution basicities are not available. Arnett's heat of protonation studies indicate 
that the order of decreasing basicity is ROR > ROH > H a O, 98 a result that is 
in agreement with gas-phase measurements." Hydrogen sulfide in the gas phase 
has basicity comparable to that of water (Table 3.18), and substitution of H by 
alkyl produces stronger gas-phase bases just as does similar substitution on oxygen. 

Comparisons among the alcohols are difficult to make in solution. Titration 
in acetic acid indicates an order of basicity isopropyl alcohol > ethyl > methyl, 
but water was found to be a stronger base than any of these alcohols, 100 a result 
in disagreement with the gas-phase data. In the gas phase (Table 3.18), the 
basicity order (strongest base to weakesJJLis _(CH 3 ) 3 COH > (CH 3 ) a CHOH > 
_CH a CH ftOH_>_ CH^OH > H g Qw\gain, more and larger_alykl -groups seem-. to 
stabilize charge. 

Substitution by an aromatic group has a marked effect on solution base 
strength. One might be tempted to attribute the low basicity of aniline, di- and 
triphenylamines, and phenol compared with reference compounds (Table 3.17) 
to partial derealization of the nonbonded electron pair on the nitrogen or oxygen 
into the -n orbital system of the ring. But gas-phase results indicate the basicity 

97 (a) See note 94 (a), p. 159; (b) R. W. Taft, M. Taagepera, K. D. Summerhays, and J. Mitsky, 
J. Amer. Chem. Soc, 95, 3811 (1973). 

98 E. M. Arnett, R. P. Quirk, and J. J. Burke, J. Amer. Chem. Soc, 92, 1260 (1970). 

99 M. S. B. Munson, J. Amer. Chem. Soc, 87, 2332 (1965). 

100 I. M. Kolthoff and S. Bruckenstein, J. Amer. Chem. Soc, 78, 1 (1956). 

162 Acids and Bases 

Table 3.17 The Effect of Phenyl Substitution on 

Solution Basicity of Oxygen and Nitrogen Bases 



C 2 H 5 OH 

C 6 H 5 OH 

NH 3 

C 6 H 5 NH 2 

(C 6 H 5 ) 2 NH 

(C 6 H 5 ) 3 N 

-5 a 

4.60 c 
0.79 c 


° E. M. Arnett, R. P. Quirk, and J. W. Larsen, J. Amer. Chem. Soc, 92, 1260 (1970). 

" See Table 3.2. 

c D. D. Perrin, Dissociation Constants of Organic Bases in Aqueous Solution, Butterworths, London, 1965. 

" Estimated from data of Arnett et al., (note a) . 

Table 3.18 Gas-phase Basicities of Selected Compounds 


Proton Affinity" 
(kcal mole -1 ) 

CH 4 

H 2 C=CH 2 

CH 3 C1 

H 2 

H 2 S 



PH 3 


CH 3 CH 2 OH 
CH 3 — O— CH 3 
(CH 3 ) 2 CHOH 
CH 3 COCH 3 

CHg S CH3 

(CH 3 ) 3 COH 

CH3CH2 — ^ — ^HgCHg 

NH 3 

CH 3 PH 2 

<£NH 2 
<£ 2 NH 
CH 3 NH 2 

<£ 3 N 
(CH 3 ) 2 PH 

(CH 3 ) 2 NH 

(CH 3 ) 3 N 

(CH 3 ) 3 P 




















207 c 





219 c 
228 c 

Increasing basicity 

188 c 

Decreasing basicity 

Except where noted, data ar<! from the compilation of J. Long and B. Munson, J. Amer. Chem. 

Soc, 95,2427 (1973). 

6 E. M. Arnett, Accts. Chem. Res., 6, 404 (1973). 

c R. H. Staley and J. L. Beauchamp, J. Amer. Chem. Soc, 96, 6252 (1974). 

" I. Dzidic, J. Amer. Chem. Soc, 94, 8333 (1972). Only relative basicities reported for these compounds. 

Lewis Acids and Bases 163 

order <£ 3 N > <£ 2 NH, <£NH 2 , and warn us that the solution order is probably again 
caused by solvation and not by internal electron distribution properties of the 
bases. 101 

The carbonyl bases constitute another important class of weak bases that 
present interesting possibilities for investigation of structural effects. In solution, 
experiments with these compounds are subject to severe difficulties. The result 
is a serious lack of agreement among different investigators about pK a . Arnett 
and co-workers point out that pK a values reported for acetophenone cover a 
range of over four units ( — 3.65 to —7.99), while those for acetone span seven 
units ( — 0.2 to — 7.2). 102 In view of these uncertainties, it is impossible to say 
whether aldehydes, ketones, or carboxylic acids are the most basic in solution. 
Gas-phase data are available for some of these substances. 

Table 3.18 summarizes gas-phase basicities for a number of compounds. It 
is possible to measure relative gas-phase basicities quantitatively, and the table 
includes proton affinity, which is the negative of the enthalpy change for reaction 
3.60. 103 

B g + H 9 + ->■ BH 9 + AH = - (proton affinity) (3.60) 

Table 3.18 contains data for three carbon bases: propene, ethylene, and 
methane. The position of methane indicates that the saturated hydrocarbons, 
among the weakest of the Brensted acids, are also among the weakest bases. The 
unsaturated hydrocarbons have electrons in higher energy orbitals and accept a 
proton more easily. There is information available, primarily from acidity 
function techniques, about solution basicities of a number of unsaturated hydro- 
carbons. 104 


In 1923 G. N. Lewis proposed a definition of acids and bases somewhat different 
from that of Brensted: 106 

An acid is an electron-pair acceptor. 
A base is an electron-pair donor. 

Lewis acids are thus electron-deficien t molecules or ions such as JH ^ or carbo - 
cations, whereas Le^wis_bajes_argjrnolec ules or ions containing a vaila ble electron s, 
sudij^amines^ etherSjjalkoxjdejcjiSj_and so forth . A Lewis acid-base reaction is 
the combination of an acid and a base to form a complex, or adduct. The 
stabilities of these adducts depend on the structures of the constituent acid and 
base and vary over a wide range. Some examples of Lewis acid-base reactions are 
given in Table 3.19. Lewis acid-base reactions abound in organic chemistry: 

101 I. Dzidic, J. Amer. Chem. Soc., 94, 8333 (1972). 

102 E. M. Arnett, R. P. Quirk, and J. W. Larsen, J. Amer. Chem. Soc, 92, 3977 (1970). 

103 See note 94 (b), p. 159. 

104 For further details see note 84 (a), p. 151. 

105 A general discussion of Lewis acids and bases is given by R. J. Gillespie in Friedel-Crqfts and 
Related Reactions, Vol. 1, G. A. Olah, Ed., Wiley-Interscience, New York, 1963, p. 169. 

106 G. N. Lewis, Valence and the Structure of Atoms and Molecules, American Chemical Society Mono- 
graph, The Chemical Catalog Co., New York, 1923. Lewis also gave a definition equivalent to that 
of Bronsted at this time, but he considered the electron-pair definition to be more general. 

164 Acids and Bases 

Table 3.19 Examples of Lewis Acid-Base Reactions 

+ / C 2 H 5 
BF 3 + C 2 H 5 — O— C 2 H 5 ^=± F 3 B— O^ 

(C 6 H 5 ) 3 C + + OH" ^^ (C e H 5 ) 3 COH 

C 6 H 6 + N0 2 + ^ 

R R O- 

\:=o + cn- ^^ c 


the electrophiles (for example N0 2 + , carbocations, Ag + , B 2 H 6) carbonyl 
carbon) and nucleophiles (OH - , Cl~, amines, carbanions, and majry others), 
which are of such great importance in organic reactions, are Lewis acids and 
bases, respectively. The theory of these interactions, still in the process of being 
developed, may well prove to be of very general application. ^ 

The relationship between the Bronsted definition and the Lewis definition 
is a subtle one, which has caused some confusion and controversy over the years. 
There is no particular problem as far as bases are concerned, for it is clear that the 
two definitions refer to the same substances. Molecules with available electrons 
are capable of accepting a proton and also of coordinating with other electron- 
deficient centers, and so fit both definitions. It is with acids that the difficulties 
arise. The proton is itself a Lewis acid, and the prototype acid-base reactions of 
Equation 3.1 and 3.2 are clearly acid-base reactions in the Lewis sense, with H + 
the acid, A ~ or B the base, and HA and BH + the acid-base complexes. For these 
reasons Lewis 107 and others 108 have considered the Bronsted acid-base reactions 
to be special cases of the more general category covered by the Lewis definition. 
Adherents of the Bronsted theory, however, maintain that since Bransted acid- 
base reactions do not involve the bare proton, and since Bronsted acids are not, 
in general, Lewis acids, it is better to regard the two definitions as distinct. 109 

The problem is that a substance HA undergoing a reaction in which it 
behaves as a Brensted acid is not behaving as an acid in the Lewis sense; it is, 
however, behaving as a Lewis acid-base adduct. The issue is further clouded by 
the fact that HA can enter into reactions in which it does behave as a Lewis 
acid, as for example in the formation of a hydrogen bond (Equation 3.61); in 
this case it is not, however, behaving as a Bronsted acid, since the proton remains 

107 See note 106. 

loa (a) W. F. Luder and S. Zufianti, The Electronic Theory of Acids and Bases, Wiley, New York, 1946; 
W. F. Luder, Chem. Rev., 27, 547 (1940); (b) D. P. N. Satchell and R. S. Satchell, Quart. Rev. (Lon- 
don), 25, 171 (1971). 

109 (a) R. P. Bell, The Proton in Chemistry, 2nd ed., Cornell University Press, Ithaca, N.Y., 1973, p. 7; 
(b) I. M. Kolthoff, J. Phys. Chem., 48, 51 (1944). 

Lewis Acids and Bases 165 

more strongly bonded to A than it is to B. In this book we shall maintain the 

HA + B ;=± B-HA (3.61) 

distinction between the two definitions and shall follow the usual convention that 
the unmodified term acid will refer to a Bronsted acid, while Lewis acids will be 
specified as such. 

Strengths of Lewis Acids and Bases 

Because the Lewis acid-base concept is an extremely useful one in chemistry, 
quantitative relationships of the types discussed in the previous sections for 
Bransted acids and bases would be helpful. The task of classifying the Lewis acids 
and bases according to some criterion of strength has nevertheless proved to be a 
difficult one, and methods being developed still yield largely qualitative results. 
Bransted acid-base reactions always involve transfer of a proton ; this common 
feature allows meaningful quantitative comparisons of strengths to be made. 
Different Lewis acid-base reactions, on the other hand, do not necessarily have 
any feature in common, and the result is that the term "strength" does not have a 
well-defined meaning. 

The problem may be illustrated by a simple example. 110 Suppose that we 
wish to compare the "coordinating power " of two Lewis bases, say an amine, 
NR 3 , and a phosphine, PR 3 . We might do this by comparing the equilibrium 

A + B v AB (3.62) 

A + B' , AB' (3.63) 

constants for Reactions 3.62 and 3.63 of the two bases, B and B', with the same 
Lewis acid, for example BF 3 . Quantitative data are not always available ; but it is 
often possible to make qualitative decisions about orders of reactivity. The 
information we have shows that the nitrogen base should be judged to have the 
greater coordinating power, since the equilibrium constant is greater for the 
formation of nitrogen base complex. 111 A similar qualitative result is found with 
H + as the reference acid. 112 If, on the other hand, the equilibrium constants for a 
nitrogen and a phosphorus base with Ag + are measured, it is found that with 
respect to this Lewis acid the phosphine has much greater coordinating power 
than does the amine. A similar situation arises with another set of bases, the 
halide ions. If H + is taken as the reference acid, fluoride is the most effective base 
in solution, followed by chloride, bromide, and iodide. With silver ion, however, 
the order is exactly reversed ; iodide forms the most stable complex and fluoride 
the least stable. 113 

Hard and Soft Lewis Acids and Bases 

Despite the apparent chaos of the picture presented by these results, it is possible 
to find some qualitative relationships that are useful. Schwarzenbach, 114 and also 

110 S. Ahrland, J. Chatt, and N. R. Davies, Quart. Rev. (London), 12, 265 (1958). 

111 W. A. G. Graham and F. G. A. Stone, J. Inorg. Nucelar Chem., 3, 164 (1956). 

112 See Table 3.13 for solution data and Table 3.18 for gas-phase data. 

113 See note 110. 

114 (a) G. Schwarzenbach, Experientia, Suppl., 5, 162 (1956); (b) G. Schwarzenbach, Advan. Inorg. 

166 Acids and Bases 

Ahrland, Chatt, and Davies, 115 c lassified Lew is a cids into two categories, Class a 
and Class b. Clasjs_aj icceptorsj jjx-jkQ sc that -fecm_their most jstable complexes 
with .donorsjjf jhe first fow ^ofthe periodic JLa.fale_i N, O, and F. Class "J acids" 
c^rriplejcliejlwithjd o nors o f t h e s econd p r ^ ub s eq uenlJxaviP 1 jj_Cl^JBr r J^ 1 x 6 

This classification scheme for Lewis acids has been generalized and ex- 
tended by R. G. Pearson. 117 He proposes that each Lewis acid and base be 
characterized by two parameters, one of which is referred to as strength and the 
other of which is called softness. Thus the equilibrium constant for a simple acid- 
base reaction (Equation 3.62) would be a function of four parameters, two for 
each partner. 

The next step in Pearson's argument is to classify acids and bases as hard or 
soft according to their properties. Hard acids correspond roughly in their behavior 
to the Class a acids of Schwarzenbach and of Ahrland, Chatt and Davies. They 
are characterized by small acceptor atoms that have outer electrons not easily 
excited and that bear considerable positive charge. Soft acids have acceptor atoms 
of lower positive charge, large size, and with easily excited outer electrons. Hard 
and soft bases are defined analogously. Hard bases contain highly electronegative 
donor atoms of low polarizability, 118 are typically difficult to oxidize, and have 
no empty low-energy orbitals available; soft bases are polarizable, have less 
electronegative donor atoms, and have empty orbitals of low energy and electrons 
that are more easily removed by oxidizing agents. Table 3.20 gives Pearson's 
classification of acids and bases into the hard and soft categories. \^ 

Having defined the terminology, we may now state Pearson's principle oj~ 
hard and soft acids and bases (commonly abbreviated HSAB principle) : Hard acids 
prefer to bind to hard bases and soft acids prefer to bind to soft bases. 119 

Shortcomings of the HSAB principle Despite the apparent success 
of the HSAB principle, there are difficulties. The proposed scheme is one in 
which two parameters, strength and softness, characterize each acid and each 
base. Although published discussions 120 have been specific about how softness is 
determined, they have said much less about the strength parameter, and most of 
the applications and examples have been considered mainly from the point of 
view of the hardness or softness of the acids and bases concerned. 

The only satisfactory way to handle the situation would appear to be to 
establish numerical scales for both strength and hardness. Although limited work 
along these lines has been done, 121 it does not appear possible to extend the 
quantitative correlations to cover the wide range of reactions that seem to fit in at 

Chem. Radiochem., 3, 257 (1961); (c) G. Schwarzenbach and M. Schellenberg, Helv. Chim. Acta, 48, 
28 (1965). 

115 See note 110, p. 165. 

116 See also J. O. Edwards and R. G. Pearson, J. Amer. Chem. Soc, 84, 16 (1962). 

117 (a) R. G. Pearson, J. Amer. Chem. Soc, 85, 3533 (1963); (b) R. G. Pearson and J. Songstad, J. 
Amer. Chem. Soc, 89, 1827 (1967); (c) R. G. Pearson, Survey of Progress in Chemistry, 5, 1 (1969). 

118 See Section 2.4. 

119 See note 117 (c). 

120 See note 117. 

121 See, for example: (a) J. O. Edwards, J. Amer. Chem. Soc, 76, 1540 (4954); (b) R. S. Drago and 
B. B. Wayland, J. Amer. Chem. Soc, 87, 3571 (1965). 

Lewis Acids and Bases 167 

Table 3.20 Pearson's Classification of Lewis Acids and Bases 





H + , Li + , Na + , K + 

Fe 2 + , Co 2 + , Ni 2 + 

Cu + ,Ag + ,Hg + 

Be 2 + , Mg 2 + , Ca 2 + , Sr 2 + , Mn 2 + 

Cu 2 + , Zn 2 + 

Hg 2 + 

Al 3 + , Cr 3 + , Co 3 + , Fe 3 + 

Pb 2 + , Sn 2 + 

BH 3 , RS + , I + 

BF 3 , B(OR) 3 

B(CH 3 ) 3 , S0 2 

Br + , HO + , RO + 

A1(CH 3 ) 3 , A1C1 3) A1H 3 

NO + , R 3 C + 

I2, Br 2 

RP0 2 + ,ROP0 2 + 

C 6 H 5 + 

Trinitrobenzene, etc. 

RS0 2 + , ROS0 2 + , S0 3 

Chloranil, quinones, etc. 

RCO + , C0 2 , NC + 

Tetracyanoethylene, etc. 

HX (hydrogen-bonding 

CH 2 , carbenes 



H 2 0, OH", F- 

C 6 H 5 NH 2) C 5 H 5 N 

R 2 S, RSH, RS- 

CH 3 COO-, P0 4 3 ", SO4 2 - 

N 3 -, Br", NO z - 

I-, SCN-,S 2 3 - 

ci-, co 3 2 -, cio 4 -, NO3- 

so 3 2 - 

R 3 P, (RO) 3 P 

ROH, RO", R 2 

N 2 


NH 3 , RNH 2 

H", R- 

Source : R. G. Pearson, Survey of Progress in Chemistry, 5, 1 ( 1 969) . Reproduced by permission of 
Academic Press and R. G. Pearson. 

least a qualitative way with the hard-soft principle. 122 Pearson has emphasized 
that the HSAB principle is meant to be used only qualitatively, as a way of 
systematizing experimental results, and we should heed this warning. 123 

Applications of the HSAB principle In considering Bronsted acidities, 
we have already met some equilibria to which we can apply the hard-soft ideas. 
In Table 3.3 we noted that within a given column of the periodic table, the 
hydrides become more acidic as one moves down. The negative ions in the lower 
rows are softer bases than the corresponding ones in the upper rows (H 2 P~ is 
softer than H 2 N"; HS~ is softer than HO~), and the softer bases bond less 
strongly to the hard proton. The limited gas-phase data (Table 3.8) suggest that 
the same order applies: RSH is a stronger gas-phase acid than ROH. Similarly, 
the hard neutral nitrogen is more basic toward hard proton than is softer neutral 
phosphorus, both in the liquid (Table 3.12) and in the gas (Table 3.18). Neutral 
oxygen and sulfur bases, however, appear to be of comparable basicity toward 
the proton in the gas phase (Table 3.18). We shall find other applications for the 
HSAB principle in later chapters. 

The theoretical basis for the hard-soft principle It is worthwhile at 
this point to discuss briefly some of the theoretical concepts behind the hard-soft 

122 (a) R. G. Pearson, H. Sobel, and J. Songstad, J. Amer. Chem. Soc, 90, 319 (1968); (b) C. D. 
Ritchie, Accts. Chem. Res., 5, 348 (1972). 

123 Pearson's hard-soft scheme has been criticized: (a) R.J. P. Williams and J. D. Hale, Structure and 
Bonding, Vol. 1, Springer- Verlag, Berlin, 1966, p. 249; (b) R. S. Drago and R. A. Kabler, Inorg. Chem., 
11, 3144 (1972); (c) R. G. Pearson, Inorg. Chem., 11, 3146 (1972); (d) R. S. Drago, Inorg. Chem., 12, 
2211 (1973). 

168 Acids and Bases 

principle. As we have emphasized, the principle is a statement summarizing 
experimental facts and cannot at present be explained in detail at the molecular 
level. Yet there are general trends in properties of acids and bases that correspond 
to their classification as hard and soft, and we might therefore look for a qualita- 
tive theoretical explanation. 

Although complete understanding can come only with full comprehension 
of chemical bonding itself, it is possible to identify various factors that appear to 
be of particular importance to the stability of Lewis acid-base complexes. These 
factors are discussed in a number of places in the chemical literature; we shall 
summarize them briefly here and refer the reader to the original papers for more 
detailed discussion. 124 The central theme of current thinking about the nature of 
the bonding may be referred to as the ionic-covalent theory; it maintains that 
hard— hard interactions involve strong ionic bonding, whereas soft-soft inter- 
actions occur mainly through covalent bonding. Speaking more specifically, one 
may say that the sites of interaction between a hard acid and a hard base combine 
relatively large charges with small size ; the result is that electrostatic (coulombic) 
forces are large. A strong, highly ionic bond results. In a soft-soft interaction, on 
the other hand, the easily polarized orbitals of the acid and base interact strongly 
to produce a bonding orbital extending over both atoms, the electron pair is 
effectively shared, and good covalent bonding results. The strengths of soft-soft 
interactions are enhanced when, in addition to those electrons directly involved 
in the formation of the a bond, the acceptor has unshared electrons ancTtlTe 
donor has low-lying vacant orbitals. These features allow covalent 77 bonding by 
donation of electrons by the acid back to the base, with resulting increase in 
stability of the complex. This factor is most important in compounds in which the 
acid is a transition metal ion. 125 


1. Using the pK a values in the table below, find, with the aid of Figure 3.1, (a) the 
fraction of each compound protonated in 60 percent H 2 S0 4 ; (b) the H 2 S0 4 -water 
mixture required to protonate 40 percent of 4,4'-dinitrobenzophenone. 

Compound pK a of Conjugate Acid 11 

Diethyl ether 






E. M. Arnett, Prog. Phys. Org. Chem., 1, 223 (1963). 

% A 0.01 molal solution of c^COH in H 2 S0 4 freezes at 10.09°C. The freezing 
point of pure H 2 S0 4 is 10.36°C, and the molal freezing-point depression constant is 
6.81 °C. Explain. 

3. What would be the pK a of a base that was 25 percent protonated in HS0 3 F 
containing 10 percent by weight SbF B ? 

124 See (a) note 110, p. 165, (b) K. S. Pitzer, J. Chem. Phys., 23, 1735 (1955); (c) K. S. Pitzer and 
E. Catalano, J. Amer. Chem. Soc, 78, 4844 (1956); (d) R. S. Mulliken, J. Amer. Chem. Soc, 77, 884 
(1955). For a summary see Pearson, notes 117 (a) and 117 (c), p. 166. 

125 S. Ahrland, Structure and Bonding, Vol. 1, Springer-Verlag, Berlin, 1966, p. 207. 

References for Problems 169 

4. Draw orbital structures for <f>CH. 2 ~ and for <j>~, and explain on the basis of the 
structures why <f>H would be expected to be a weaker acid than <f>GH a and why a might 
be different for the two compounds. 

5. In cyclopropane, the C — C — C bond angle is 60°, but it is thought that the 
angle between the orbitals is greater, that is, that the bonds are bent outwards so that the 
electron density is not a maximum along the C — C line but rather is maximum along 
some curve passing outside the C — C line. If the H — C — H bond angles are 119°, find 
the angle between the two hybrids the carbon uses to form C — C bonds to its neighbors. 
Find the percent s character of the C — C and of the C — H bonds, and compare the 
percent s character of the C — H bonds with that of C — H bonds in acetylene, ethylene, 
and cyclohexane. Compare these results to the acidities in Table 3.9. (Information 
needed to solve this problem is in Appendix 1 to Chapter 1.) 


5. See Appendix 1, Chapter 1. The H — C — H bond angle quoted is the average of 
values obtained by O. Hassel and H. Viervoll, Acta Chem. Scand., 1, 149 (1947) 
(118.2°, electron diffraction) and by Hs. H. Gunthard, R. C. Lord, and T. K. 
McCubbinJr., J. Chem. Phys., 25,768 (1956) (120°, vibration-rotation spectrum). 

Chapter 4 



A large number of organic reactions, differing often in mechanism and in the 
nature of the attacking reagent, are overall substitution reactions on carbon in 
which Y replaces X. Equation 4.1, which, in order to be as general as possible, 
ignores charges, bonding electrons, and substituent groups, is a schematized 
representation of these displacements. 

Y + C— X > C— Y + X (4.1) 

Nucleophilic aliphatic substitution is the displacement from saturated carbon of a 
group with its bonding electrons by a group with an extra pair of electrons 
(Equation 4.2). 

R R 

I I 

Y: + R— C— X > Y— C— R + X: (4.2) 

R R 

B x AB 2 ABj B a 

Since both the entering group (or nucleophile) and the leaving group are Lewis 
bases, Equation (4.2) is an example of a Lewis acid-base reaction in which 
one base replaces another in the Lewis acid-base adduct. Reactions corresponding 
to Equation 4.2 fall mainly into four charge types. 1 In these the Lewis bases are 
either uncharged or carry a single negative charge. 2 

1 E. D. Hughes and C. K. Ingold, J. Chem. Soc, 244 (1935). 

2 Some few nucleophiles such as S2O3 2 " carry a double negative charge. 


Stfl and S#2 Substitution Mechanisms 171 
















-> R— I + Cl- 

> R— OH 2 + I- 

> R— CI + NH 3 

NH 3 + R— SR 2 > RNH 3 + SR 2 

I" + RC1 — 
H 2 + R— I 

CI" + RNH 3 


In 1933 the two still widely accepted mechanisms for nucleophilic displacement 
reactions were proposed by Hughes, Ingold, and Patel. 4 They found that 
decomposition of quartenary ammonium salts, R 4 N + Y _ , to give R 3 N and RY 
exhibited two different kinds of kinetic behavior depending on the ammonium 
salt used. For example, when methyl alcohol was formed from trimethyl-n- 
decylammonium hydroxide (Equation 4.3), the rate of formation of methyl 
alcohol was found to be second-order, first-order each in trimethyl-n-decylam- 
monium cation and in hydroxide ion as in Equation 4.4. On the other hand, 
the rate of formation of diphenylmethanol from benzhydryltrimethylammonium 

CH 3 



CH 3 -5-N— CH 2 ( CH 2 ) 8 CH 3 
CH 3 

-»■ HOCH 3 + :N— CH 2 (CH 2 ) 8 CH 3 (4.3) 
CH 3 

rate = A(CH 3 ) 3 NC 10 H 21 ][OH-] (4.4) 

hydroxide was found to be overall first-order — dependent only on the ammonium 
ion concentration as in Equation 4.6. Added hydroxide ion did not change the 
rate. This and related evidence led the authors to postulate that these reactions, 

H CH 3 H 

jrfow^ / \_ c+ + , N _CH 3 -^U / V-C— OH 

H CH 3 

/ \— C— N— CH 3 

CH 3 


rate = A 1 [^ 2 CHN(CH 3 ) 3 ] (4.6) 

so closely related in starting materials and products, nevertheless proceed by two 
different mechanisms. 

In the decomposition of trimethyl-n-decylammonium hydroxide (Equation 
4.3) , they suggested, OH ~ attacks one of the methyl groups, forcing the substi- 
tuted amine to depart. Both ammonium and hydroxide ions are part of the 

3 Comprehensive reviews of S N 2 substitution can be found in: (a) S. R. Hartshorn, Aliphatic Nucleo- 
philic Substitution, Cambridge University Press, London, 1973; (b) A. Streitwieser, Solvolytic Displace- 
ment Reactions, McGraw-Hill, New York, 1962; (c) C. K. Ingold, Structure and Mechanism in Organic 
Chemistry, 2nd ed., Cornell University Press, Ithaca, N.Y., 1969. 

4 E. D. Hughes, C. K. Ingold, and C. S. Patel, J. Chem. Soc, 526 (1933). 



Y: +- 

Y + :X 

Reaction coordinate 
Figure 4.1 Proposed reaction coordinate diagram for the S N 2 reaction. 

activated complex of this single-step reaction, and therefore both enter into the 
rate equation. 

The decomposition of benzhydryltrimethylammonium hydroxide (Equation 
4.5), on the other hand, according to Ingold, proceeds by initial slow formation of 
the relatively stable diphenylmethyl carbocation 5 and subsequent fast attack on 
the carbocation by hydroxide. Because hydroxide is not part of the activated 
complex of the slow step of this reaction, it does not enter into the rate equation. 

Hughes a nd_ Ingold. in 1935. went on tojostjdatejhat these mechanisms, or 
a combination of them h vwh'eh tr| e mir-lee-phile plays an inter mediate rp le in the 
departure .of_i:li^Je.aizirig_grniip j are general f or all aliphatic nu c leophilic substi- 
tut ions. 6 

Broadly, then, if the substitution site is primary, and therefore access to it is 
not hindered sterically, the nu cleophile^ approaches it ..andjjjy^ donation of its 
eiectron_gair, forms a partial bond to, carbon while the leaving-group — carbon 
bond begins to break (Equation 4.7). At the transition state, both bonds partially 

Y: + — C— X 



Y— C— + :X 


transition state 

exist, although bond making and bond breaking need not have occurred to the 
same extent. When the reaction is over, the role of the Lewis bases is reversed 

fivTmj4iat ir| trie starting materia] • V is sharing i't§ lone pa ir but X is .not. Thus Y is 
qne unit less and X one unit more ne gatively charged , Tjiis is rajjerHjieS^ (sub- 
s titution-nucleophilic-bimo lecular) mechanism. 

The reaction coordinate diagram that corresponds to this proposed 
mechanism for the direct displacement reaction is shown in Figure 4. 1 . Although 

5 We use the term carbocation to refer to any cationic carbon species. For more about the nomen- 
clature of carbocations, see Chapter 6, p. 288. 

6 J. L. Gleave, E. D. Hughes, and C. K. Ingold, J. Chem. Soc, 236 (1935). 

S w l and S w 2 Substitution Mechanisms 173 


Reaction coordinate 
Figure 4.2 Proposed reaction coordinate diagram for the S w l reaction. 

the figure indicates that there is no energy minimum on the reaction coordinate 
between reactants and products, we. cannot be absolutely sure that this is an 
accurate representation. A small energy dip prior to rate-determining attack of Y: 
on the substrate would be very difficult to detect experimentally. 7 

The se cond mechanis m js the usual pathway if the substitution site has three 
alkyjjjroups on it or is conjugated with Jwo aromatic rings. In this case the bond 
to the leaving group cleaves heterolytically and a carbocation is formed. Then, in 
a second step, the nucleophile attacks this highly reactive intermediate as shown 
in Equation 4.5. In Lewis acid-base language, Reaction 4.5 can be described as 
follows : Th e Lewis jicicb= ha s p adrhi ct dissociate s-te-a-Le w is a ci d-(thf-carbocation) 

and a Lewis base (the lea ving gr oup_)_;,the rarhnratimiJhenJmrnediatety -forrns a 
second Lewis 'acicPBaseaidduct ^with a new base (the nucleophile). The net result 
of tHFreaction, asjn Reaction 4.3, is that the two Lewis bases have exchanged 

Figure 4.2 shows the reaction coordinate diagram for this mechanism. The 
carbocation is a real intermediate and thus lies at an energy minimum; energy 
maxima occur both when the C — X bond is stretched, and when the C — Y bond 
is formed. This process will be considered in detail in Chapter 5. A number of 
modifications of the original Ingold S N 1 mechanism must be made to accommodate 
the results of more recent investigations. 

The mechanism shown in Reaction 4.7 is still widely accepted as one of the 
two general mechanisms for nucleophilic aliphatic substitution. It is widely 
accepted today because in the intervening years a large bulk of experimental evi- 

7 Sneen and Larsen have proposed that processes that are called S„2 may involve initial rapid 
formation of an ion pair followed by rate-determining attack of a nucleophile on the ion pair as in 
the following equation: 


RX =± R+X- - > RY 


We mention the Sneen-Larsen mechanism again in Section 5.4. It is controversial, and for the 
purposes of the discussion in this chapter we shall use the traditional Ingold S N 2 model. The case 
for the ion-pair S„2 mechanism is given by: R. A. Sneen and J. W. Larsen, J. Amer. Chem. Soc, 91, 
362, 6031 (1969); R. A. Sneen, G. R. Felt, W. C. Dickason, J. Amer. Chem. Soc, 95, 638 (1973); 
and R. A. Sneen, Accts. Chem. Res., 6, 46 (1973). For one of the arguments against it, see V. F. Raaen, 
T. Juhlke, F.J. Brown, and C.J. Collins, J. Amer. Chem. Soc, 96, 5928 (1974). 

174 Bimolecular Substitution Reactions 

dence has been found that suggests that this is indeed a good description of the 
pathway of a class of displacement reactions. We shall examine the evidence 
below, but first, since this is the first chapter on reaction mechanisms, let us 
emphasize that a mechanism is "good" only insofar as it explains the experimental data, 
and that, therefore, although the experimental results that follow can be thought of as the 
"characteristics" of the S N 2 mechanism, they are in fact the observable data on whose basis 
it has been conjectured. The data are facts; the mechanism is a theory deduced from those facts. 


In the 1890s, many years before the mechanism of direct substitution was pro- 
posed by Hughes and Ingold, Walden had observed that some reactions of 
optically active compounds give products of opposite absolute configuration 
from the starting materials. 8 Walden, however, was not able to discover what 
conditions brought about this inversion of configuration. His task was compli- 
cated by the fact that two compounds of the same absolute configuration may 
nevertheless have opposite signs of optical rotation. In the following 40 years a 
great deal of work and thought was given to the problem of the relation of Walden 
inversion, as it is still called, to mechanism. 9 Then, in 1935, Hughes and co- 
workers in ingenious experiments clearly showed that Walden inversion occurs in 
direct nucleophilic substitution. 10 

These workers studied the exchange reaction of optically active j-octyl 
iodide with radioactive iodide ion in acetone (Equation 4.8) and found that: (1) 
the kinetics are second-order, first-order each in octyl iodide and in iodide ion, 

*I- + CH 3 (CH 2 ) 5 CHCH 3 > I" + CH 3 (CH 2 ) 5 CHCH 3 

I I (4-8) 

I *I 

and thus the mechanism is bimolecular; and (2) the rate of racemization is 
twice the rate of incorporation of labeled iodide ion into the organic molecule. 
The rate of racemization must be twice the rate of inversion. (If an optically 
active compound begins to racemize, each molecule that undergoes inversion is 
one of a racemic pair of molecules; for example, pure levorotatory starting 
material is 100 percent racemized when only 50 percent of it has been converted 
to the dextrorotatory isomer.) So, if the rate of racemization is twice the rate of 
incorporation of radioactive iodide, then each attacking iodide ion inverts the molecule 
it enters. 

This one-to-one correlation of inversion with displacement must mean that 
the incoming iodide enters the molecule from the side of the substitution site 
opposite to the departing iodide every single time. It initially attacks the back 
lobe of the sp 3 orbital used for bonding with the iodide. The transition state pro- 
posed by Hughes and co-workers is shown in 1. Carbon has rehybridized and is 

8 P. Walden, Cfem. Ber., 26, 210 (1893); 29, 133 (1896); 32, 1855 (1899). 

9 For a comprehensive summary of this work see Ingold, Structure and Mechanism in Organic Chemistry, 
pp. 509ff. 

10 (a) E. D. Hughes, F. Juliusburger, S. Masterman, B. Topley, and J. Weiss, J. Chem. Soc, 1525 
(1935); (b) E. D. Hughes, F. Juliusburger, A. D. Scott, B. Topley, and J. Weiss, J. Chem. Soc, 1173 
(1936); (c) W. A. Cowdrey, E. D. Hughes, T. P. Nevell, and C. L. Wilson, J. Chem. Soc, 209 (1938). 

Stereochemistry of the S N 2 Reaction 175 

R 12 °\R 


using three sp 2 orbitals for bonding with the nonreacting ligands and the remain- 
ing p orbital for forming partial bonds with X and Y. The geometry is that of a 
trigonal bipyramid with the entering and leaving groups in the apical positions. 
Because of its accordance with experimental facts, and because of its compati- 
bility with our ideas about bonding, this transition state has been universally 
accepted. See Section 10.3 for a further discussion of the Sjv 2 transition state. 

Inversion of configuration in the displacement of iodide by radioactive 
iodide and in all reactions of charge type 1 might be explained on the grounds 
that the bipyramidal transition state shown in 1 allows the entering and leaving 

Scheme 1 

CH 3 
/ V- C*— CI 





CH 3 

/ Y_ C *_ S — H 

GH 3 I 

CH 3 
/ \_c*— NH 2 

CH a 


/ V-*C-S(CH 3 ) 2 

CH 3 

/ \_*c_N 3 + 

GHq — S— CHq 

CH 3 

/ \—*C— NH a 


176 Bimolecular Substitution Reactions 

groups, both of which carry a partial negative charge, to be as far away from 
each other as possible, thus minimizing electrostatic repulsion. 11 That this 
explanation is not correct is shown by the fact that even reactions of charge type 3, 
in which the entering and leaving groups bear opposite charges, go by inversion. 12 
Hughes and co-workers carried out the reactions shown in Scheme 1 . 

A sample of optically active 1-phenylethyl chloride was converted to the 
corresponding azide with sodium azide while another was converted to the thiol 
with sodium hydrogen sulfide. Both of these second-order reactions are of charge 
type 1, processes already shown to proceed with inversion. Thus both the thiol 
and the azide have the configuration opposite to that of the starting chloride. 
The azide was then reduced with hydrogen over platinum to the corresponding 
amine, and the thiol was converted to the dimethylsulfonium salt. Neither of these 
processes disturbs the chiral center, and therefore both of these compounds have 
the opposite configuration to that of the starting material. Then, in another 
second-order substitution reaction, the sulfonium salt was converted to the azide 
and the azide reduced to the amine. This amine had the opposite configuration 
of the amine produced by the first route, and therefore the substitution (of charge 
type 3) of azide ion on the sulfonium salt must occur with inversion of configura- 

There is now a great deal of evidence that all S^ reactions of all charge 
types proceed with inversion. 13 

Substitution in Bridged Ring Compounds 

Proof that a site incapable of undergoing inversion is also incapable of under- 
going a second-order substitution reaction has been obtained from bicyclic 
compounds. The bridgehead carbon of rigid bicyclic systems cannot invert with- 
out fragmenting the molecule, and indeed, compounds such as 1-bromotripty- 
cene (2) and 7,7-dimethyl-[2.2.1.]-bicydoheptyl-l-/>-toluenesulfonate (3) are 
completely inert when treated with a nucleophile under S^ conditions. 14 

H^C ,CH 3 

11 N. Meer and M. Polanyi, Z. Phys. Chem., B19, 164 (1932). 

12 S. H. Harvey, P. A. T. Hoye, E. D. Hughes, and C. K. Ingold, J. Chem. Soc, 800 (1960). 

13 See (a) note 10, p. 174; (b) note 12; (c) H. M. R. Hoffmann and E. D. Hughes, J. Chem. Soc, 
1252, 1259 (1964). 

14 (a) P. D. Bartlett and L. H. Knox, J. Amer. Chem. Soc, 61, 3184 (1939); (b) P. D. Bartlett and 
E. S. Lewis, J. Amer. Chem. Soc, 72, 1005 (1950). 

The Solvent, Substrate, Nucleophile, and Leaving 



The nature of the solvent and the structures of the substrate, nucleophile, and 
leaving group all help determine whether a nucleophilic displacement proceeds 
by a unimolecular or bimolecular pathway. They also all affect the rate of reac- 

The Solvent 15 

In solvating a charged species, a^lyen^dis^erses, .the ^charge overajarger area, 
which lower^jh^eji_er^y:_of_the jsysterru. For example, when a sodium ion is dis- 
solved in water, the positive charge on the sodium is dispersed among many 
water molecules. This is shown schematically in 4. 

H N i V H 
a+O— Na — O « + 

H ' ' 6 H 

H /,tX H 

The effect that increasing the solvent polarity has on the reaction rate 
depends in part on the relative charge densities in the starting material and in the 
transition state. If_the_staxtiiig-Jnatejaais_have^^ 

activated complex the charge is_alrgady dispersed, a more polar, sol vent shou ld 
lowerTHeT energy^Tthelstarting material-mere than the-energy of .the Jtransitipn 
siaJ^The result:wo.uld_be an 

This situation is shown in Figure 4.3a. On the other hand, if the trans ition .stale 
has^a hi gher charge densjtyjJtian the starting materia^iricreasingscdvexiLp^arity 
shouJgLlo^erJiie_^cji^jic^L£ner gy and i nc re as e th eratejTigure 4.3b). 

S w 2-reactions of charge types 1, 3, and 4 (see p. 171) all have more highly 
dispersed charge in the transition state than in the ground state. The effect on 


♦ K 

+ K 

x 1 

Y: + C 


X + 

-Y---C — X J - 

«-Y •C-X" 

•A' xi+ 

Charge type 1" 

Charge type 3 

Charge type 4 

them of changing solvent polarity is therefore described by Figure 4.3a; an 

inr.rea^ejmjLolyentpolaritysho m reaction rate. 

The only S w 2 reactions in which the transition states have a higher charge 

15 For a recent review of solvent effects on S„2 reactions see A. J. Parker, Advan. Phys. Org. Chem., 5, 

173 (1967). 




• — More polar solvent 
— Less polar solvent 

■ — — More polar solvent 
^— Less polar solvent 

Reaction coordinate 

Reaction coordinate 

(a) (b) 

Figure 4.3 (a) Reaction coordinate diagram for a reaction in which starting material has a 
higher charge density than transition state, (b) Reaction coordinate diagram 
for a reaction in which the transition state has a higher charge density than the 
starting materials. 

density than the starting materials are those of charge type 2 in which two neutral 
starting materials produce a dipolar transition state. 


Y: + 



a + Y- -C- ••X*- 


Charge type 


Qnlyjhese^jhen ,_wcm Id be_expected toshow a.rateincxease3¥h.eii-xuft4fi-a-Biore 

These predictions of effect of solvent polarity on reaction rates were first 
made by Hughes and Ingold in 1935. They searched the literature of direct 
displacement reactions and found that for charge types 1-3 the experimental 
facts agreed with their predictions. For example, the reaction of ethyl iodide with 
triethylamine (Equation 4.9) an S N 2 displacement of type 2, does proceed more 

(CH 3 CH 2 ) 3 N: + CH 3 CH 2 I * (CH 3 CH 2 ) 4 N + + I" (4.9) 

rapidly in alcohols than in hydrocarbons; 16 and on the other hand, both the rate 
of bromine exchange between radioactive bromide ion and n-butyl bromide in 
acetone (Equation 4.10), a substitution of charge type 1, and the rate of alkaline 

*Br" + BrCH 2 CH 2 CH 2 CH 3 

-+ BrCH 2 CH 2 CH 2 CH 3 + Br" 


hydrolysis of trimethylsulfonium ion (Equation 4.11) in water /methanol (charge 

OH" + (CH 3 ) 3 S + * CH 3 OH + (CH 3 ) 2 S (4.11) 

type 3), are slower if water is added to the solvent. 17 

16 N. Menshutkin, Z. Pkysik. Chem., 5, 589 (1890). 

17 (a) L.J. LeRoux and S. Sugden, J. Chem. Soc, 1279 (1939) ; (b) L.J. LeRoux, C. S. Lu, S. Sugden, 
and R. H. K. Thomson, J. Chem. Soc, 586 (1945) ; (c) Y. Pocker and A. J. Parker, J. Org. Chem., 31, 
1526 (1966). 

The Solvent, Substrate, Nucleophile, and Leaving Group 179 

It is only more recently that reactions of Charge type 4 have been known 
and studied, but the theory proposed by Hughes and Ingold predicted the results 
accurately here too, for the reaction of trimethylamine with trimethylsulfonium 
ion (Equation 4.12) proceeds more rapidly in nonpolar than in polar solvents. 18 

(CH 3 ) 3 N + (CH 3 ) 3 S + * (CH 3 ) 4 N + + (CH 3 ) 2 S (4.12) 

In fact, most of the data that have accumulated since 1935 are qualitatively in 
accord with their predictions, 19 but the predictions should not be used indis- 
criminately without considering the effect the solvent may have on nucleophile 
and leaving-group reactivity (see pp. 190-194). 

Substrate Alkylation 

It i s awell-estab lished^ fact jhat_Sj^2 .reactions occur less readily m molecules 
where the « or / 3 carbjQnshear..alkyl substituents. For example, the relative reacti- 
vities shown in Table 4.1 are derived from studies of 15 different S w 2 reactions in 
various solvents. Several explanations have been proposed for this trend. The 
first supposes that alkyl groups bonded to saturated carbon are electron-donat- 
ing. 20 According to this hypothesis, in the ground state the central carbon is 
slightly electron-deficient because of the electron-withdrawing ability of the 
leaving group, but in the activated complex the positive charge on the carbon 
has diminished due to the presence of a second Lewis base with its unshared pair 
of electrons. Thus electron-donating groups stabilize the ground state more than 
the transition state and thereby increase the activation energy. 21 

However, recent experiments show that the polar 22 influence of a methyl 

Table 4.1 Average Relative S w 2 Rates of Alkyl Systems 
R in R — X Relative Rate 




3.3 x 10- 2 


1.3 x 10- 2 


8.4 x 10-* 


5.5 x 10" 5a 


3.3 x 10- 7 





Source: Data from A. Streitwieser, Solvolylic Displacement Reactions, McGraw-Hill, New York, 1962, 
p. 13. Reproduced by permission of McGraw-Hill. 

This value is not from Streitwieser but is the reactivity of (-butyl bromide to S N 2 substitution by 
free CI " in DMF at 25°C relative to the reactivity of CH 3 Br under the same conditions [D. Cook 
and A.J. Parker, J. Chem. Soc. B, 142 (1968)]. This value is corrected for the substitution that actu- 
ally precedes by an elimination addition mechanism. 

18 E. D. Hughes and D. J. Whittingham, J. Chem. Soc, 806 (1960). 

19 For other examples see: (a) note 15, p. 177; (b) C. K. Ingold, Structure and Mechanism in Organic 
Chemistry, 2nd ed., Cornell University Press, Ithaca, N.Y., 1969, pp. 457-463. 

20 (a) C. N. Hinshelwood, K. J. Laidler, and E. W. Timm, J. Chem. Soc, 848 (1938) ; (b) P. B. D. de 
la Mare, L. Fowden, E. D. Hughes, C. K. Ingold, and J. D. H. Mackie, J. Chem. Soc, 3200 (1955). 

21 A. Streitwieser, Solvolylic Displacement Reactions, McGraw-Hill, New York, 1962, p. 14. 

22 The term polar effect refers to the influence, other than steric, that nonconjugated substituents exert 
on reaction rates. It does not define whether the mechanism for its transmission is through bonds 
(inductive effect) or through space (field effect). 


group when bound to sp 3 carbon is not electron-donating. Alkyl groups, due to 
their greater polarizability than hydrogen, appear to be either electron-with- 
drawing or electron-donating depending on the electronic demands of the neigh- 
boring atoms 23 (see Section 3.4). In any case the difference between the polar 
effect of methyl and that of hydrogen is very small — much too small to account 
for the large retardation observed with increasing substitution. 24 This is especially 
obvious in the neopentyl system, where the branching is one carbon atom re- 
moved from the reaction site but the rate of substitution is ca. 10 ~ 5 times slower 
than in the ethyl system. 

An explanation standing on firmer experimental ground is that the decrease 
in rate with increasing substitution is caused by nonbonding interactions in the 
transition state. This explanation was first proposed by Dostrovsky, Hughes, and 
Ingold 25 and was later refined in a series of eight papers 26 that were then 
summarized by Ingold. 27 

In the ground state all H — C — H and H — C — X bond angles in CH 3 X are, 
of course, approximately 109.5°. The activated complex of an S N 2 reaction on this 
substrate is more crowded: the H — C — X bond angles have decreased to 90°, 
whereas the H — C — H bond angles increase to 120° and an additional atom or 
group of atoms (Y:) is included which also forms an angle of only 90° with the 
protons. Ingold et al. calculated that in CH 3 X, because the protons are small, 
there is little, if any, increase of nonbonding interaction between X and Y and 
the protons in going from the ground state to the transition state. However, when 
one of the H's is replaced by the much larger CH 3 group (i.e., when CH 3 CH 2 X 
is the substrate), the interference between X and Y and the methyl group does 
increase as the angle between them decreases. This leads to (1) compressions of 
the covalent bonds to lengths shorter than normal and (2) a corresponding in- 
crease in potential energy. 28 Thus the activated complex of the ethyl system has 
a higher potential energy relative to the starting material than that of the methyl 

A closely related argument for the decrease in rates with increasing substi- 
tution, put forward by Bauer, Ivanoff, and Magat, 29 is that it is not the enthalpy 
(through the potential energy), but the entropy of activation that is affected. 
They propose that the greater number of atoms associated with the transition 
state as compared to the ground state restricts the motion of these atoms ; this 

23 (a) H. Kwart and L. J. Miller, J. Amer. Chem. Soc, 83, 4552 (1961) ; (b) H. Kwart and T. Take- 
shita, J. Amer. Chem. Soc., 86, 1161 (1964); (c) R. C. Fort and P. v. R. Schleyer, J. Amer. Chem. Soc, 
86, 4194 (1964); (d) V. W. Laurie and J. S. Muenter, J. Amer. Chem. Soc, 88, 2883 (1966); (e) 
J. I. Brauman and L. K. Blair, J. Amer. Chem. Soc, 90, 6561 (1968); (f) N. C. Baird, Can. J. Chem., 
47, 2306 (1969). 

24 (a) H. D. Holtz and L. M. Stock, J. Amer. Chem. Soc, 87, 2404 (1965); (b) H. J. Hinze, M. A. 
Whitehead, and H. H. Jafft, J. Amer. Chem. Soc, 85, 148 (1963). 

25 I. Dostrovsky, E. D. Hughes, and C. K. Ingold, J. Chem. Soc, 173 (1946). 

26 F. B. D. de la Mare, L. Fowden, E. D. Hughes, C. K. Ingold, and J. D. H. Mackie, J. Chem. Soc, 
3169 (1955) et seq. See also C. K. Ingold, Structure and Mechanism in Organic Chemistry, pp. 544ff. 

27 C. K. Ingold, Quart. Rev. (London), 11, 1 (1957); see also D. Cook and A.J. Parker, J. Chem. Soc. 
B, 142 (1968). 

28 See Figure 2.0. 

29 N. Ivanoff and M. Magat, J. Chim. Phys., 47, 914 (1950) ; E. Bauer and M. Magat, J. Chim. Phys., 
47, 922 (1950). 

The Solvent, Substrate, Nudeophile, and Leaving Group 181 

causes a decrease in the entropy of the system, which in turn raises the free energy 
of the transition state. 

Streitwieser points out that these enthalpy and entropy effects are inter- 
related. 30 If, in the transition state of a direct displacement reaction of Y: on 
CH 3 CH 2 X, the C — X and C — Y bonding distances were identical to those in a 
similar substitution on CH 3 X, the nonbonding interactions would be so great as 
to cause a large decrease in the freedom of the CH 3 group and thus a large de- 
crease in entropy. If, however, the distances between C and X and Y were so 
great at the transition state that no decrease in entropy occurred, there would 
be little bonding between C and X and between C and Y; in such a case the 
potential energy and thus the enthalpy of the transition state would be raised. 
What probably happens is that a compromise is achieved and the system adopts 
that configuration for the transition state that has the smallest increase in free 

When studying Table 4. 1 it may be surprising to see that neopentyl systems, 
in which all the substituents are in the j3 position, are substituted more slowly than 
i-butyl systems in which the substituents are directly on the reaction site. Ap- 
parently, steric hindrance is less important when the larger substituents are a, 
because in the activated* complex they all lie in a plane perpendicular to X and Y 
and thus are fairly well out of the way; only one /3 substituent can lie in this plane, 
as shown in Figure 4.4. If there are only one or two j3 substituents, it is still 
possible to rotate them out of the way of entering and leaving groups. However, 
when there are three, as in the neopentyl group, it is not possible, and substantial 
steric hindrance occurs in the transition state. 31 

Heteroatoms in the Substrate 

If the suggestion mentioned on p. 179, that there is less positive charge on the 
central carbon in the transition state than in the ground state, is correct, then 
electron-withdrawing substituents should decrease the rate of S w 2 substitutions. 

A variety of experiments testing this suggestion have been carried out, giving 
inconsistent results. Sometimes electron-withdrawing substituents accelerate and 
sometimes they decelerate S w 2 reactions. 32 

For example, the rate of displacement of bromide by thiophenoxide ion in 
l-bromo-2-chloroethane is slowed down by a factor of 5 compared to substitution 
in the structurally similar 1-bromopropane (Equations 4.13 and 4.14). 33 But the 

Figure 4.4 Transition state for S N 2 substitution in the neopentyl system. 

™ A. Streitwieser, Solvent Displacement Reactions, p. 23. 

31 C. K. Ingold, Structure and Mechanism in Organic Chemistry, pp. 547ff. 

32 For a summary see Streitwieser, Solvent Displacement Reactions, pp. 16-20. 

33 J. Hine and W. H. Brader, Jr., J. Amer. Chem. Soc, 75, 3964 (1953). 

182 Bimolecular Substitution Reactions 

Rel. rate 
C e H 5 S- + CH 2 CH 2 Br >CH 2 CH 2 SC 6 H 5 + Br" 1 (4.13) 

I ■ I 


C 6 H 5 S- + CH 3 CH 2 CH 2 Br > CH 3 CH 2 CH 2 SC e H 5 + Br" 5 (4.14) 

rate of reaction of />-chloro benzyl chloride with thiosulfate is 1.4 times the rate of 
the nonsubstituted compound (Equations 4.15 and 4.16) 34 

rel. rate 

1.4 (4.15) 

+ S 2 3 2 - > + CI" . 1 (4.16) 

In fact, as can be seen from Table 4.2, all para-substituted benzyl chlorides, 
whether the substituent be electron-donating or -withdrawing, 35 react faster than 
the unsubstituted compound with thiosulfate. 

Possibly one of the reasons for this apparent inconsistency in experimental 
results is that the view of the transition state represented above is correct for 
some, but not all, S#2 reactions. 

As we know, in the activated complex of an S^2 reaction, bond making and 
bond breaking have not necessarily occurred to the same extent. If the entering 
group (Y) is very nucleophilic and_do nates electrons more than the leaving 
group (X) is withdrawing them, then the positive charge on the carbon should 

Table 4.2 Relative Rates of Reaction of X — P \— CH 2 C1 
with S 2 3 2_ in 60% Aqueous Acetone 



ative Rate 

— t-Bu 


— CH 3 


— i-C 3 H 7 




— H 


— F 




— N0 2 


Source: R. Fuchs and D. M. Carleton, J. Amer. Chem. Soc, 85, 104 (1963). Reproduced by permis- 
sion of the American Chemical Society. 

34 R. Fuches and D. M. Carleton, J. Amer. Chem. Soc, 85, 104 (1963). 

36 Methyl attached to an sp or sp 2 carbon seems always to be electron-releasing, if not by electron 
transfer, by polarization of the ir-electron system. See, for example, the calculations of Hoffmann : 
L. Libit and R. Hoffmann, J. Amer. Chem. Soc, 96, 1370 (1974). 

The Solvent, Substrate, Nucleophile, and Leaving Group 183 

decre ase and we have the situation already discussed above in which electron- 
withdrawing groups increase the rate; but if X is an excellen t leaving group jind 
withdraws.eJectr_ons more than Y supplies them J _then.the partial positive charge 
on the reacting carbon should increase and electron- withdrawing substituents 
should decrease the rate. 36 (Of course, if the situation just described becomes very 
pronounced, the mechanism will change to S N 1.) The nature of the substrate also 
plays a role in determining the relative extents of bond making and breaking. If 
it can form a relatively stable carbocation, bond breaking is likely to have pro- 
ceeded further. Thus it is not surprising that the rates of S N 2 reactions that differ 
in nucleophile, leaving group, and/or substrate show a variable dependence on 
the polar influence of substituents. 

Another reason for the apparent inconsistencies in experimental data is that, 
depending on the nature and position of the substituent, steric and conjugative 
effects often outweigh polar influences. In order to study pure polar effects, Holtz 
and Stock have carried out rate studies of displacements by thiophenoxide ion on 
4-Z-bicyclo-[2.2.2]-octylmethyl toluenesulfonate (Equation 4.17). 37 


+ -oso 2 



This system has the virtues of (1) being completely rigid so that changing Z 
does not change the steric environment of the transition state and (2) having the 
substituent so far removed from the reaction site through saturated bonds that 
conjugation is impossible. They found that although alkyl substituents had little 
effect on the reaction rate, electron- withdrawing groups in general did increase 

Table 4.3 Relative Rates of 4-Z-Bicyclo[2.2.2]ocTYLMETHYL 
Toluenesulfonate with Thiophenoxide Ion 


Relative Rate 



CH 3 


CH 2 OH 


C0 2 Et 






Source: H. O. Holtz and L. M. Stock, J. Amer. Chem. Soc, 87, 2404 (1965). Reproduced by per- 
mission of the American Chemical Society. 

36 C. G. Swain and W. P. Langsdorf, Jr. , J. Amer. Chem. Soc, 73, 2813 (1951). See, for example, the 
calculations of R. F. W. Bader, A.J. Duke, and R. R. Messer, J. Amer. Chem. Soc, 95, 7715 (1973). 

37 See note 24 (a), p. 180. 

184 Bimolecular Substitution Reactions 

the rate (see Table 4.3). In these displacements thiophenoxide, which is an 
excellent nucleophile (see p. 189), is always the attacking reagent and therefore 
the results are not surprising within the context of the above argument. 

Carbonyl or Cyano Substitution 

Compound s tha thave_an ^,^car^orryJLgr_a :: mtrile^ group are usually p artirjjWjy 
reactive lrTSflgJ^reji^ionsJor example, when treated with potassium iodide in 


acetone, a-chloroacetone (C1CH 2 CCH 3 ) reacts 35,000, and a-chloroacetonitrile 
(C1CH 2 C=N) 3000 times faster than n-butyl chloride. 38 The probable reason 
for this increased reactivity is that there is partial bonding between the incoming 
nucleophile and the electrophilic carbon of the carbonyl or cyano group in the 
transition state. For example, Figure 4.5 shows an orbital representation of the 
activated complex for the displacement of chloride by iodide in a-chloroacetone. 
Bartlett and Trachtenberg have studied the kinetics of Reactions 4.18 and 
4.19, and their results provide strong support for this hypothesis. 39 When 7,5- 
dinitro-3-coumaranone (5) reacts with potassium iodide in acetone (Reaction 
4.18), the enthalpy of activation is 20 kcal mole -1 higher than when w-(4-aceto- 
2,6-dinitro)-phenoxyacetophenone (6) undergoes the analogous reaction (Reac- 
tion 4.19). 

2 N 

H 3 C 

ANt = 31.3 kcal mole- 1 

3 I + I II A//t = 10.2 kcal mole" 1 (4.19) 


N0 2 

s J. B. Conant, W. R. Kirner, and R. E. Hussey, J. Amer. Chem. Soc., 47, 488 (1925). 
s P. D. Bartlett and E. D. Trachtenberg, J. Amer. Chem. Sec, 80, 5808 (1958). 

The Solvent, Substrate, Nucleophile, and Leaving Group 185 

Figure 4.5 Transition state for S N 2 displacement of iodide ion on a-chloroacetone. 

Figure 4.6 Transition state for S w 2 displacement of iodide ion on 7,5-dinitro-3-coumara- 

In order to carry out a backside displacement on 5, the iodide must attack the 
reacting carbon in the plane of the ring. The carbonyl n bond is, however, per- 
pendicular to the plane of the ring and, due to the rigid ring structure of 5, cannot 
rotate to overlap with the incoming iodide. The transition state for this reaction is 
shown in Figure 4.6. On the other hand, the activated complex of iodide sub- 
stitution on 6 is probably very similar to that of substitution on a-chloroacetone 
(Figure 4.5). 

Nucleophilicity 40 

In an S w 2 reaction the role of the entering Lewis base is to use its unshared pair of 
electrons to "push" away the leaving Lewis base with its bonding pair. Thus a 
good nucleophile is one that readily donates its unshared pair to the substrate, 
allowing rapid reaction. If 8^2 reactions on carbon only are considered, a re- 
agent that is a good nucleophile for one substrate is usually a good nucleophile 
for all substrates in the same type of solvent. In fact, Swain and Scott have proposed 
that the nucleophilicity of a reagent can be represented by a constant value, n, 
which holds for carbon S w 2 reactions in protic solvents in general. The rate of an 

40 Two recent reviews of nucleophilicity are (a) R. G. Pearson, H. Sobel, and J. Songstad, J. Amer. 
Chem. Soc, 90, 319 (1968); (b) K. M. Ibne-Rasa, J. Chem. Educ, 44, 89 (1967). 


S w 2 reaction in a protic solvent can be predicted quantitatively if the n value of 
the attacking reagent and a second parameter, s, which represents the sensitivity 
of the substrate to the reagent's nucleophilicity, are known. 41 The quantitative 
relationship between these two parameters and the rate is the linear free-energy 
relationship (see Section 2.2) 

log 7— = ns 

in which k is the rate of an 8^2 reaction in which the nucleophile has nucleo- 
philicity n and the substrate has sensitivity s. The constant k is the rate of the 
standard reaction to which all others are compared. Swain and Scott have chosen 
the reaction of methyl bromide with water at 25°C as that reaction. The sub- 
strate, methyl bromide, is arbitrarily assigned an s value of 1 . 

The parameter n for a given nucleophile, Y, then is defined by the following 
equation : 

n = log ***»*•+* (4.20) 

*CH3Br + H a O 

To determine n directly for a specific nucleophile, its rate of reaction with methyl 
bromide is measured at 25°C ; the log of the ratio of this rate to the rate of reac- 
tion of the same substrate with H 2 gives n. If Y is a better nucleophile than 
water, n will be positive; if Y is a worse nucleophile, n will be negative. Water 
itself has an n value of zero. In Table 4.4 are listed the majority of the n values 

Table 4.4 Nucleophilic Constants (n Values) 

Nucleophile n Nucleophile n 





Br" 3.89 

Source: Data from C. G. Swain and C. B. Scott, J. Amer. Chem. Soc, 75, 141 (1953). Reproduced by 
permission of the American Chemical Society. 

41 C. G. Swain and C. B. Scott, J. Amer. Chem. Soc, 75, 141 (1953). 

H 2 



NH 2 — C— NH 2 

N0 2 



>— 0- 

N0 2 



CH 3 — C 


O" 1 ™- 






The Solvent, Substrate, Nucleophile, and Leaving Group 187 

Table 4.5 Nucleophilic Constants («ch 3 i Values) 


"CH 3 I 


pK a of Conjugate 
Acid in Methanol 

N0 3 " 

^ 3 Sb 

so 4 2 - 

SnCl 3 - 


ch 3 c— o- 


tf>— c— o- 

^4 3 As 

(^CH 2 ) 2 S 


^S0 2 NH" 

(CH 3 0) 3 P 

(<£CH 2 ) 2 Se 


(CH 3 CH 2 ) 2 S 

N0 2 " 

NH 3 

(CH 3 ) 2 S 

N(CH 3 



N 3 " 


CH 3 0" 

(CH 3 ) 2 Se 

NH a OH 

NH 2 NH 2 

(CH 3 CH 2 ) 3 N 


































































































Table 4.5 {Continued) 

Nucleophile «ch 3 i «pt a P^a of Conjugate 

Acid in Methanol 


<£S0 2 NCr 
(C a t 

(C 2 H 5 ) 2 NH 

(CH 3 0) 2 PO- 


SC(NH 2 ) 2 





SO 2 ~ 

[(C a H 8 ) a N] a P 

(C 4 H 9 ) 3 P 

(C 2 H 5 ) 3 P 
























































9.92 7.17 6.52 


-Se" ~ 10.7 

Source: Data from R. G. Pearson, H. Sobel and J. Songstad, J. Arner. Chern. Soc, 90, 319 (1968). 
Reproduced by permission of the American Chemical Society. 

. ^Pt(PvMClo + Y 

" n Pt = log- 

that have been determined. Since so few are known, they are of limited useful- 
ness. Table 4.5, however, gives some of the more plentiful, analogous n CH;jl 
values, 42 which are defined in just the same way as n values except that the 
arbitarily chosen standard reaction is the displacement on CH 3 I by methanol in 
methanol solvent. 43 Thus 

, *CH3l + Y /. q,n 

«ch 3 i = !°gT (4-21) 

'tcHai + CHaOH 

The s parameter for a particular substrate RX is determined by measuring 
the rate of a number of S w 2 reactions of RX with nucleophiles of known n. 
Log k/k is determined for each reaction, and these values are plotted against the 
corresponding n values. The best straight line that can be drawn through those 
points has slope s. A substrate that is more dependent than methyl bromide on the 
nucleophilicity of the attacking group will have an s value greater than 1, and 
one that is less dependent will have a smaller value. Table 4.6 lists s values for a 
few substrates. 

42 See note 40 (a), p. 185. 

43 There is a linear relationship between Swain's n values and Pearson's n C H 3 i values: n CH3l = 1.4 n. 

The Solvent, Substrate, Nucleophile, and Leaving Group 189 
Table 4.6 Substrate Parameters for Nucleophilic Attack 



CH 3 CH 2 OTs 

(Ethyl toluenesulfonate) 


— C 





/ V-CH Z C1 (Benzyl chloride) 


C1CH 2 CH 2 S 

(Mustard cation) 


CH 3 Br 

(Methyl bromide) 


Source: C. G. Swain and C. B. Scott, J. Amer. Chem. Soc, 75, 141 (1953). Reproduced by permission 
of the American Chemical Society. 

The first four compounds have lower s values than methyl bromide because 
each is quite reactive in itself and therefore is not very dependent on help from 
the nucleophile : /-toluenesulfonate is a good leaving group and does not need 
much assistance to begin to depart ; ring strain in propiolactone and in the mustard 
cation make a ring-opening S w 2 reaction very favorable; and the transition state 
of benzyl chloride is stabilized by resonance and therefore is easily reached. 

To get a better understanding of what the Swain-Scott equation means, 
we have rewritten it in Equation 4.22 in the form that makes the linear free- 
energy relationship more apparent. 

AG* = -2.303(RT)sn + AG * (4.22) 

AG* and AG * are the free energies of activation of the reaction under considera- 
tion and of the standard reaction, respectively. The latter is, of course, a constant, 
and at constant temperature, the quantity RT is also constant. Therefore, if a 
series of displacements are carried out on the same substrate in protic solvents 
but with different nucleophiles, Equation 4.22 says that the free energy of acti- 
vation depends linearly on the power of the nucleophile. Likewise, if the nucleo- 
phile and solvent are kept constant but the substrate is varied, the equation says 
that the free energy of activation depends linearly on the susceptibility of the 
substrate to changes in nucleophilicity. 

Use of the Swain-Scott equation can identify powerful nucleophiles in 
protic solvents, but it does not tell us why they are so. On first consideration we 
might expect that a strong base toward a proton would also be a good nucleo- 
phile. But in protic solvents the correlation of nucleophilicity with basicity is not 
good. In Table 4.5 the nucleophiles are arranged in order of increasing n CH;jI 
values, but a glance at the right-hand column shows that the pK a 's of their con- 
jugate acids jump around. Further analysis of Table 4.5 shows that atoms in a 
single row of the periodic table carrying like charges do decrease in both nucleo- 
philicity and basicity going from left to right (compare, for example, methoxide 
("ch 3 i = 6.29, pK a = 15.7) with fluoride ion (« CH3l = 2.7, pK a = 3.45)). How- 
ever, in a single group nucleophilicity increases but basicity decreases in going 


down the column. For example, the nucleophilicity of the halogens increases in 
the order F~<Cl~<Br~<I _ but the order of the basicity is exactly the 
opposite, I~ < Br" < Cl~ < F~. 

An explanation that has been frequently given for the observed order of 
nucleophilicity in protic solvents (as in Tables 4.4 and 4.5) is that a good nucleo- 
phile must be polarizable. But the role of the polarizability and even its direction 
have received varying interpretations. The most familiar hypothesis is that, as 
the reaction commences, the large electron cloud of the polarizable nucleophile 
is distorted toward the substitution site, resulting in appreciable bonding be- 
tween the entering reagent and the substrate with little attendant increase in 
steric strain at the transition state. More recently, Swain and Scott have suggested 
that polarization of the nonbonding electrons on the nucleophile away from the 
substrate at the transition state reduces the electrostatic repulsion between the 
two negatively charged species — the nucleophile and the leaving group — thus 
reducing the energy of the transition state and increasing the rate of reaction. 44 
Edwards and Pearson have, however, pointed out that if electrostatic repulsion 
were diminished in this way, so too would bonding between nucleophile and 
substrate in the transition state be diminished and the balance might well not be 
favorable. These authors suggest that the electrostatic repulsion considered by 
Swain is negligible compared to the much greater repulsion due to the Pauli 
exclusion principle between the electrons around the nucleophile and those 
around the substrate needing to occupy the same space at the same time. They 
conclude that it is the low-lying empty orbitals of polarizable nucleophiles that 
make them more reactive. In the transition state the entering group can accom- 
modate some of its lone pairs in those of its low-lying empty orbitals that are 
directed more away from the substrate than the ground-state orbitals would be — 
with a resultant decrease in energy. 45 

When S N 2 reactions are carried out in aprotic solvents, the nucleophilicity 
of reagents is dramatically different from that in protic solvents, and the n and 
"ch 3 i values of Tables 4.4 and 4.5 do not apply. The requirement that a base must 
be polarizable in order to be a good nucleophile becomes much less important, 
and there is a better correlation between proton basicity and nucleophilicity. For 
example, SeCN ~ reacts 4000 times as fast as CI ~ with methyl iodide in methanol 
at 0°C, but in dimethylformamide (DMF) also at 0°C, CI ~ reacts twice as fast as 
SeCN". 46 Even the order of halide reactivity can be reversed. Bromide reacts 18 
times as fast as Cl~ with methyl iodide in methanol, but in DMF, CI" reacts 
twice as fast as Br - . 47 

The apparent cause for this striking behavior is the difference in degree of 
solvation of the small negative ions in the two kinds of solvents — protic and 
aprotic. 48 In protic solvents such as methanol or water, these ions are highly 
solvated by hydrogen bonding (see Section 2.4). Thus their effective sizes are very 
large and their negative charges dispersed. 49 Solvation decreases in the same order 

44 See note 41, p. 186. 

45 J. O. Edwards and R. G. Pearson, J. Amer. Chem. Soc, 84, 16 (1962). 

46 B. O. Coniglio, D. E. Giles, W. R. McDonald, and A.J. Parker, J. Chem. Soc. B, 152 (1966). 

47 A. J. Parker, J. Chem. Soc. A, 220, (1966). 

48 A.J. Parker, Quart. Rev. (London), 16, 163 (1962). 

49 See also D. K. Bohme and L. B. Young, J. Amer. Chem. Soc, 92, 7354 (1970). 

The Solvent, Substrate, Nucleophile, and Leaving Group 191 

as charge density: OH~, F~ »C1~ > Br~ > I - > SeCN". The large ions, 
which are both relatively unsolvated and more polarizable, are much better 
nucleophiles. However, in aprotic solvents there is no possibility for stabilization 
of the negative charge on the small ions by hydrogen bonding, and they become 
more reactive, sometimes even overtaking the more polarizable larger ions. 50 

Pearson and Songstad have suggested that the nucleophilicity of a reagent 
can also be described in terms of hard and soft acid and base theory. 51 In Lewis 
acid-base terms, the mechanism of an S w 2 displacement can be written as in 
Equation 4.23. We already know that methyl cations (and, by analogy, other 

Bj + A— B 2 > [B 1 --A--B a ]* > BjA + B (4.23) 

alkyl cations) are considered moderately soft acids. If we make the reasonable 
assumption that the charge on the alkyl group does not change much in going 
from the ground state to the transition state, an alkyl group will also be soft in the 
transition state of an S w 2 reaction. Solvents such as methanol and water act as 
hard acids when their protons are used for hydrogen bonding, and therefore hard 
bases such as F~ or OH" interact preferentially with them rather than with 
moderately soft alkyl substrates. Aprotic solvents such as dimethyl sulfoxide are 
very soft acids : when displacements are run in them, the hard bases do not inter- 
act with them and thus are freer to react with alkyl substrates. 

Note that the n Pt values in Table 4.5, which give relative rates for Reaction 
4.24 with various bases in methanol, are highest for very soft bases [e.g., (C 6 H 5 ) 3 P, 

B + Pt(Py) 2 Cl 2 > Pt(Py) 2 ClB + CI" (4.24) 

(C 2 H g ) 3 As] which carry no charge on the donor atom and which have little 
attraction for the proton. Thus compared to Pt 11 , CH 3 + is only a moderately 
soft acid. It is thus apparent that nucleophilic strength at one substrate should not 
parallel the strength at another unless the two substrates are of comparable hard- 
ness or softness. 

Edwards has proposed an equation for the correlation of S w 2 reaction rates 
that can be used in different types of solvent systems and that emphasizes the 
dependence of nucleophilicity on basicity and polarizability. 52 The equation is 

log — = «£„+ pH (4.25) 

where //is the pK a of the conjugate acid of the nucleophile plus 1.74 and E n is a 
parameter that measures polarizability. Edwards first suggested that E n be 
defined in terms of the oxidation potential of the nucleophile, but more recently 
proposed a new definition based on the molar refractivity of the nucleophile. 
The constants a and /3 are determined experimentally for each substrate to give 
the best fit with experimental data. An advantage of the two-parameter equation 
is that it allows for a variation in relative nucleophilic reactivity when the sub- 

50 For further examples of the difficulty in assigning a reagent with an "intrinsic nucleophilicity," 

see C. D. Ritchie, Accts. Chem. Res., 5, 348 (1972). 

61 R. G. Pearson and J. Songstad, J. Amer. Chem. Soc, 89, 1827 (1967). 

52 J. O. Edwards, J. Amer. Chem. Soc, 76, 1540 (1954); J. O. Edwards, J. Amer. Chem. Soc, 78, 1819 

(1956). For another theoretical treatment of nucleophilic reactivities, see R. F. Hudson, Chimia, 16, 

173 (1962). 


strate is changed since the magnitude of a relative to /3 may change. A disadvan- 
tage is the larger number of parameters. The effect of solvent on nucleophilic 
reactivity is implicitly taken into consideration in the Edwards equation if// and 
E n are determined in the same solvent system used for the S^2 reactions. 

The Leaving Group 

Since the leaving group begins to pull a pair of electrons toward itself in the 

transition state of an S#2 reaction, it is to bee xpected that the be stjeaving groups 

wiirhg_those that, ran best stahjHze^jij^xtra_pair of electrons, that is, weakJLewis 

bases. This is usually the case. For example, Tables 4.7 and 4.8 indicate that the 

reactivity of the halogens seems always to be I > Br > CI > F. Furthermore, 

groups that have a positive charge in the original molecule but become small 

+ + + 

neutral molecules after they have departed, such as — SR 2 , — OH 2 , and — N 2 , 

often make good leaving groups. This can be very useful because displacements 
with leaving groups such as — OH, — OR, and — SH do not occur readily be- 
cause OH ~ , OR ~ , and SH ~ are strong bases. If such groups are simply pro- 
tonated, they can often be displaced. 

However, one cannot predict the relative reactivities of two leaving groups 
simply by a comparison of the p^ a 's of their conjugate acids. And indeed it 
would be surprising if one could, since we are here again dealing with the 
strengths of C — X, not H — X bonds. But this is not the only problem, as an 
examination of Tables 4.7 and 4.8 reveals. The relative reactivities of the leaving 
groups are dependent on the nucleophile and on the solvent. For example, in 
Table 4.7 we see that in ethanol with /(-toluenethiolate as the nucleophile, the 
reactivity ofp-toluenesulfonate ("tosylate," OTs) as a leaving group lies between 
that of bromide and that of chloride (cf. reactions 1, 3, and 5) — approximately 
what would be expected from the pK a values — but in the same solvent with 
ethoxide ion as the nucleophile, tosylate becomes more reactive than iodide 
(Reactions 2, 4, 6 in Table 4.7). The explanation suggested by Hoffmann is that 
the reactivity of tosylate relative to the halides is a function of the amount of 
substrate-leaving-group bond breaking in the transition state. 53 When the 
attacking reagent is the excellent nucleophile, /j-toluenethiolate (« C h 3 i of C 6 H 5 S" 
= 9.92), according to Hammond's postulate, the transition state occurs very early 
in the course of the reaction, before there has been much bond breaking. Then 
tosylate behaves normally in comparison to the halides. When the much poorer 

9 <T"W „ o JL/A 

O— S— </ V- CH 3 < y 0=S— (' V- CH n 

O O 


0=S— (/ y- CH 3 < y etc. (4.26) 


53 H. M. R. Hoffmann, J. Chem. Soc, 6753 (1965) and references therein. In Section 5.2 we conclude 
that although k , rs lk Br is a good measure of the extent of bond breaking in S K 2 reactions, this criterion 
cannot be extended to S N ] reactions. 

The Solvent, Substrate, Nucleophile, and Leaving Group 193 

Table 4.7 Dependence of Leaving-Group Reactivity on the Nucleophile 

Leaving Group, Reaction Substrate and Nucleo- Temp. k x /k Br Ref." 

X Number phile a (°C) 

I 1 rcC 3 H 7 X + />-CH 3 C 6 H 4 S- 25 3.5 * 

I 2 C 2 H 5 X + C 2 H 5 0- 25 1.9 

Br 1.0 

CI 3 nC 3 H 7 X +/>-CH 3 C 6 H 4 S- 25 0.0074 " 

CI 4 C 2 H 5 X + C 2 H s O- 40 0.0024 

— OS0 2 — / \-CH 3 5 nC 3 H 7 X + />-CH 3 C 6 H 4 S- 25 0.44 » 

-oso 2 -f\ 

CH 3 6 C 2 H 5 X + C 2 H s O- 25 3.6 " 

" All reactions were run in ethanol solvent. 

6 H. M. R. Hoffmann, J. Chem. Soc, 6753 (1965), and references therein. 

c A. Streitwieser, Solvolytic Displacement Reactions, McGraw-Hill, New York, 1962, pp. 30-31 and 

references therein. 

d The relative reactivity here was estimated by using the k oso2 -/ V-Br/^Br value of 5.8 calculated by 

Streitwieser (Ref. c above, p. 30) and multiplying that by 0.63, the relative reactivity of tosylate to 
benzene sulfonate (M. S. Morgan and L. H. Cretcher, J. Amer. Chem. Soc, 70, 375 (1948). Since the 
latter value is for reaction at 35°C, the real k or Jk Br value might be a little smaller. 

Table 4.8 Effect of Solvent on Leaving-Group Reactivity 



10 4 A 2 



CH 3 I + N 3 " 
CH 3 I + N 3 ~ 



3.1 x 
3.0 x 

10 3 
10" 2 

1 x 10 5 

CH 3 Br + N 3 - 
CH 3 Br + N 3 - 




2.7 x 

10" 2 

1.7 x 10 4 

CH 3 C1 + N 3 - 
CH3CI + N 3 " 



2.0 x 

10- 4 

5 x 10 3 

CH 3 I + SCN" 
CH 3 I + SCN" 





CH 3 Br + SCN" 
CH 3 Br + SCN" 





CH 3 C1 + SCN" 
CH 3 C1 + SCN" 



2.0 x 
4.9 x 

10" 2 

10- 4 


Source: The data in the Table are from B. O. Coniglio, D. E. Giles, W. R. McDonald, and A.J. 
Parker, J. Chem. Soc. B, 152 (1966). Reproduced by permission of The Chemical Society and A.J. 

nucleophile, ethoxide (« CH3 i of CH 3 0~ = 6.29), is used, the leaving group already 
has a substantial negative charge on it in the transition state. In such cases tosylate, 
which is able to delocalize the charge by resonance, thereby decreasing the electro- 
static repulsion between entering and leaving groups, is a better leaving group 
than the halides (see Equation 4.26). 

Now let us turn to the effect of solvent on leaving-group activity. Examples 
of the pertinent experimental data for S w 2 reactions of charge type 1 are shown 
in Table 4.8. As we would predict from the previous discussion for reactions of 


this charge type (see p. 178), changing from the polar solvent methanol to the 
nonpolar solvent DMF greatly increases the rates of all the reactions. However, 
note that in the series of displacements by azide ion, when the leaving group is 
iodide, the rate is increased 10 5 times by the solvent change; when it is bromide, 
1.7 x 10* times; and when chloride is departing, the factor is only 5 x 10 3 . A 
similar series is observed when thiocyanate is the nucleophile. The explanation 
for this is very similar to that given for the solvent dependence of nucleophilicity. 
Apparently methanol is able to solvate the smaller activated complex 
[Y-CHg-Cl] - much better than it can [Y--CH 3 --I]". Therefore, although 
changing solvents from DMF to methanol is unfavorable for all the reactions in 
Table 4.8, it is not as unfavorable for methyl chloride, where the transition state 
can be effectively solvated, as for methyl iodide, where it cannot. 


There has been great interest in recent years in bimolecular nucleophilic displace- 
ment reactions on organic compounds where the site of substitution is not carbon 
but oxygen, sulfur, or silicon. Since there is not room to discuss each of these 
reactions here, we shall briefly consider bimolecular nucleophilic displacements 
on sulfur as an example and refer the reader to recent reviews of displacement at 
oxygen 55 and silicon. 56 

Bimolecular displacements on sulfur occur when sulfur is di-, tri-, or tetra- 
coordinated. Examples are shown in Equations 4.27-4.29. 57 

/ \— S— S0 3 " + CN" > / V-SCN + S0 3 2 


a^ILq + 1- -_ qJ-i + qJL (4,8) 

o o 


/ \— CH 2 — S— O-menthyl + ^-CH 3 — C 8 H 4 MgBr > 



/ \— CH 2 — S— C 8 H 4 — CH 3 -6 + BrMgO— menthyl (4.29) 

V^ II 


54 (a) E. Ciuffarin and A. Fava, Prog. Phys. Org. Chem., 6, 81 (1968); (b) W. A. Pryor, Mechanism of 
Sulfur Reactions, McGraw-Hill, New York, 1962, pp. 59-70; (c) W. A. Pryor and K. Smith, J. Amer. 
Chem.Soc, 92, 2731 (1970). 

55 For recent reviews of nucleophilic attack on oxygen, see: (a) R. Curci and J. O. Edwards, in 
Organic Peroxides, Vol. 1, D. Swern, Ed., Wiley-Interscience, New York, 1970, p. 199; (b) J. B. Lee 
and B. C. Uff, Quart. Rev. (London), 21, 429 (1967); (c) E.J. Behrman and J. O. Edwards, Prog. 
Phys. Org. Chem., 4, 93 (1967); (d) J. O. Edwards, in Peroxide Reaction Mechanisms, J. O. Edwards, 
Ed., Wiley-Interscience, New York, 1962, p. 67. 

56 For a comprehensive review of substitution reactions at silicon, see L. H. Sommer, Stereochemistry, 
Mechanism and Silicon, McGraw-Hill, New York, 1965. 

57 (a) J. L. Kice and J. M. Anderson, J. Org. Chem., 33, 3331 (1968); (b) J. L. Kice and G. Guaraldi, 

Bimolecular Nucleophilic Substitution at Sulfur 195 

Figure 4.7 Overlap of a d orbital on sulfur with a p orbital on an entering nucleophile. 

Dicoordinated Sulfur 

In its outer electronic shell divalent sulfur has two s and four p electrons, and it 
also has five empty 3</orbitals. A bimolecular nucleophilic displacement reaction 
on sulfur might then occur in a single step; or an intermediate such as 7, in which 
the sulfur accepts the pair of electrons of the entering Lewis base into one of its 


+ I 

Y: + X— S— R >• Y— S— R 


empty d orbitals, might be on the reaction path. For example, Figure 4.7 shows 
the overlap of an empty 3d orbital with a full/) orbital on an incoming nucleophile. 
The available evidence suggests that a one-step displacement is the usual 
pathway, but that some reactions may involve an intermediate. 58, 59 For example, 
if 7 does lie on the reaction path, then electron-withdrawing substituents on sulfur 
should stabilize it and the transition states for its formation and decomposition: 
The reaction should be faster than if there are electron-releasing groups on sulfur. 
The data in Table 4.9, however, show that for Reaction 4.27 the rate is acceler- 
ated by electron-withdrawing and electron-donating substituents in much the 
same way as are rates of direct displacements on para-substituted benzyl chlorides. 
An intermediate such as 7 thus seems precluded from the pathway for this 
reaction. Substitutions on divalent sulfur normally proceed in a one-step dis- 
placement in which both bond making and bond breaking occur at the transition 
state. When electron-donating substituents are present in the substrate, bond 
breaking is further advanced than bond making; and when electron-with- 
drawing groups are there, the opposite is true. In either case the transition 
state can be stabilized (see also Section 4.3, p. 183). 

J. Amer. Chem. Soc, 90, 4076 (1968); (c) M. A. Sabol and K. K. Andersen, J. Amer. Chern. Soc, 91, 
3603 (1969). 

58 For recent summaries of cases in which an intermediate may be involved in nucleophilic substi- 
tution on dicoordinate sulfur, see: (a) E. Ciuffarin and F. Griselli, J. Amer. Chem. Soc, 92, 6015 
(1970); (b) JL. Senatore, E. Ciuffarin, and A. Fava, J. Amer. Chem. Soc, 92, 3035 (1970); (c) E. 
Ciuffarin, J. Org. Chem., 35, 2006 (1970). 

59 Pryor has suggested that the addition-elimination mechanism involving intermediate 7 occurs 
when the attacking group is highly nucleophilic, the leaving group poor, and the central sulfur highly 
electronegative (see note 54 (c), p. 194). These same criteria for a two step mechanism would also 
arise from a consideration of a two-dimensional reaction coordinate diagram. 

196 Bimolecular Substitution Reactions 

Table 4.9 Effect of Electron-Donating and -Withdrawing Substituents 
on the Rate of Displacement Reactions on Carbon and Sulfur 

k z /k a 

Z CN- + Z— ^V-S— SO - .7.-/ V-SCN + SCV" ■ S„<V- + Z^^^-CH,CI .Z^^V-CH a S,0,- + Cl" 

CH 3 Tl L5 

H 1.0 1.0 

CI 1.8 1.4 

Br 1.3 — 

N0 2 1.3 2.1 

" Data from M. A. Sabol and K. K. Andersen, J. Amer. Chem. Soc, 91, 3603 (1969). 
6 Data from R. Fuchs and D. M. Carletan, J. Amer. Chem. Soc, 85, 104 (1963). 
Reproduced by permission of the American Chemical Society. 

Table 4.10 Comparison of the Rates of Sjv2 Reactions at Sulfur and at Carbon 

Relative Rates 


R— S— S0 3 -+S0 3 2 - 


-S— SR+-SR' 

RSCN+C 4 H 9 NH 2 RCH 2 X + Y- 

CH 3 



C 2 H 5 





i-C 3 H 7 


1.0 3.0 




0.000125 0.0011 

Source: Data from E. Ciuffarin and A. Fava, Prog. Phys. Org. Chem., 6, 81 (1968). Reproduced by 
permission of Wiley-Interscience. 

Even in a one-step S w 2 displacement, sulfur might use one of its empty d 
orbitals to accept the incoming pair of electrons at the same time as the leaving 
group begins to break away. If this did occur, backside displacement, which 
occurs in the S N 2 displacement on carbon because of the stereoelectronic require- 
ments of the transition state, would not be required, and the nucleophile could 
enter forming a very small angle with the leaving group. Evidence against even 
this kind of participation of the d orbitals comes from, the decrease in rates for 
Reactions 4.30-4.32 as the substrates are increasingly substituted with alkyl 
groups. As Table 4.10 shows, the decreases in rate due to increasing steric 

r_S_S0 3 - + SO3 2 - > R— S— SO3- + S0 3 2 " (4.30) 

R— S— S— R + R'S- > R— S— S— R' + RS" (4.31) 

R_S— CN + C 4 H 8 NH 2 > R— S— NHC 4 H 9 + HCN (4.32) 

requirements of the central sulfur run parallel to those of analogous substi- 
tutions on carbon. 60 The similarity in relative rates probably arises from a 
similarity in transition states — that is, bimolecular displacement at divalent 
sulfur, as at tetrahedral carbon, occurs from the back side (8) . 

60 For similar data for other displacements on dicoordinated sulfur, see : (a) C. Brown and D. R. 
Hogg, Chem. Commun., 38 (1967); (b) E. Ciuffarin and A. Fava, Prog. Phys. Org. Chem., 6, 81 (1968), 
p. 86. 

Bimolecular Nucleophilic Substitution at Sulfur 197 



If the entering and leaving groups made an angle considerably less than 1 80° in 
substitution on sulfur, then the bulky R groups could have more space, reducing 
the steric effect of R. It might be thought that backside attack is preferred in 
Reactions 4.30 and 4.31 in order to minimize the electrostatic repulsion of the 
entering and leaving groups, both of which bear partial negative charges. But in 
the transition state of Reaction 4.32 these groups carry opposite charges (9), and 
electrostatic forces would bring them as close together as possible. The fact that 

C 4 H 9 — N—S--CN 

r i- *- 

H R 

the steric effect of substituents is about the same for this reaction as for the 
others shows that frontside S#2 displacement probably does not occur even when 
the conditions for it are most favorable and therefore that d orbitals are usually 
not employed. 61 

Tricoordinated Sulfur 62 

The mechanisms of nucleophilic displacements on tricoordinated sulfur are not 
yet fully understood. The stereochemistry can be determined by studying the 
relative configuration of starting materials and products. 63 The substituents 
attached to tricoordinated sulfur form a tetrahedron with the lone pair occupying 
one of the apices (10) but, unlike its nitrogen-containing analog, the sulfur 

\ y. R i 

R 2 R3 

tetrahedron inverts only at high temperatures. Therefore sulfur compounds that 
have three different substituents (actually four counting the lone pair) on sulfur 

61 See D. R. Hogg and P. W. Vipond, Int. J. SulfurChem. C, 6, 17 (1971) for additional evidence that 
the transition state is linear. 

62 It might be useful at this point to review bonding in sulfur compounds. Remember that 

O o- 


R— S— R and R— S + — R 

are two ways of writing the same compound. Writing the first structure implies back bonding 
between a pair of electrons on oxygen and a d orbital on sulfur. 

63 K. K. Andersen, Int. J. SulfurChem. B, 6, 69 (1971); T. R. Williams, A. Nudelman, R. E. Booms, 
and D. J. Cram, J. Amer. Chem. Soc, 94, 4684 (1972) and references therein; D.J. Cram, J. Day, 
D. C. Garwood, D. R. Rayner, D. M. v. Schriltz, T. R. Williams, A. Nudelman, F. G. Yamagishi, 
R. E. Booms, and M. R.Jones, Int. J. SulfurChem. C, 7, 103 (1972). 

198 Bimolegular Substitution Reactions 

occur in resolvable enantioneric pairs, and those in which sulfur is part of a sub- 
stituted ring system form isolable geometric (cis-trans) isomers. In most cases, 
the product of a nucleophilic substitution on tricoordinated sulfur is found to 
have the opposite configuration from the starting material. 

For example, by optical rotary dispersion studies, Mislow has shown that 
Reaction 4.33 goes with 100 percent inversion of configuration. 64 


,, + CH 3 CH 2 MgBr > S + BrMgOC 10 H 19 (4.33) 

Similarly, Johnson has carried out the following two-step isomerization: 65 



+ (CH 3 CH 2 ) 3 OBF 4 - 

BF 4 - I CI 

r > />~^ s -^ -^ T^ /0"A° ,4^4, 


The product was obtained completely inverted in 93 percent yield from the sul- 
fonium ion. Since inversion on sulfur could not have taken place in the O- 
alkylation step, which involves only the oxygen atom, it must have occurred 
during the displacement of ~OCH 2 CH 3 by ~OH. 

What is the structure of the transition state or intermediate that leads to 
inversion ? All stable tetracoordinated sulfur compounds closely resemble trigonal 
bipyramids. 66 Thus it seems most likely that the tetracoordinated species leading 
to substitution on tricoordinated sulfur will also be a trigonal bipryamid. We 
might immediately assume that the position the entering and leaving groups take 
up in this structure is the same as their position in the transition state for S N 2 
substitution at carbon — that is, that the transition state or intermediate would 
be 11 in which the entering and leaving groups occupy the apical positions. 

R \ /■ 



64 K. Mislow, M. M. Greene, P. Laur, J. T. Mellilo, T. Simmons, and A. L. Ternay, Jr., J. Amer. 
Chem. Soc, 87, 1958 (1965). 

65 C. R.Johnson, J. Amer. Chem. Soc, 85, 1020 (1963). 

66 D. J. Cram, J. Day, D. R. Rayner, D. M. v. Schriltz, D. J. Duchamp, and D. C. Garwood, J. 
Amer. Chem. Soc, 92, 7369 (1970). 

Bimolecular Nucleophilic Substitution at Sulfur 199 

But Westheimer has pointed out that inversion would also result if the entering 
and leaving groups occupy radial positions as in 12. 67 

R— S— R 


Some displacements on tricoordinated sulfur in which entering and leaving groups 
are linked proceed with inversion on sulfur. These apparently must have a transi- 
tion state similar to 12. For example, in Reaction 4.35 the entering and leaving 
groups are most likely part of the same six-membered ring in the activated com- 
plex — a formation that cannot be accommodated by 11 (180° bond angles be- 
tween X and Y) but can be by 12. 68 Cram has suggested that if the entering and 

H 3 C N 

:— S->0 + 2TsN=S=N— Ts 



Hs ?,o- 



r* • O 

Br | 



TsN = 


H 3 C X 







•NTs (4.35) 


leaving groups are the most electronegative groups of the trigonal bipyramid 
and if the entering and leaving groups are not tied together in a ring system, 
then structure 11 is of lower energy. If either of these conditions is not fulfilled, 
then 12 may be more stable. 

Retention of configuration can only occur, in a reaction that has a trigonal 
bipyramidal transition state, if the leaving group occupies an apical, and the 
entering group a radial position (or vice versa), as in 13. Three cases of retention 

R >• 

Y---S— R 


67 (a) P. C. Haake and F. H. Westheimer, J. Amer. Chem. Soc, 83, 1 102 (1961). (b) The electron pair 
in 12 is shown in the equatorial rather than in the axial position because the axial positions are pre- 
ferred by the more electronegative groups and the equatorial by the more electropositive groups. 
(c) The structure shown in 1 1 arises from attack of the nucleophile on the face of the tetrahedron 
opposite to the apex occupied by the leaving group. We have already discussed the simple bonding 
model for 1 1 in Section 4.2 (p. 1 75) ; it is readily apparent from this model that 1 1 could be a transi- 
tion state for nucleophilic substitution on any sp 3 hybridized atom. The structures 12 and 13, on the 
other hand, arise from attack of the nucleophile on an edge of the tetrahedron. If the central atom is 
carbon or some other element that does not have empty d orbitals, then there is no simple bonding 
model that corresponds to 12 or 13; if d orbitals are present, oriented toward the edge of the tetra- 
hedron being attacked, they can accept the electrons of the nucleophile. 

68 See note 63, p. 197 and 66, p. 198. 


in nucleophilic substitutions on sulfoxides have now been reported. 69 (Equation 
4.36 gives an example.) 


H,C^ VL 

H 3 C 


-CH 3 + S=0 18 — 


H 3 C 

H 3 C. P. 18 CH 3 

s - X 

O CH, 

O O 18 

GH3 — S — CH3 + CjHj 

S— CH, 


In all of these reactions it is possible that the entering and leaving groups are part 
of a four-membered ring in the activated complex. If so, 13, with its 90° bond 
angle between X and Y, could certainly accommodate the activated complex 
better than either 11 or 12. 

Does bimolecular substitution on tricoordinate sulfur involve the formation 
of an intermediate, or is it a one-step process ? The evidence is somewhat incon- 
clusive. For example, when sulfite ester (14) is hydrolyzed with HO" containing 
18 0, 18 is found in the product but no significant amount is present in the 
recovered unreacted ester. 70 Bunton and co-workers interpreted this to mean 
that the mechanism shown in Reaction 4.37 in which the intermediate 15 is 
formed in a rapid equilibrium prior to the transition state for the reaction, is 
ruled out. If 15 were so formed, they reasoned, it would rapidly equilibrate with 
isoenergetic 16. Then loss of HO~ from 16 would result in 18 in recovered 



18 OH" + O P 

~O x "OH 

o /S ^o 




-> HOCH0CH0— S— 18 OH 


OH + 



o /S \) 

HO 18 0" 

o- S "o 





-> HOCH 2 CH 2 — S— OH 

69 (a) S. Oae, M. Yokoyama, M. Kise, and N. Furukawa, Tetrahedron Lett., 4131 (1968); (b) B. W. 
Christensen and A. Kjaer, Chem. Commun., 934 (1969); (c) B. W. Christensen, J. Chem. Soc. D, 597 

70 C. A. Bunton, P. B. D. de la Mare, P. M. Greasely, D. R. Llewellyn, N. H. Pratt, and J. G. Tillett, 
J. Chem. Soc, 4751 (1958); C. A. Bunton, P. B. D. de la Mare, and J. G. Tillett, J. Chem. Soc, 4754 

Bimolecular Nucleophilic Substitution at Sulfur 201 

starting material. Thus 15 must either be formed in a slow, nonreversible first 
step, or 15 is a transition state, not an intermediate. 71 

Kice, however, has suggested that this 18 exchange experiment is incon- 
clusive. 72 If hydroxide ion attacks 14, the most likely first intermediate would be 
17, in which the five-membered ring spans an apical and an equatorial position 
and in which O ~ and the electron pair (which are less electronegative than OH 73 ) 
occupy equatorial positions. This intermediate is not isoenergetic with 18, the 

o""\ o 

H 18 0— S— O ia O— S — O 

/ \ / \ 

-O • HO 

17 18 

result of a simple proton transfer, because in 18 the most electronegative ligand, 
OH, occupies an equatorial position. 74 Kice suggests that 17 might be formed in a 
rapid preequilibrium, and its presence might not be detected in the experiment 
described above. 

Tetracoordinated Sulfur 

The mechanism of nucleophilic displacements on tetracoordinated sulfur has 
not yet been much studied, but the formation of an intermediate seems possible. 

For example, when sulfonate esters are hydrolyzed with ie O-enriched 
hydroxide (Reaction 4.38) the product sulfonic acids contain 18 but the starting 
material recovered after 50 percent reaction does not. 75 By the arguments out- 
lined on p. 200 this might be evidence for either a one-step displacement or a two- 
step mechanism with the first step rate-determining. The latter is made more 

O O 


H 18 0" + R— S— OR > H 18 0— S— R + "OR (4.38) 


O O 

plausible by the work of Ciuffarin, who has studied the reactions of several 
nucleophiles with 19 and has found that the rates of displacement of X are very 
similar for X = CI, Br, and I. If departure of the leaving group were involved in 



71 In other reactions on tricoordinate sulfur, not yet well understood, intermediates analogous to 15 
are formed. See, for example, B. M. Trost, R. LaRochelle, and R. C. Atkins, J. Amer. Chem. Soc, 91, 
2175 (1969) and references in this paper and in E. N. Givens and H. Kwart, J. Amer. Chan. Soc., 90, 
378, 386 (1968). See also N. E. Hester, Int. J. Sulfur Chem., 8, 1 19 (1973). 

72 J. L. Kice and C. A. Walters, J. Amer. Chem. Soc, 94, 590 (1972). 

73 See note 67 (b), p. 199. 

74 See note 67 (b), p. 199. 

75 D. R. Christman and S. Oae, Chem. Ind. (London), 1251 (1959). 

202 Bimolecular Substitution Reactions 

the rate-determining step, one would expect that the rates of reaction would 
decrease in the order I > Br > CI. 76 Ciuffarin and co-workers interpret their 
results as evidence for a reaction path in which the formation of the intermediate 
is rate-determining. 

The usual stereochemical course for substitution on tetracoordinated sulfur 
seems to be inversion. 76,77 For example, Sabol and Andersen showed, by optical 
rotary dispersion measurements, that the product of reaction 4.39 has the con- 
figuration opposite to that of the starting material. 78 


O 18 

+ / \- CH 2 — S — O— menthyl 

\==/ \)18 

CH 3 

O 16 

/ \— CH 2 — S— O 18 + BrMg—O— menthyl (4.39) 

CH 3 

The Nucleophile in Displacement Reactions on Sulfur 

The relative reactivities of nucleophiles toward sulfur differ a great deal 
depending on whether the sulfur is di-, tri-, or tetracoordinated, This is to be 
expected from the theory of hard and soft acids and bases. As the oxidation state 

O O 

of sulfur in the series — S — , — S — , — S — increases, so also does the hardness of 


sulfur as a Lewis acid. Table 4.1 1 shows the relative reactivities of some nucleo- 
philes toward sulfenyl, sulfinyl, and sulfonyl sulfur, all in 60 percent aqueous 
dioxane. Note the great increase in rate on sulfenyl sulfur ( — S — ) as the nucleo- 
phile becomes softer and more polarizable. For harder sulfinyl sulfur, the rate 
increase is less pronounced and, as has been pointed out by Kice, in polar 
solvents, the relative reactivities of nucleophiles toward this oxidation state of 
sulfur are very similar to those toward sp 3 hybridized carbon. 79 Finally, note that 
for hard sulfonyl sulfur the rate with fluoride is 10 5 times faster than with 
chloride. 80 

78 E. Ciuffarin, L. Senatore, and M. Isola, J. Chem. Soc, Perkin 2, 468 (1972). 

77 M.J.Jones and D.J. Cram, J. Amer. Chem. Soc, 96, 2183 (1974). See also note 57 (c), p. 195. 

78 See note 57 (c), p. 195. 

76 J. L. Kice, G.J. Kasperek, and D. Patterson, J. Amer. Chem. Soc, 91, 5516 (1969) and references 


80 With the exception of F", the relative reactivities of nucleophiles toward sulfonyl sulfur are very 

similar to their relative reactivities in the same solvent toward carbonyl carbon. J. L. Kice and E. 

Legan, J. Amer. Chem. Soc, 95, 3912 (1974). 

Bimolecular Electrophilic Substitution at Saturated Carbon 203 

Table 4.11 Relative Rates of Reaction of Various Nucleophiles with Different 
Oxidation States of Sulfur in 60% Aqueous Dioxane 






Toward — S — ° 

Toward — S — " 


. — S— " 

Toward sp 3 C° 














5.4 x 10 3 


1.4 x 10 4 




6.2 x 

10 3 




3.7 x 

10 5 


H 2 

8.5 x 10" 6 

1.2 x 

10" 1 

1 x 10- 3 

"J. L. Kice and G. B. Large, J. Amer. Chem. Soc, 90, 4069 (1968). 
"J. L. Kice, G.J. Kasperek, and D. Patterson, J. Amer. Chem. Soc, 91, 5516 (1969). 
Data from C. G. Swain and C. B. Scott, J. Amer. Chem. Soc, 75, 141 (1953). 
Reproduced by permission of the American Chemical Society. 


There are two polar alternatives for simple substitution on saturated carbon. 
In the first the leaving group is more electronegative than carbon and there- 
fore departs, taking with it the pair of electrons that formerly bound it to 
carbon. To make up the deficiency the group entering must bear an extra pair of 
electrons. This is, of course, a description of aliphatic nucleophilic substitution. In 
the second alternative, the leaving group, less electronegative than carbon, 
departs stripped of the bonding electrons. To bond with carbon the entering 
group must now be able to accept an extra pair of electrons. The latter alter- 
native is aliphatic electrophilic substitution. Because most elements less electro- 
negative than carbon are metallic, electrophilic substitution ordinarily occurs on 
organometallic compounds. 

In analogy to the traditional terms S^l and S w 2, which refer to the ex- 
treme aliphatic substitution mechanisms, workers in the field of electrophilic 
substitution refer to S £ l (for substitution-electrophilic-unimolecular) and S E 2 
(substitution-electrophilic-bimolecular) mechanisms. Equations 4.40 and 4.41 

R— M -^-f R- + M+ -^U RE S £ l (4.40) 

E + + R— M ► RE + M+ S £ 2 (4.41) 

show these mechanisms in their simplest representations. In this chapter we are 
concerned mainly with one-step, second-order substitutions, but as we shall see, 

81 For recent reviews of electrophilic substitution see (a) F. R. Jensen and B. Rickborn, Electrophilic 
Substitution of Organomercurials, McGraw-Hill, New York, 1968; (b) O. A. Reutov, Pure and Appl. 
Chem., 17, 79 (1968); (c) D. S. Matteson, Organometal. Chem. Rev. A., 4, 263 (1969); (d) C. K. Ingold, 
Structure and Mechanism in Organic Chemistry, 2nd ed., Cornell University Press, Ithaca, N.Y., 1969, 
pp. 563-584. 

204 Bimolecular Substitution Reactions 

most of these reactions do not follow the reaction path implied in Equation 4.41. 
Rather, the path usually followed includes a cyclic transition state (Equation 
4.42) in which the electrophile enters as the metallic leaving group departs while 

E— L + RM 


-* RE + ML S £ i (4.42) 

at the same time a ligand originally attached to the electrophile is transferred to 
the leaving group. Thus, it is not necessary that the electrophile lack a pair of 
electrons at the start of the reaction; loss of the ligand with its bonding electrons 
during the course of the reaction enables the electrophile to take over the pair of 
electrons on carbon formerly used for bonding to the leaving group. We shall 
call the mechanism shown in Equation 4.42 the S £ i mechanism (in which the 
"i" is for "internal"). 

Although nucleophilic substitutions have been much studied for over 40 
years, the corresponding electrophilic substitutions aroused little interest until the 
1950's. Since then, because mercury usually forms truly covalent bonds 82 and 
because organomercurials can be prepared in optically active form and do not 
subsequently racemize, the majority of mechanistic studies in this area have used 
organomercurials as the substrate. Thus, to stay in the most brightly lighted area 
of a field, at best dimly lighted, we shall limit our short discussion of bimolecular 
electrophilic aliphatic substitutions almost entirely to reactions of organo- 

Electrophilic Cleavage of Organomercurials 

Mercury compounds are often used as electrophiles in displacements on 
organomercurials. There are five possible combinations of reactants in such 
"mercury exchange" reactions. A dialkylmercurial substrate may be attacked 
either by a mercury salt (Reaction 4.43) or by a monoalkylmercurial (Reaction 
4.44) ; and likewise a monoalkylmercurial may react either with a mercury salt or 
with another monoalkylmercurial (Reactions 4.45 and 4.46) . Finally, a dialkyl- 
mercurial may react with another dialkylmercurial (Reaction 4.47). (In Reac- 
tions 4.43-4.47 and in other reactions in this section, one of the reactants, and 
the fragments derived from that reactant in the products, are written in italics. 
This is done to make it easier to follow the course of the reaction.) 

RHgR + XHgX > RHgX + XHgR (4.43) 

RHgR + RHgX * RHgR + XHgR (4.44) 

RHgX + XHgX * KHgX + XHgX (4.45) 

RHgX + RHgX > RHgR + ATHgX (4.46) 

RHgR + RHgR ;► RHgR + RHgR (4.47) 

82 In the gas phase, divalent mercury has been shown to be linear and therefore to be sp hybridized. 
However, in solution the X — R — X, R — Hg — X, or R — Hg — R bond angle in divalent mercury 
compounds varies from 130 to 180°. The variation in geometry is not yet entirely understood, so we 
shall follow Jensen's example and assume that, even in solution, divalent mercury is sp hybridized 
and that if a divalent mercury compound donates one empty orbital to coordinate with a Lewis base 
it rehybridizes to sp 2 (F. R. Jensen and B. Rickborn, Electrophilic Substitution of Organomercurials, 
pp. 35, 36). 

R R 


— — \ 

M I! ^C 

Bimolecular Electrophilic Substitution at Saturated Carbon 205 


Figure 4.8 Transition state for backside S E 2 displacement. 




Figure 4.9 Transition state for frontside S £ 2 displacement. 

We shall only discuss experiments that shed light on the first three types 
(Reactions 4.43-4.45), but the characteristics of all five types of mercury exchange 
reactions seem to be very similar. 

The first question we shall ask is whether bimolecular mercury exchanges 
proceed with retention or inversion of configuration at the central carbon. We 
shall then see if we can decide whether the transition state is open (S E 2 mecha- 
nism) or cyclic (S £ i mechanism). If the reactions proceed with inversion of con- 
figuration, then the mechanism must be S £ 2. The geometry of the activated 
complex leading to inversion would be very similar to that leading to S lV 2 substi- 
tution. The electrophile, attacking the carbon from the back side, would cause 
carbon to rehybridize from sp 3 to sp 2 so that the remaining p orbital could be 
shared by it and the leaving group (Figure 4.8). The difference between this 
transition state and the transition state for backside displacement in the S A ,2 reac- 
tion is, of course, that in the S E 2 reaction the three participating atomic orbitals 
share a total of two electrons whereas in the S w 2 reaction they share a total of 
four. Retention of configuration could result from either an S E 2 or an S E i mechan- 
ism. In either case the electrophile would attack the sp 3 orbital used in bonding 
with the leaving group from the front side (Figure 4.9). 

The first detailed study of the stereochemistry of a mercury exchange reac- 
tion that was known to be bimolecular was carried out as follows. 83 Di-5-butyl- 
mercury was prepared by reacting optically active i-butylmercuric bromide with 
racemic 5-butylmagnesium bromide as shown in Equation 4.48. 

CH 3 CH 3 

CH 3 CH 2 — C*— HgBr + BrMg— C— CH 2 CH 3 ► 

H H 

CH 3 CH 3 

I I 

CH 3 CH 2 — *C— Hg— C— CH 2 CH 3 + MgBr 2 (4.48) 

H H 

83 (a) H. B. Charman, E. D. Hughes, and C. K. Ingold, J. Chem. Soc, 2530 (1959); (b) F. R.Jensen, 
J. Amer. Chem. Soc, 82, 2469 (1960); (c) O. A. Reutov and E. V. Uglova, Bull. Acad. Sa. USSR, 
Chem. Div. Scl, 1628 (1959). 


Since the mercury-carbon bond is not disturbed in any way in this reaction, one 
(and only one) of the 5-butyl groups in the di-5-butylmercury should have an 
optically active center. The mercury exchange reaction of Equation 4.49 was 
then carried out on the di-5-butylmercury thus formed, and the optical rotation 

CH 3 CH 3 CH 3 

HgBr 2 + CH 3 CH 2 — *C— Hg— C— CH 2 CH 3 ► 2CH 3 CH 2 — C— HgBr (4.49) 

H H H 

of the product was compared to that of .f-butylmercuric bromide used as starting 
material. If the substitution had proceeded with retention of configuration 
(Equation 4.50), then the specific rotation of the product would be half that of 

C// 3 CH3 CH 3 

I I I 

CH 3 CH 2 — *C— Hg — C— CH 2 CH 3 + HgBr 2 ► CH 3 CH 2 —*C—Hg— Br + 

I I I 

H H H 

CH 3 CH 3 CH 3 . 

BrHg— C— CH 2 CH 3 + CH 3 CH 2 —*C— HgBr + BrHg— C— CH 2 CH 3 (4.50) 

H H H 


the original j--butylmercuric bromide. If the substitution had proceeded with 
racemization (Equation 4.51), the specific rotation should be one-quarter that of 

CH 3 CH 3 CH 3 

I I I 

CH 3 CH 2 — *C— Hg— C— CH 2 CH 3 + HgBr 2 *■ CH 3 CH 2 —*C—HgBr + 

H H H 


CH 3 CH 3 CH 3 

I I I 

CH 3 CH 2 — C— HgBr + CH 3 CH 2 —C— HgBr + KrHg— C— CH 2 CH 3 (4.51) 

I I I 

H H H 


the starting material. Finally, if the substitution had proceeded with inversion 
(Equation 4.52) , the product should be racemic. 

C/13 LHa CjH 3 

I I I 

CH 3 CH 2 — *C— Hg— C— CH 2 CH 3 + HgBr 2 ► CH 3 CH 2 —*C—HgBi + 

H H H 

CH 3 CH 3 CH 3 

I I I 

CH 3 CH 2 — C— HgBr + CH 3 CH 2 —*C— HgBr + CH 3 CH 2 — C— H^Br (4.52) 

I I I 

H H H 


Bimolecular Electrophilic Substitution at Saturated Carbon 207 

The specific rotation of the initial j-butyl bromide used by Charman, 
Hughes, and Ingold was — 15.2°. The specific rotation of the product of the 
mercury exchange reaction was exactly half that, — 7.6°. When mercuric acetate 
or mercuric nitrate was used as the cleaving salt, the products showed a specific 
rotation of —7.5° and —7.8°, respectively. Thus this electrophilic substitution 
clearly proceeds with retention of configuration. 

Stereochemical studies on other mercury exchange reactions have been 
carried out, and all point to retention as the predominant pathway. 84 

A possible "justification" for frontside attack in electrophilic substitution 
is that ab initio molecular orbital calculations for the CH 5 + cation, the species 
that would be formed if H + attacked methane, indicate that the most stable 
structure would not be a trigonal bipyramid, in which carbon uses ajb orbital to 
bond to two protons, but would be a relatively unsymmetrical structure that 
has a smallest H — C — H bond angle of about 37° (Figure 4.10). 85 For further 
discussion of S B 2 substitution on carbon, see Section 10.3. 86 

Let us now turn to whether the transition state is open (S £ 2) or cyclic 
(S £ i). The exchange of radioactive mercury shown in Equation 4.53 is a second- 

CH 3 CH 3 

CH 3 CH 2 C— HgX + *HgX 2 ^=^ CH 3 CH 2 C— *HgX + HgX 2 (4.53) 

H H 

X = Br 
N0 3 

order reaction. 87 Furthermore, it is identical in the forward and reverse direc- 
tions. Ingold reasoned that the mercury coordinated with the anion of highest 
ionizing ability would be the most electrophilic and, therefore, if the S £ 2 

Figure 4.10 Optimum structure for CH S + . From W. A. Lathan, W. J. Hehre, and J. A. 
Pople, Tetrahedron Lett., 2699 (1970). Reproduced by permission of Pergamon 

84 (a) H. B. Charman, E. D. Hughes, C. K. Ingold, and F. G. Thorpe, J. Chem. Soc., 1121 (1961); 
(b) E. D. Hughes, C. K. Ingold, F. G. Thorpe, and H. C. Volger, J. Chem. Soc, 1133 (1961); (c) 
E. D. Hughes, C .K. Ingold, and R. M. G. Roberts, J. Chem. Soc, 3900 (1964). 

85 W. A. Lathan, W. J. Hehre, and J. A. Pople, Tetrahedron Lett., 2699 (1970). See also A. V. Kemp- 
Jones, N. Nakamura, and S. Masamune, J. Chem. Soc D, 109 (1974) and references therein. 

86 F. R. Jensen and B. Rickborn, Electrophilic Substitution of Organomercurials, pp. 153ff. 

87 See note 84 (b). 


mechanism were followed the rates should be HgBr 2 < Hg(OAc) 2 < Hg(N0 3 ) 2 . 
He reasoned further that the anion of lowest ionizing ability would be the best 
coordinator and therefore if the mechanism is S £ i the rates should be reversed : 
HgBr 2 > Hg(OAc) 2 > Hg(N0 3 ) 2 . The order found was HgBr 2 < Hg(OAc) 2 < 
Hg(N0 3 ) 2 . The open S £ 2 mechanism, originally proposed by Ingold, and shown 
in Equation 4.54, cannot be correct because the mechanism in the forward 
direction would be different from that in the reverse direction and therefore 
the law of microscopic reversibility would be defied. 88 Jensen also ruled out a 

RHgX + *HgX 2 



HgX 2 

RHgX 2 


RHgX + HgX 2 (4.54) 

revised mechanism proposed by Ingold, 89 shown in Scheme 2, because the rate of 
reaction is not depressed by addition of X~. (A higher concentration of X" 
would drive the first equilibrium to the left and thereby decrease the overall rate 

Scheme 2 

HgX 2 

HgX + X 

RHgX + HgX 



•. * 

:± RHgX + HgX 

of reaction. Jensen and Rickborn suggest that, contrary to Ingold's conclusions, 
the transition state shown in 20 might well accommodate the experimental 
results. 90 They dispute the original assumption made by Ingold that the ionizing 






and bridging abilities of anions are inversely proportional to one another; they 
suggest that the capacity of nitro and acetate groups to form six-membered rings 
when bridging (as shown in 21 and 22, respectively) might make them better 
coordinators than halide ions, which can form only four-membered rings. They 
point out that the electrophilicity of the attacking mercury is also important in 

88 (a) See note 81 (c) and F. R. Jensen and B. Rickborn, Electrophilic Substitution of Organomercurials, 
pp. 153ff; (b) the law of microscopic reversibility states that in a reversible reaction, if a certain 
percentage of the molecules follow one path in the forward direction, the same percentage will 
follow that path in the reverse direction. 

89 See note 81 (d), p. 203. 

90 See note 86, p. 207. 


Bimolecular Electrophilic Substitution at Saturated Carbon 209 









;c— ch. 



Hg O 

Hg O 





the S E i mechanism of mercury exchange and might be more important than the 
coordinating power of the anions. 

If all three alkyl groups are identical, mercury exchanges of the type shown 
in Equation 4.44' are also identical in the forward and reverse directions. The 
law of microscopic reversibility taken in conjunction with the kinetics of the 
reaction again suggest a cyclic transition state (by the arguments outlined above), 
but the observed order of reactivity of the electrophiles again is RHgBr < 
RHg(OAc) 2 < RHgN0 3 . It therefore seems likely that even reactions such as 
those shown in Equation 4.49 and Equation 4.43, in which the forward and re- 
verse reactions are different but in which the order of reactivity of the mercury 
salts is the same as in Reaction 4.53, 91 proceed through a cyclic S £ i mechanism. 
In fact, since almost all bimolecular electrophilic substitutions on carbon in 
organometallic compounds of which the stereochemistry have been studied 
proceed with retention of configuration, the transition state of Figure 4.9 may be 
general for substitutions in organometallics. 

Bimolecular Electrophilic Substitutions at Carbon-Hydrogen Bonds 

Recently Olah has found a means of studying electrophilic bimolecular 
substitutions on the C — H and the unstrained C — C bond and concluded that the 
"triangular" transition state shown in Figure 4.9 is also involved here. 92 For 
example, in DF — SbF 5 , a superacid medium, 93 adamantane rapidly exchanges 
hydrogen for deuterium with great preference for the bridgehead positions, as 
shown in Equation 4.55. In this rigid bicyclic system, backside attack is im- 
probable. There is no strong base, so a carbanion cannot form. Structure 23 then 
seems like the most likely representation of the transition state. 

H f H. D "1 1 D 

+ SbF,— DF 


91 See note 83 (a), p. 205. 

92 G. A. Olah, Y. Halpern, J. Shen, and Y. K. Mo, J. Amer. Ckem. Soc, 93, 1251 (1971). See also 
G. A. Olah and J. A. Olah, J. Amer. Chem. Soc, 93, 1256 (1971) and G. A. Olah and H. Lin, J. Amer. 
Chem. Soc, 93, 1259 (1971). For a discussion of attack of H + on a strained (cyclopropane) C — C 
bond, see Section 6.2. 

93 Antimony pentafluoride (SbF 5 ) is a strong Lewis acid, so the equilibrium 

SbF 5 + HF ^==: "SbF 6 + H + 
lies to the right, giving rise to unsolvated and therefore very reactive protons. 



1. Predict which would be more reactive as a nucleophile in S N 2 substitution: 

or (CH 3 CH 2 CH 2 ) 3 N: 

2. Suggest an explanation for the fact that the order of reactivity of the halides 
toward re-butyl brosylate in acetone is CI" > Br~ > I" when (C 4 H 9 ) 4 N + is the cation 
of the halide salt but I - > Br" > CI" when Li + is the cation. 

3. Suggest a reason for the secondary isotope effect, £ H /A; D = 1 . 10 in the reactions : 

CH 3 I + I*- 
CD a I + I* 

CH 3 I* + I- 
■CD 3 I* + I- 

4. Nucleophiles such as NH 2 OH and NH 2 NH 2 , which have an electronegative 
atom with one or more pairs of unshared electrons adjacent to the nucleophilic center, 
are more reactive than might be expected from the nature of the nucleophilic center, as 
can be seen from Table 4.5. Suggest a reason for this increased reactivity (this pheno- 
menon is called the a-effect). 

5. Silicon compounds of the type R 3 SiOR undergo nucleophilic substitution. 
From the following experimental observations, decide whether the most likely mechan- 
ism is 

(a) S„l: 

(b) S„2: 

(c) Two-step: 

R 3 SiOR' 
R 3 SiOR' 
R 3 SiOR' 

-»■ R 3 Si + "OR 

-»■ R 3 SiY 

<■ Y— SiR 3 + 

Y- (fast). _ - s , ow 

R 3 SiOR 

> R 3 SiY + -OR 

(d) Two-step: R 3 SiOR' 


-► R 3 SiOR 


± R 3 Si— Y + OR 

Experimental observations : 

(a) Substitution almost always proceeds with retention or inversion — never with 

(b) The reaction shown below gives only the product depicted. No 

Si — CH 2 CH 3 
CH 2 CH 3 

is formed. 

+ BrMg— CH 2 CH 3 

References for Problems 211 

(c) Acyloxysilanes (leaving group R' — C — O) are considerably more reactive than 

6. The stereochemistry of the reaction shown below depends on the amount of 
butanol in the solvent. For example, when 2.3 percent by volume butanol is present, the 
reaction proceeds with 100 percent retention of configuration. When the solvent is 
100 percent butanol, the reaction proceeds with 77 percent inversion. 

+ nC 4 H 9 0-M + benzene > , v ^ ^f +M + "OCH 3 

nC 4 H e OH r - A ' 3 

Suggest a reason for the change in stereochemistry and draw probable transition states. 

7. Bimolecular nucleophilic displacements on peroxide oxygen have been 
observed to occur. Would you expect the relative nucleophilicity of iodide to chloride in 
protic solvents to be (a) about the same toward peroxide O as toward sp 3 C; (b) greater 
toward peroxide O than toward sp 3 C ; (c) smaller toward peroxide O than toward sp 3 C ? 

8. Nucleophiles that have more than one atom that may attack the substrate are 
called ambident. Using HSAB theory, predict with which atom the ambident nucleo- 

o o o- o 


CH 3 — C— CH— C— OCH 2 CH 3 ^* CH 3 — C=CH— C— OCH 2 CH 3 

will attack : 

(a) CH 3 I (b) CH 2 — OCH 3 


9. Predict whether, in the following reaction, the rate of reaction will be much 
faster, much slower, or about the same when R = — CH 3 than when 

CH 3 

R = — CH 2 — C — CH 3 . 

CH 3 

Explain your reasoning. 

RHgX + HgX 2 ^ RHgX + HgX 2 


1. H. C. Brown and N. R. Eldred, J. Amer. Chem. Soc, 71, 445 (1949). 

2. S. Winstein, L. G. Savedoff, S. Smith, I. D. R. Stevens, and J. S. Gall, Tetrahedron 

Lett, 9, 24 (1960). 

3. M. Wolfsberg, Accts. Chem. Res., 5, 225 (1972). 

4. S. R. Hartshorn, Aliphatic Nucleophilic Substitution, Cambridge University Press, 

London, 1973. 

212 Bimolecular Substitution Reactions 

5. L. H. Sommer, Stereochemistry, Mechanism, and Silicon, McGraw-Hill, New York, 1965, 

pp. 48/; p. 67. 

6. L. H. Sommer and H. Fujimoto, J. Amer. Chem. Soc, 90, 982 (1968). 

7. J. O. Edwards, in Peroxide Reaction Mechanisms, J. O. Edwards, Ed., Wiley-Inter- 

science, New York, 1962, pp. 68-69. 

8. R. G. Pearson and J. Songstad, J. Amer. Chem. Soc, 89, 1827 (1967). 

9. E. D. Hughes and H. C. Volger, J. Chem. Soc, 2359 (1961). 

Chapter 5 





In this chapter we take up unimolecular and borderline substitutions and discuss 
carbocations, carbanions, and carbenes, three of the important reactive organic 


Diphenylchloromethane (benzhydryl chloride, 1), when dissolved in solvents 
such as aqueous ethanol, aqueous acetone, acetic acid, or formic acid, undergoes 
substitution of chloride by a nucleophilic group derived from the solvent. 

*V- CI 



Equation 5.1, in which SOH stands for a molecule of some hydroxylic solvent, 
illustrates the process. This type of reaction, where the solvent takes the role of the 

\ /CI j*. /OS 

C + SOH ► ff + HC1 (5.1) 

+ ' X H + ' H 

nucleophile (Lewis base) in the substitution, is called solvolysis. 

1 Unimolecular substitutions are discussed in detail in the following sources: (a) C. A. Bunton, 
Nucleophilic Substitution at a Saturated Carbon Atom, Elsevier, Amsterdam, 1963; (b) C. K. Ingold, 
Structure and Mechanism in Organic Chemistry, 2nd ed., Cornell University Press, Ithaca, N.Y., 1969; 
(c) A. Streitwieser, Jr., Solvolytic Displacement Reactions, McGraw-Hill, New York, 1962; (d) E. R. 
Thornton, Solvolysis Mechanisms, Ronald Press, New York, 1964. 


214 Unimolecular Substitutions and Related Reactions 

The observed kinetics of the solvolysis is first-order in the benzhydryl chloride. 
This fact alone tells little about the mechanism because t he nucleop hi le, being t he 
soh/£nt v js_always present in jarge excess. As vye have seen in_SectionJ^5jjx j)2), 
itsjxmoejrrtration Jherefqre undQVgo^a^n^\i^^j^opo^gn^chaj\ge^ind^Yii\l 
not_enler_auto_lhe_rate ^xpressio.rjL_£yen JLiLM^ involved^ atjpr befbxe the rate- 
determining s tep. ^Adde d nucleophiles have relatively small effects o nthe rate. 
and ratex^vdth^vajious_jvucleQrAilic ^sa4^^ 

Mostadded salts accelerate the pr ocess, but c o mmon io n salts (chlorides irt the 
case of ben zhydrj^jchloride) make it slower.— A ddition of sodium _azide_causes 
formation of some benzhydryl azi de, b ut affects_the rate in_thejame way as 
QtEex_nojtcomrnoo-iori- saltsr 2 The stereochemistry of the substitution can be 
investigated by starting with a chiral analog such as />-chlorobenzhydryl chlo- 
ride. The solyolysk products are„ almost completely, racemic^ Although these 
results have been known for many years, 3 a number of questions about details of 
mechanism remain unanswered. 

The S N 1 Mechanism 

Early investigators, notably Hughes, Ingold, and co-workers, accounted for the 
solvolysis results by proposing the S^l me chanism; 4 whi^h p f ?stll.lgt^s_ ? rate- 
H/^ prr "ining p!i««nr i a ti n n tn a r arhnfgtj on follow ed b y rap id ^captl lrf * pf the ipn 
by_aJiucleophile. Equations 5.2 and 5.3 delineate the S w l route for the case of ion 
capture by solvent. 

RC1 . R + + CI- (5.2) 

R + + SOH — ^-> ROS + H+ (5.3) 

The reverse of the second step, although it should be included to be rigorously 
correct, is frequently omitted because the final product in many cases is suffi- 
ciently unreactive that no experimentally significant amount will return to 
carbocation during the time the reaction is under observation. 

This simple two-step mechanism, when combined with the stationary-state 
assumption for the presumably highly reactive positive ion (see Section 2.5, 
p. 93), leads to the prediction given in Equation 5.4 for the rate of product 
formation. (See Problem 1.) The term in parenthese s in Equati on^ .4 will 

r educe to unity wh enever J^fSO H] » A _ 1 [C1~] ; in that case a simple firsfcorder 

2 (a) L. C. Bateman, E. D. Hughes, and C. K. Ingold, J. Chetn. Soc, 974 (1940); (b) C. G. Swain, 
C. B. Scott, and K. H. Lohmann, J. Atner. Chetn. Soc-, 75, 136 (1953) ; (c) D. Kovacevic, Z. Majerski, 
S. Borcic, and D. E. Sunko, Tetrahedron, 28, 2469 (1972). 

3 For early work on benzhydryl solvolysis, see L. C. Bateman, M. G. Church, E. D. Hughes, C. K. 
Ingold, and N. A. Taher, J. Chetn. Soc, 979 (1940), and references cited therein. 

4 The mechanism was proposed by S. C. J. Olivier and G. Berger, Rec. Trav. Chitn., 45, 712 (1926); 
A. M. Ward, J. Chetn. Soc, 2285 (1927) ; and C. K. Ingold, Ann. Repts. Chetn. Soc, 24, 156 (1927). It 
was set out in detail by E. D. Hughes, C. K. Ingold, and C. S. Patel, J. Chetn. Soc, 526 (1933); the 
S K 1 terminology was introduced by J. L. Gleave, E. D. Hughes, and C. K. Ingold, J. Chetn. Soc, 
236 (1935). 


Kinetics and Stereochemistry 215 

kinetic behavior is predicted, and *his_is mi^ly what k nhjgrvgH A <niffjripntly 
\^rp^addexf?nnc.mtratjnn of thfTTeaving grnup (in t his case Clr}j night lead to a 
rate, .depression, caljed_a„ MmawRJaiLjeffectiJtjwas to this cause that Hughes and 
Ingold attributed the observed rate decrease for benzhydryl chloride with added 
chloride salts. 5 Az ide ion di verts the carbocation to stable alkyl azide: the 
amojmLgf_azide formed is consistent only with its formation from an intermedi- 
ate,, presu med to be tneTiL + ion , which also produces the soJyoJysis_projduct. 6 The 
stereochemistry of the benzhydryl reactions is also consistent with the Ingold 
mechanism. As we shall see in more detail in Section 5.3, tjjere is now abunda nt 
evide nce that carbo cations exist and that jthey prefer a_ geometrv~in whic h the 
qaUpnic carbon and the three atoms attached to it are coplanar ^A carbon cation 
i n this preferred conformation ha s a planejrfjjymmetry and so cannot be chiral; 
attgfV ™ thp inn hy q nnrlpnphjle from the iw p side s of the plane, ^yielding the 
*wo e n^^t'^^T s " f the p rod uct (Equation 5.5 ), must occur _at_ equal rates. 

R3 N— C^ 

N:- -C+ « :N-<% V Rl (5.5) 


Ri R 

R 3 K * 

2 * C— N 

R iR 2 

Using rate, product, and stereochemical evidence, Hughes, Ingold, and 
their co-workers assigned mechanisms to a number of systems and pointed out 
that many cases could not be clearly categorized as either S w l or S N 2. 7 

It is now recognized that the two-step sequence of Equations 5.2 and 5.3 is 
oversimplified, and that a good deal more needs to be said about the details of the 
mechanism. In the first place, it is clear that when the ionization occurs, dipolar 
solvent molecules will be more strongly attracted to the ions than they were to the 
neutral substrate, and there will be a change in solvation. But ultimately, in the 
product, a solvent molecule will become bonded to the cationic center; it will be 
a difficult matter to determine experimentally whether some bonding of solvent 
to carbon, more specific than the general solvation forces, is occurring simul- 
taneously with the departure of the leaving group and so is assisting ionization. 
If this assistance by solvent is occurring, the process has some of the charac- 
teristics of an S N 2 reaction, and should not be classified as pure S N L We shall 
return to this point in Section 5.4; for the time being, it is useful to postulate a 
mechanism at the S N l end of this range, just as in Chapter 4 we considered a 
mechanism at the S N 2 end. We th erefore define as a limiting unimolecular (S w l) 
mechanism a process in which the ionization yields solvated ions without any 
bonding by solvent m olecules to the developing cationic center other than those 
ggjiexalji oncovaler^ -xiojidir£ctional interactions involved in solvation. 

In view of evidence that we shall consider in more detail in Section 5.4, 
it appears that the early work placed in the limiting class some systems that do not 
really belong there, and that probably limiting reactions are restricted to tri- 

6 See note 3. 

6 See note 2(a). 

7 C. K. Ingold, Structure and Mechanism in Organic Chemistry, pp. 427-457. 

216 Unimolecular Substitutions and Related Reactions 

arylmethyl, benzhydryl, 8 tertiary alkyl, and allylic systems. Even the limiting 
S N 1 process is not without complication, however, because it is possible to show 
that, in some instances at least, the ionization process consists of more than one 

Ion Pairs 

If two chemical processes occur through the same intermediate, the products 
should be identical. Inj>oJ ; yoh/sjs_jxacti©«*<rir^^ 

carbon, p1iminatinr^*^hirlT.rnrisistg nf loss n£ a-p=fri*ffl-4f> r r iv r a i rn Vfin, gfTPralVy, 
accoma aiuesZsubstitution . We illustrate this process for solvolysis of i-butyl 
halide in Scheme 1 . Intermediacy of fr e e carbocations requir es the dis tributionjof 

Scheme 1 

H3C CH 3 yH 3 

\ / I 

C ► C + + x- 

/ \ 
H-C X 

/ y 
h 3 c ch 3 

H 3 C CH 3 H 3 C H 

\ / \ / 

H + + C C=C + H + 

H 3 C OS H 3 C H 

products^between elimination and substitution to be independent of thejeaying- 
groupuX. Table 5. 1 gives results of tests of this prediction for various solvents. 
The data are in agreement with the free ion mechanism for the high-dielectric- 
constant solvent water; for solvents of lower dielectric constant, such as ethanol 
and acetic acid, they are not. 

A second difficulty arises from consideration of allylic systems. Because the 
resulting cationic center is stabilized by interaction with the ir electrons, allylic 
halides ionize readily to produce the delocalized allylic ion, 2. The freejOBJLheory 
r^edktjjdiaxJsiamgric—allylic- halidfs that give the same intermediate -upon- 
ionizaiion should yield a prod uct distribution independ ent pf the isnmerJc-odgm 
oLthe-ion. Scheme 2 illustrates the argument. The prediction is sometimes, but 

Table 5.1 Partition Between Elimination and Substitution in *-Butyl-X Solvolysis 

Mole Percent Olefin 

H 2 

C 2 H 5 OH 


X in <-bu-X 


75°C ' 














S + (CH 3 ) 3 C10 4 - 




Source : Reprinted with permission from M. Cocivera and S. Winstein, J. Amer. Chem. Soc, 85, 1 702 
(1963). Copyright by the American Chemical Society. 

8 For evidence that even benzhydryl systems may not always solvolyze by the limiting route, see 
D.J. McLennan and P. L. Martin, Tetrahedron Lett., 4215 (1973). 

9 See Chapter 7. 

Kinetics and Stereochemistry 217 

not always, verified in practice; there is a marked tendency in many systems to 
favor the unrearranged product. 10 

Scheme 2 

H H 

I l X x X H H / | | 


H 3 C C H H 3 C C x H „ 

a \ // \ / _ v \ / \ / Pi 

c c + * — y c + c 

H ' c v.Av/ H /" 2 \ H 'VV H + H * 


;c N c ^ c 



P1/P2 are 'he same starting from a or b. P 2 

Finally, we note that although solvolysis products of chiral benzhydryl 
derivatives in good dissociating solvents are almost completely racemic, the situa- 
tion is different for other systems classified by Ingold and Hughes as S^l. Ingold 
lists a number of these cases, and states the rule that ". . . mechanism Sjvl in- 
volves inversion of configuration mixed with racemization in any proportions to 
both limits. . . ." n In view of more recent work discussed in Section 5.4, we 
would have to reclassify some of the "S^l" examples into a borderline category; 
nevertheless, the variety of stereochemical result of substitution through carbo- 
cations seems well established. 12 

The mechanistic hypothesis that explains the discrepancies we have de- 
scribed is the ion pair. In 1940 Hammett applied this idea to solvolysis in a form 
close to that now accepted. 13 According to the ioii^rmirJivqjathesis,- a- dissociation 
of a covalent molecule JLX should proceed through at Jeast.two_stage&;..firs.t, the 
ionization to an ion pair^in .which- the specific directed valence forces -binding X 
to carborua re -overcome and the Lewis acid R + and-Lew-k base X- are left still 
clgse_together j^cL&tir^ J&ondirectkmal ionic foie-es ; and second, dissocia- 
tion, in which the two ions separate. 14 

'1'heTon-pair proposal is helpful in accounting for the experiments cited 
above. 15 If the second step in a substitution (or elimination) takes place from the 
ion pair instead of from the free ion, the departing group will still be sufficiently 
closely associated with the carbocation to affect the partition between the two 
alternative pathways. Failure to find complete racemization is also reasonable, 
because the ion pair, in contrast to the free ion, is still chiral. Granted that it will 
racemize rapidly, the substitution may nevertheless occur before chirality is lost, 

10 R. H. DeWolfe and W. G. Young, Chem. Rev., 56, 753 (1956), give an extensive table (pp. 794- 

11 C. K. Ingold, Structure and Mechanism in Organic Chemistry, pp. 521, 525. 

12 A. Streitwieser, Solvolytic Displacement Reactions, p. 59. 

13 L. P. Hammett, Physical Organic Chemistry, 1st ed., McGraw-Hill, New York, 1940, pp. 171-173. 

14 For a general discussion of ion pairs see (a) M. Szwarc, Accts. Chem. Res., 2, 87 (1969); (b) M. 
Szwarc, Ed., Ions and Ion Pairs in Organic Reactions, Vol. I, Wiley-Interscience, New York, 1972. 

15 L. P. Hammett, Physical Organic Chemistry, 2nd ed., McGraw-Hill, New York, 1970, pp. 157-158. 

218 Unimolecular Substitutions and Related Reactions 

Table 5.2 Rate Processes in Solvolysis Reactions 

Reaction" Rate Constant Notation 

RX + SOH J- ROS + HX k t 

rf-RX or /-RX >• optically inactive products k a 

</-RX or /-RX >- dl-KX * rao 

RX + *X~ , R— *X + X" k ex 

♦O O 

II ^ II 

R— O— C— Ar ;=^: R— *0— C— Ar * 6q 

° * denotes isotopically labeled atom; d- or /- indicates a chiral and dl- a racemic substance. 

and preference for backside attack (Chapter 4) means that net inversion will 
occur. Ion pairs in which the anion remains closer to the carbon to which it was 
originally attached could likewise accommodate the allylic product spread. 

In Scheme 3 we modify the simple S N 1 mechanism to include the ion-pair 
idea. Change of substrate structure so as to make the carbocation less reactive, 

Scheme 3 

rx r -1 "^ R + x- 

R + X" + SOH — ^->- ROS + X- + H + 
R + X- , * 3 ' R+ + X" 

k- a 

R + + SOH — ^ ROS + H + 

or change of the solvent so as to aid ion separation, will favor the dissociation 
step k z relative to direct reaction of the ion pair (k 2 ) , and will give results more 
characteristic of the free ions. Elimination can occur in competition with substitu- 
tion either at the ion-pair stage or at the free-ion stage. 

Winstein and his research group elaborated the ion-pair mechanism in a 
series of experiments reported during the 1950s and 1960s. 16 Several kinds of 
kinetic information about solvolysis reactions can be obtained in addition to the 
rate of product formation, k t , determined by titration of acid formed. These 
various rates are summarized in Table 5.2. Winstein's group found that for 
substrates that have the leaving group bound to a chiral center, k a frequently 
exceeds k t by substantial factors. 17 For example, with />-chlorobenzhydryl 
chloride in acetic acid, the ratio k a jk t is between 30 and 70, and is about 5 in 
aqueous acetone. 18 The excess of rate of loss of optical activity, k a , over rate of 
product formation, k t , means that some process racemizes the substrate more 
rapidly than the substrate can form products. The observation that in these same 
systems k a is also larger than k ex rules out the possibility that racemization occurs 

16 For a summary and complete references, see P. D. Bartlett, "The Scientific Work of Saul Win- 
stein," J. Amer. Chem. Soc, 94, 2161 (1972). 

17 (a) S. Winstein and D. Trifan, J. Amer. Chem. Soc, 74, 1154 (1952); (b) S. Winstein and K. C. 
Schreiber, J. Amer. Chem. Soc, 74, 2165 (1952). 

18 S. Winstein, J. S. Gall, M. Hojo, and S. Smith, J. Amer. Chem. Soc, 82, 1010 (1960). 

Kinetics and Stereochemistry 219 

through free ions. 19 If free ions were forming, the X~ anions would become 
equivalent to any other X~ ions present; if isotopically labeled *X~ ions are 
added, the process shown in Equation 5.6 would have to occur. Since the experi- 
mental results show that racemization is faster than this process, there must be 

R + + *X- ► R— *X (5.6) 

present some intermediate or intermediates, presumably ion pairs, in which the 
C — X bond is broken, but in which the X~ ion is still closely associated with the 
particular C + ion to which it was bonded and to which it can return. It is im- 
portant to note that formation of ion pairs an d their return to the coyalently 
b ondecTs tate does notgive rise to the common jon rate depression. 20 As long as 
the X~ ion remains associated with a particular carbocation in the ion pair, it is 
part of a species chemically distinct from the free X~ ions. 

Excess of rate of racemization over rate of product formation supports the 
idea of ion pairs that can return to substrate; nevertheless, as it is possible that 
some, or even most, of the ion pairs return without racemizing (Scheme 4), 
considerable doubt remains about k t , the rate of formation of the ion pairs. The 
difficulty is that there is no way to detect the event represented by k t if it is fol- 
lowed immediately by k _ ( . We shall know that something has happened only when 
k t is followed by k T or by k p . If k_ i competes with these processes, some ionization 
will go undetected. 

Scheme 4 

C— X 

c b 


*« \ 

T " C + X- 

*- A 

c b , 





\ \ 
C— X + C— X 

A /i 

c b be 


*• , \ 

> C + X 

*- A 

c b 


+ C 

b c 



Goering and his collaborators developed a method for finding a better 
approximation to the ionization rate. 21 Their technique uses as leaving group 
an aryl ester, usually a />-nitrobenzoate. Equation 5.7 illustrates that if one 
oxygen of the carboxyl group in the substrate is labeled, ionization and return 
to the covalent state may bring about equilibration of the label between the two 
oxygens. The structural change necessary to make the two oxygens equivalent 

*? 'I ? •? 

R— O— C— Ar »■ R+-p— Ar ► R— *0— C— Ar + R— O— C— Ar 

° (5-7) 

19 See note 18. 

20 S. Winstein, E. Clippinger, A. H. Fainberg, R. Heck, and G. C. Robinson, J. Amer. Chem. Soc., 
78, 328 (1956). 

21 (a) H. L. Goering, R. G. Briody, and J. F. Levy, J. Amer. Chem. Soc, 85, 3059 (1963); (b) H. L. 
Goering and H. Hopf, J. Amer. Chem. Soc, 93, 1224 (1971). 

220 Unimolecular Substitutions and Related Reactions 

in the ion pair is undoubtedly less than that required for racemization (Scheme 
4), where the cation must turn over. Indeed, in various substituted benzhydryl 
systems, racemization of unreacted substrate is slower than equilibration of the 
oxygens. 22 The a-phenylethyl systems yield similar results. 23 Oxygen equilibra- 
tion thus provides a more sensitive test for ionization followed by return than 
does loss of chirality. It should nevertheless be pointed out that even this tech- 
nique is not definitive. It is still possible that, after the ionization but before the 
two oxygens become equivalent, there might be time for the oxygen originally 
bonded to carbon to return. 

Allylic systems have also provided fertile ground for investigation of ion- 
pair phenomena. Young, Winstein, and Goering established the importance of 
ion pairs in solvolysis of these compounds. They showed that ion pairs are 
responsible for the rearrangement of a,a-dimethylallyl chloride to y,y-dimethyl- 
allyl chloride (Equation 5.8). 24 Goering's labeling methods have subsequently 
supplied a number of details about allylic ion-pair structure. 25 

One further detail of the ion-pair mechanism remains. Winstein's work 
demonstrated that.. in some system s_at least, there is more than o neTtind j>fion 
paj r~on the sn jyolyjis pathway. The evidence originates mainly with the effect of 
added salts on rates. Nearby ions affect the free energy of an ion in solution; 
hence, a change in the concentration of dissolved salt will alter the rate of any 
elementary step in which ions form or are destroyed. For S M 1 so l vnlysps J thp rat e 

in rr pagpQ-wiri=t-^Mitinn r»f nnn-rnmmon 10" ™l f In the USUal Solvolysis Solvents, 

for example acetic acid, aqueous acetone, and ethanol, the increase follows the 
linear Equation 5.8, where k salt is the rate constant with added salt and k is the 
rate constant in the absence of salt. 26 

*sait = * (1 + *[salt]) (5.8) 

Certai n systems d e part fr om this beh avior. A ddition of a low conce ntration 
of a non-comm on ion salt such as lithium perchlorate causes a. large increase ijiT f; 
but as more-salL is addeTT th^lncrease levek-off and Jinally-parallels-the -expected 
linear- relation.~This special salt effect 2 - is illustrated in Figure 5.1 for solvolysis 
of the rearranging system 3. Note that k a exhibits only the normal linear salt 

H 3 C- 

23 See note 21, p. 219. 

23 H. L. Goering, R. G. Briody, and G. Sandrock, J. Amer. Chem. Soc, 92, 7401 (1970). 

24 W. G. Young, S. Winstein, and H. L. Goering, J. Amer. Chem. Soc, 73, 1958 (1951). 

25 (a) H. L. Goering and E. C. Linsay, J. Amer. Chem. Soc, 91, 7435 (1969); (b) H. L. Goering, 
G. S. Koermer, and E. C. Linsay, J. Amer. Chem. Soc, 93, 1230 (1971); (c) H. L. Goering, M. M. 
Pombo, and K. D. McMichael, J. Amer. Chem. Soc, 85, 965 (1963). 

26 (a) A. H. Fainberg and S. Winstein, J. Amer. Chem. Soc, 78, 2763, 2780 (1956). Salt effects in 
nonpolar solvents such as ether are of dramatic magnitude, and follow a more complex relationship. 
See S. Winstein, E. C. Friedrich, and S. Smith, J. Amer. Chem. Soc, 86, 305 (1964). In water, the 
relationship is logarithmic. See note 13, Chapter 7. (b) C. L. Perrin and J. Pressing, J. Amer. Chem. 
Soc, 93, 5705 (1971) discuss the mechanism of the linear salt effect. 

37 S. Winstein and G. C. Robinson, J. Amer. Chem. Soc, 80, 169 (1958). 

Kinetics and Stereochemistry 221 

0.03 0.06 



Figure 5.1 Effect of added LiC10 4 on k a and k t in solvolysis of </jreo-3-/>-anisyl-2-butyl-/!>- 
bromobenzenesulfonate (3) in acetic acid. Reprinted with permission from S. 
Winstein and G. C. Robinson, J. Amer. Chem. Soc, 80, 169 (1958). Copyright by 
the American Chemical Society. 

effect. A related phenome non is t hej nduced com mon io n effect. A ddition of X ~ ions 
to RX_solvolyzin g in the presence of lithium perchloratejnay partly cancel the 
speciaLaalt effect rate acce leration even though X ~ Jojis_dQJiQt, depress the rate 
in the a bs ence of the pe r chl orate^ These, results-fecpaire a second kind of ion. 
p air, called a sol vent-separated or external ion pair (4), in which a solvent molecule 
is between the two ions. 

R + || X- 

Scheme 5 depicts Winstein's complete solvolysis mechanism. 29 Ion-pair 
return can be from the intimate ion pair {ion-pair return or internal return), from the 
external ion pair {external ion-pair return), or from the free ions {external ion return). 
The term external return refers to the sum of external ion-pair return and external 
ion return. The special salt effect operates by diversion of the external„.ion pair, 
probably through the mechanism shown in Equation 5.9, so that it can no longer 

28 S. Winstein, P. E. Klinedinst, Jr., and G. C. Robinson, J. Amer. Chem. Soc, 83, 885 (1961). 

29 See note 27. 

222 Unimolecular Substitutions and Related Reactions 

return to RX. 30 The net rate of disappearance of RX therefore increases more 

Scheme 5 3 1 

± R + X- k R+ || X" . R + + X- 

Intimate Solvent- Free ions 

ion pair separated 


ion pair 





ROS + H + ROS + H + 

ROS + H + 

than it would if the new salt were exerting only the normal linear salt effect. 
Racemization ajifLoxygenxquilibration occ ur throughj he intirflate-ion-pair-and 
areno ^ subject to , the sperjaXsa lr effect 3 2 T he origi n of the induced c ommon io n 

R + || X- + Y" t " R + || Y- + X- (5.9) 

e ffect lies in th e production through Equa tion 5.9 of free X~ ions; added X" 
reverses 5.9 by the usual mass law mechanism, lewer ioffpairTafe diverted, more 
can return to RX, and part of the acceleration caused by Y ~ is canceled, Benz- 
hydryl systems show special salt effects with added azide through Equation 5.10; 
in this case the R + || N 3 " ion pair collapses to RN 3 , which is stable and accum- 


X- + N 3 


N a 

+ x- 


ulates as one of the products. 33 

It should be pointed out that not all solvolyzing systems will exhibit the 
phenomena associated with Scheme 5 ; except for those systems that yield relative- 
ly stable carbocations, capture by the solvent at an early stage will preclude 
observation of some or all of these subtle effects. 


In the previous section we den ned a limiting unimo l ecular sub stitution as one in 
whicji-tiie4eavmg groupndepar^sj^ith_rKi^s^ist L ance from solvent other than non- 
coyalen±_solyatipn o f the incipient io ns^We shall return in Section 5rCto the prob- 
lem of how to decide experimentally whether a reaction is following the limiting 
pathway; here we want to look at predictions of the limiting S w l mechanism 
concerning the influence of structures and conditions on rates and on products. 

30 See note 28, p. 221. 

31 Adapted with permission from S. Winstein and G. C. Robinson, J. Amer. Chem. Soc, 80, 175 
(1958). Copyright by the American Chemical Society. 

32 In certain favorable cases of rearranging systems, the occurrence of internal return distinct from 
external ion-pair return can be demonstrated without recourse to optical rotation or isotopic 
labeling experiments. See S. Winstein and A. H. Fainberg, J. Amer. Chem. Soc, 80, 459 (1958); 
S. Winstein, P. E. Klinedinst, Jr., and E. Clippinger, J. Amer. Chem. Soc, 83, 4986 (1961). 

33 See note 17(b), p. 218. 

Effects of Structure and Solvent 223 

Table 5.3 Relative Reaction Rates for Some Common 
Leaving Groups in & n 1 Reactions' 1 

Group ^x/^Br References 

-OS0 2 CF 3 (— OTf, trinate) 5 x 10 8 

-OS0 2 — / \— Br (— OBs, brosylate) 1.5x10* 

_OS0 2 — <f \— CH 3 (— OTs, tosylate) 5 x 10 3 b, c 

Br 1 b 

CI 2.5 x 10" 2 b, d 


— O— C— / \— N0 2 (— OPNB) 2 x 10 ~ e e 

° Relative rates are approximate because they are not independent of the structure of the rest of the 

solvolyzing molecule. All comparisons except — OBs and — OPNB are for bridgehead solvolyses. 

/>-Bromobenzenesulfonate is compared with — OTs for 3-anisyl-2-butyl; — OPNB is compared with 

— CI for benzhydryl (data for chloride obtained by extrapolation). 

6 R. C. Bingham and P. v. R. Schleyer, J. Amer. Chem. Soc, 93, 3189 (1971). 

c S. Winstein and G. C. Robinson, J. Amer. Chem. Soc, 80, 169 (1958). 

* L. C. Bateman, M. G. Church, E. D. Hughes, C. K. Ingold, and N. A. Taher, J. Chem. Soc, 979 


' H. L. Goering and H. Hopf, J. Amer. Chem. Soc, 93, 1224 (1971). 

The Leaving Group 

The simple S^l mechanism, without ion pairs, predicts that the leaving group 
should not affect the products; we have seen in the previous section how the 
presence of ion pairs modifies this anticipated behavior. Since the leaving 
group is involved in the rate-determining step, it should have an important 
influence on rate. The experimental results confirm this prediction. 

We have considered in Section 4.3 (p. 192) the structural features that make 
a good leaving group for S N 2 substitutions ; most of the same arguments hold for 
S w l reactions. Egr a sub stitution to followjhe S j ,l p at h, it is genera lly necessary 
that X he one o fth e bTtteO elymglgroups^joi^ exam ple ; a halide ion^ a weakly 
b asic oxyanion , or a ne utral ox y_g£ii^.iii trogen7 or suEir Jgavm ggroup such as 
HaQ^N^jOxSR?- Table 5.3 lists a few ofthe common anionic leaving groups with 
approximate relative reactivities. As the ratios are subject to changes with varia- 
tion of solvent and substrate structure, these data have only qualitative signifi- 
cance. Comparison with Table 4.7 (p. 193) shows that th e S.,1 rate is much more 
sensitive to the jiature ofthe lea vin g group than is the S^rate^--^, 

H. M. R. Hoffmann investigated the variation in the tosylate to bromide 

224 Unimolecular Substitutions and Related Reactions 


RX + N:" 

+ xr 

Reaction coordinate 

Figure 5.2 S N 2 reaction. Curve a: Good nucleophile causes rapid reaction; transition state 
is early, charge separation small. Curve b: Poor nucleophile results in slower 
reaction ; transition state is later, charge separation large. 

R + X~ 


Reaction coordinate 

Figure 5.3 S N 1 reaction. Curve a: Stable ion gives rapid reaction; transition state is early, 
charge separation small. Curve b: High-energy ion causes less rapid reaction; 
transition state is late, charge separation large. 

rate ratio (k 0T Jk Bv ) and concluded that a large ratio is characteristic of a large 
degree of charge development on the leaving group in the transition state. (See 
the discussion for S w 2 reactions in Section 4.3, p. 192.) For solvolysis reactions in 
the absence of a strong nucleophile he found that the large ratios occurred with 
those substrate structures and solvents that had high reaction rates, and because 
he considered the cause of the difference between the two leaving groups to be 
the more effective negative charge stabilization in the larger arenesulfonate ion. 

Effects of Structure and Solvent 225 

he stated that "the faster an S N 1 . . . reaction, the more ionic its transition 
state." 34 

Since Hoffmann's work appeared, the k OT Jk Br ratio has come into use as 
one of the tools for measuring transition state charge separation. Nevertheless, 
we might profitably examine the argument more closely. In Figures 5.2 and 5.3 
the . Hammond postu l ate is th e guid e for cons tructing reaction coordinate dia- 
g rams of Sj y2 and S w l pathways in which some feature oTthe substrate structure 
or_(in_the S N ?, rase) pnteringgj^aipxiudeophilicity causesja change of rate. As 
we have seen in Section 4.3, Hoffman n's proposa lis-io-ac cord with the xationale 
provid ed by these d' ___j_"S fpr th" S ; . 9 prnrpss (Fig u re 5.? , ) _TJT_____tinns with 
b^ tter~nu^eop hlI^2curve a) are expected_toJiaye_jsaxLierJransition statesjwith 
l ess charge _ d evelop ment onjthe leaving-group; these are the cases with small 
^oTs/^Br ratios. Thejaster LS^l__reactions ^(Figure 5.3) should_also_be._those.with 
less charge development (curve a]j jej_rjerimentally_ these are the ones with large 

OTs/ Br I*3X10S* 

Using dependence of rate on solvent, a technique we discuss further in 
Section 5.4, Bingham and Schleyer were unable to detect any significant varia- 
tion in transition state charge separation in a series of bridgehead derivatives of 
varying reactivity. 35 They also pointed out a difficulty arising from Hoffmann's 
having based his conclusions on data drawn from reactions of tertiary, secondary, 
and even primary substrates. Hoffmann had assumed that reactions carried out 
in solvents favorable to ion formation (such as water or formic acid) would be 
limiting S N 1 processes, and had concluded that the differences in k OT Jk Br that he 
observed with different substrates arose primarily from different amounts of 
charge separation at the transition state. It now appears that at least the primary 
substrates, and probably also the secondary ones, solvolize with substantial 
assistance by nucleophilic attack of solvent. Bingham and Schleyer have pro- 
posed that the more bulky tosylate is subject to greater crowding in a tertiary 
substrate than is bromide, and tJjat these steric effects are largely responsible for 
the variations in k OT Jk Br ratio. 3 ___ur conclusion is that, as a measure of transition 
state charge separation in limiting S w l reactions, the k OT Jk Br ratio is of little 
useT/We shall return to the problem of location of the transition state along the 
reaction coordinate in Section 5.4. 

An imp ortant neutral lea v ing group is N 9 . Diazotization of alkyl amines 
(Equation 5.11) leads to the unstable alkyl diazonium ions, which immediately 
lose nitrogen, leaving carbocations. 

C— NH 2 + HONO 

\ ♦ 

C— N=N : 
/ N 
R 2 R; 


X- ► C + + N 2 + X- (5.11) 

/ V 
Ra R3 

R 3 LR 2 ^3 J R 2 R 3 

Interpretation of the reactions of these ions has proved difficult. Product distribu- 
tions and stereochemistry differ from those typical of solvolysis; 37 the large energy 

34 H. M. R. Hoffmann, J. Chem. Soc, 6753, 6762 (1965). 

35 R. G. Bingham and P. v. R. Schleyer, J. Amer. Chem. Soc, 93, 3189 (1971). 

36 See note 35 and J. Slutsky, R. C. Bingham, P. v. R. Schleyer, W. C. Dickason, and H. C. Brown, 
J. Amer. Chem. Soc, 96, 1969 (1974). 

37 For further discussion see Section 6. 1 . 

226 Unimolecular Substitutions and Related Reactions 

Table 5.4 Solvolysis Rates of Alkyl Chlorides" 

Compound R = H R = CH 3 R = <f> kcnJk H *«/*ch 3 

CH 3x R 

C 1.57 x 10" 6 0.086 394 55,000 4580 

CH 3 / X C1 

GH 3x R 

C 0.216 394 19,900 1,800 50 

<j/ CI 

<j> R 

^C^ 575 19,900 578,000 34.6 29 

f CI 

Source: Reprinted with permission from H. C. Brown and M. Rei, J. Amer. Chem. Soc., 86, 5008 

(1964). Copyright by the American Chemical Society. 

° First-order rate constants, corrected to 25°C in ethanol, 10 e X sec -1 . 

release that attends loss of the stable N 2 molecule may leave the ion in a vibra- 
tionally excited state (the hot ion theory), 38 or some products may arise from the 
diazonium ion directly. 39 It is also likely that ion-pair phenomena play an 
important role. 40 Collins 41 and Moss 42 have reviewed aspects of the subject, and 
Friedman 43 has discussed it at length. The field is one with much room for further 

The Substrate 

In_an Sjvl reaction the low-energy substrat e ionizes to the high-energy ion pair. 
The HarnmoTicTpostuIate jpredic ts that the trans ition state shou ld fes eniLle^the 
ion jDairJsee Figure 5.3) ;jh^ncearvy_structur al change that lowers the carbocation 
energy jshould lower_Jxansition stat e_engrg y and incr ease, reaction rate. The 
evidence provides unequivocal confirmation of this prediction. Schleyer and co- 
workers 44 estimate that for limiting S^l reactions, with no assistance to ionization 
by nucleophiles, the substitution of H by CH 3 on the reacting carbon accelerates 
the rate by a factor of 10 8 , a difference in activation energy of about 11 kcal 
mole -1 . Other data of a similar sort, but subject to uncertainty because of un- 
certain mechanisms, are given by Brown and Rei. 45 Some of this information is 
reproduced in Table 5.4. The differences are not as large as that given by 
Schleyer, because reactions of secondary substrates are being accelerated by 
nucleophilic attack of solvent; nevertheless, the trends are clear. 

38 D. Semenow, C.-H. Shih, and W. G. Young, J. Amer. Chem. Soc, 80, 5472 (1958). 

39 (a) A. Streitwieser, Jr. and W. D. Schaeffer, J. Amer. Chem. Soc, 79, 2888 (1957); (b) A. Streit- 
wieser, Jr., J. Org. Chem., 22, 861 (1957). 

40 C. J. Collins, Accts. Chem. Res., 4, 315 (1971). 

41 See note 40. 

42 R. A. Moss, Chem. & Ertg. News, 49, No. 48, p. 28 (1971). 

43 L. Friedman, in Carbonium Ions, G. A. Olah and P. v. R. Schleyer, Eds., Wiley-Interscience, New 
York, 1970, Vol. II, p. 655. 

44 J. L. Fry, E. M. Engler, and P. v. R. Schleyer, J. Amer. Chem. Soc, 94, 4628 (1972). 

46 (a) H. C. Brown and M. Rei, J. Amer. Chem. Soc, 86, 5008 (1964) ; (b) See also G. A. Olah, P. W. 
Westerman, and J. Nishimura, J. Amer. Chem. Soc, 96, 3548 (1974). 

Effects of Structure and Solvent 227 

Whereas substitution of hydrogen directly attached to the cationic center by 
alkyl or aryl has a large stabilizing effect, substituents at more remote positions 
are more subtle in their influence. We might expect, on the basis of the ability 
of alkyl groups to stabilize charge, that cation 6 should be more stable than cation 
5. This prediction is indeed correct for the isolated ions in the gas phase. In 

\ + ^ \ + 

C— C^ ,C— C-^i 

'4 4 

5 6 

solution the order is reversed, and 5 is more stable. 46 

Arnett has observed that heats of reaction for carbocation formation in 
highly acidic media (Equation 5.12) correlate well with solvo lysis rates. 47 This 

RX-HA > R+ + HAX- (5.12) 

result supports the idea that ion and solvolysis transition state are closely related 
structurally, and that we can safely use ideas about ion stability to predict 
solvolysis rates and vice versa. 

When atoms_wi th unshared pairs of electrons are bonded to the reaction 
rentpr 3 two effects must be consider ed_LJ;he inductive effect, which is usually 
ejectrqnr withdrawing. and th e electron-donating conjugati ve effect (7). For the 
more bajig_a toms, O , N, S, c onjugation is dominant, as the relative solvolysis 

\+ \ + 

C— E: < >- C=E 

/ 7 / 

rates of 8 and 9 show. Insulation from the conjugative influence by one CH 2 

C 2 H 5 — O— CH 2 — CI CH 3 CH 2 CH 2 CH 2 — CI C 2 H 5 — O— CH 2 CH 2 — CI 

8 9 10 

Relative rate: 10 9 1 0.2 

group (10) leaves the inductive effect to cause a rate depression. 48 Mechanisms 
are unlikely to be limiting in 9 and 10, but should be more nearly so in 8; the 
relative rates therefore probably have only qualitative significance. W ith ot^ 
halogens, the two effects are more nearly balance d. Fluorine is h igiily--£l£C.tro- 
negatiye_and d ecreases the rate slightLy_despite.ils unshared .electrons ; chlorine 
anH prnm ine incr ease rates, bu tmuch less than does oxygen (& x /^h ratios 10 to 500), 
presumably because of the less effective overlap with carbon of the large 3p or \p 
orbitals that contain the unshared pairs in these atoms. 49 Chemical shifts in 13 C 
nuclear magnetic resonance spectra independently demonstrate the decreasing 
effectiveness of donation of electron density by conjugation to an adjacent 
positive carbon in the order F > CI > Br. 50 

Another important consequence of structural change, first observed and 

46 J. W. Larsen, P. A. Bouis, M. W. Grant, and C. A. Lane, J. Amer. Chem. Soc., 93, 2067 (1971). 

47 E. M. Arnett and J. W. Larsen, in Carbonium Ions, G. A. Olah and P. v. R. Schleyer, Eds., Vol. I, 
p. 441. 

48 A. Streitwieser, Jr., Solvolytic Displacement Reactions, pp. 102-103. 
46 See note 48. 

50 G. A. Olah, Y. K. Mo, and Y. Halpern, J. Amer. Chem. Soc, 94, 3551 (1972). 

228 Unimolegular Substitutions and Related Reactions 

Table 5.5 Approximate Solvolysis Rates of Bridgehead Systems Relative to <-Butyl 


Relative Rate" 

(CH 3 ) 3 C— X 

io- a 




° Calculated for tosylates in acetic acid at 70°C using data of R. C. Bingham and P. v. R. Schleyer, 
J. Amer. Chem. Soc, 93, 3189 (1971) and of E. Grunwald and S. Winstein, J. Amer. Chem. Soc, 70, 
846 (1948). 

explained by Bartlett and Knox for the apocamphyl system (11), is thejresisjance 
to-xatieft-_fiirmajiaii_^aL a bridgehead position. 51 Table 5.5 lists approximate 

H 3 C Ns XHH 3 

rates for some bridgehead systems relative to /-hutyl A Qarhg^^tior °k"iilH prefer 
tn.,.h r p l?"^'- J anH p ]anarit y in thgc p B ^ ^t^rps fntRil s a large in CTgasejn ring 
^trajn. The systems with the greatest strain increase upon passing from ground 
state to transition state react slowest. Reaction rates and calculated strain 
energies correlate well. 52 

The bridgehead ions, even though they cannot achieve a coplanar geometry, 
are nevertheless stabilized by hyperconjugative electron donation from attached 
groups. In bridgehead systems, the conformation is fixed by the rings, and the 
transition state for S N 1 solvolysis is usually 12. The numbering in 12 is keyed to the 

51 P. D. Bartlett and L. H. Knox, J. Amer. Chem. Soc, 61, 3184 (1939). 
62 See note 35, p. 225. 

Effects of Structure and Solvent 229 
1-adamantyl cation (13), a typical bridgehead ion. The carbon C 3 is in the trans 




Cl C 3 ° 2 



c A Hl 




periplanar position with respect to the leaving group. The system 14, which 
solvolyzes at roughly 3 x 10 -5 times the rate of 1-adamantyl (13), has the con- 
formation 15, with a cis periplanar hydrogen and no trans periplanar group. It 
thus app ears that h ^peroOTrju^ajtive^djextror^ occurs more readily at_ the 

backjj f an incipient electron -deficient, renter than at the fro nt, 53 just as in Sjy2 
substitutions a ttack by nucleophile from the side opposite the departing group is 
more favorable than attack from the same side. 

The influence of electron-donating and -withdrawing groups can best be 
studied by use of the Hammett and Taft linear free-energy relationships, 
which were discussed in Chapter 2 (p. 60). Studies in the bridgehead bicyclo- 
[2.2.2]octyl (16) and adamantyl (17) series have been carried out by Schleyer 
and Woodworth. 54 Correlations with the Taft inductive ct* CH2 parameter had the 
negative slope expected for a reaction accelerated by electron-donating groups. 
The electron-donating inductive effect of the alkyl groups increases along the 




series methyl < ethyl < isopropyl < i-butyl. The rate differences on which this 
order is based are small, a factor of 2 between methyl and i-butyl in 16 and of 3 in 
17. The position of hydrogen in the series is different in 16 and 17; this fact, and 

63 See note 35, and W. Parker, R. L. Tranter, C. I. F. Watt, L. W. K. Chang, and P. v. R. Schleyer, 

J. Amer. Chem. Soc, 96, 7121 (1974). 

54 P. v. R. Schleyer and C. W. Woodworth, J. Amer. Chem. Soc, 90, 6528 (1968). 

230 Unimolecular Substitutions and Related Reactions 

the small rate differences, make it unclear whether alkyl groups are electron- 
donating or -withdrawing compared to hydrogen in these compounds. 

The Hammett a—p correlation has proved useful in studying substituent 
effects of aryl-substituted systems. 55 In Section 6.1 we consider applications of 
this linear free-energy relationship to solvolysis with rearrangement. 

Isotopic substitution will also affect rates. 56 Most of the isotope effects ob- 
served in S„l substitutions are for H-D substitution; the isotopically substituted 
bond is not broken in the reaction, and the observed secondary isotope effect 
ratios (Section 2.7, p. 109) k K lk D are less than 1.5. Substitution of H by D on the 
carbon to which the leaving group is attached leads to the a-isotope effect, with 
k^jk-Q ratios of between 1.22 and 1.25 for systems with sulfonate leaving groups 
which appear to react by a limiting S w l mechanism, and somewhat lower 
(CI x 1.15, Br x 1.13) for limiting reactions with halide leaving groups. 57 
As we have seen in Section 2.7, the origin of the rate change is in the out of plane 
bending vibration, which decreases in frequency on going from the .^-hybrid- 
ized starting Vnaterial to the transition state, where hybridization is approaching 
sp 2 . The presence of the leaving group and an entering nucleophile nearby 
stiffens the bond and makes the frequency change smaller; hence S N 2 reactions 
show little or no rate change on isotopic substitution. The a-isotope effect is thus a 
measure of the degree of participation by nucleophile at the transition state. 58 
Substitution of D for H at the /?-carbon produces effects typically around A: H /A; D 
1.07 per deuterium, but as high as 1.44 for favorable conformations. These effects 
are thought to reflect derealization of the positive charge to the /J=C — H 
bonds, a point we shall consider further in Section 10.2, and thus to measure 
the degree of charge development at the transition state. 59 This interpretation 
has, however, been questioned. 60 

The Entering Group 

The limiting S w l mechanism predicts that an added nucleophile, unless it is 
the common ion, will have no effect on reaction rate. We have seen in Section 
5.1 how the inclusion in the mechanism of ion pairs accounts for the observed 
deviations from this principle ; the point of interest here is the product distribu- 
tion obtained when more than one nucleophile is present. 

If none of the products re-ionize to a detectable extent during the time the 
system is under observation, their relative amounts will be kinetically controlled 

55 (a) A. Streitwieser, Jr., H. A. Hammond, R. H. Jagow, R. M. Williams, R. G. Jesaitis, C. J. 
Chang, and R. Wolf, J. Amer. Chem. Soc, 92, 5141 (1970); (b) Streitwieser, Solvolylic Displacement 
Reactions, pp. 179-180. 

66 For discussions see: (a) H. Simon and D. Palm, Angew. Chem. Int. Ed., 5, 920 (1966) ; (b) A. Streit- 
wieser, Solvolytic Displacement Reactions, pp. 172-174 (a effects) ; pp. 98-101 (/3 effects). 

57 (a) J. M. Harris, R. E. Hall, and P. v. R. Schleyer, J. Amer. Chem. Soc, 93, 2551 (1971) ; (b) V. J. 
Shiner, Jr., and R. D. Fisher, J. Amer. Chem. Soc, 93, 2553 (1971) ; (c) T. W. Bentley, S. H. Liggero, 
M. A. Imhoff, and P. v. R. Schleyer, J. Amer. Chem. Soc, 96, 1970 (1974); (d) E. A. Halevi, Prog. 
Phys. Org. Chem., 1, 109 (1963); (e) V. J. Shiner, Jr., W. E. Buddenbaum, B. L. Murr, and G. 
Lamaty, J. Amer. Chem. Soc, 90, 418 (1968) ; (f) A. Streitwieser, Jr. and G. A. Dafforn, Tetrahedron 
Lett., 1263 (1969); (g) G. A. Dafforn and A. Streitwieser, Jr., Tetrahedron Lett., 3159 (1970). 

58 See note 56. 

59 See note 56 and (a) V. J. Shiner, Jr., J. Amer. Chem. Soc, 82, 2655 (1960); (b) V. J. Shiner 
and J. G. Jewett, J. Amer. Chem. Soc, 86, 945 (1964). 

60 L. S. Bartell, Tetrahedron Lett., No. 6, 13 (1960). 

Effects of Structure and Solvent 231 




Reaction coordinate 


Reaction coordinate 

Figure 5.4 (a) A slow ionization (large AG*) yields a high-energy intermediate which is 
relatively unselective (small AAG*) and reacts with Y and Z at nearly equal 
rates, (b) Rapid ionization (small AGf) produces a more stable intermediate 
which is more discriminating (large AAG*) and favors combination with Z 
strongly over Y. 

and will be in direct proportion to the relative rates of reaction of the intermediate 
with the different nucleophiles. On the basis of the Hammond postulate, we 
anticipate that a highly reactive intermediate, facing low activation barriers, will 
find small differences between various paths and will be relatively nondiscriminat- 
ing in its choice of reaction partner ; whereas a less reactive one, confronted with 
higher barriers, will encounter larger differences and be more particular. When 
coupled with the expectation that a less reactive ion forms faster, this principle 
predicts a correlation between solvolysis rate and selectivity for S^l processes. 
Figure 5.4 illustrates the reasoning and Figure 5.5 presents the experimental 

232 Unimolecular Substitutions and Related Reactions 

logfc -5 






12 3 

log fc N Iky, 

Figure 5.5 Correlation between stability, measured by solvolysis rate in 80 percent aqueous 
acetone, and selectivity, determined by relative rate of reaction with azide ion 
(k N ) and water (k w ), for carbocations derived from alkyl chlorides. Reprinted 
with permission from D. J. Raber, J. M. Harris, R. E. Hall, and P. v. R. 
Schleyer, J. Amer. Chem. Soc., 93, 4821 (1971). Copyright by the American 
Chemical Society. 

evidence. 61 Caution is necessary in using this argument, because solvation has not 
been taken into account. 

The Solvent 

The solvent is a component of critical importance in S^l reactions. A high di- 
electric constant favors charge separation; ability to solvate ions is also essential 
for rapid reaction. The nucleophilicity, on the other hand, should not affect a 
limiting S^l process. Grunwald and Winstein developed a linear free-energy 
relation (Equation 5.13) for solvent ionizing power, defined in terms of the 
solvolysis rate of f-butyl chloride, a system assumed to react by a limiting mech- 
anism. 62 In Equation 5.13, A; s is the solvolysis rate in the solvent S; k a0% Et0H is 


= rriY 


61 D.J. Raber, J. M. Harris, R. E. Hall, and P. v. R. Schleyer, J. Amer. Chem. Soc, 93, 4821 (1971). 

62 E. Grunwald and S. Winstein, J. Amer. Chem. Soc, 70, 846 (1948) ; a compilation of Y values may 
be found in A. H. Fainberg and S. Winstein, J. Amer. Chem. Soc, 78, 2770 (1956). 

Carbocations 233 

the rate in the standard solvent, 80 percent aqueous ethanol; m measures the 
sensitivity of the particular system to solvent change; and Y is the ionizing power 
of solvent S, determined from £-butyl chloride solvolysis rates by defining m = 1 
for this substrate. 

In addition to allowing comparison among experiments carried out in dif- 
ferent solvents, the m-Y system serves as an important tool for study of mech- 
anism. Sensitivity to ionizing power, measured by m, is an index of the degree of 
charge separation at the transition state. The ratio of rates in two solvents of 
equal Y but different nucleophilicity provides evidence about nucleophilic 
assistance by a solvent molecule during the ionization. 

Other solvent parameters based on the influence of solvent on electronic 
excitation energies have been developed by Kosower; 63 Smith, Fainberg, and 
Winstein; 64 and Dimroth and co-workers. 65 

Despite its usefulness, the Y parameter system is not without flaw. Like 
most linear free-energy correlations, it fails if rigorously applied to compounds of 
diverse structural types. Thus when a given substrate is studied in different 
solvent systems (for example acetone-water, ethanol-water, acetic acid-formic 
acid), slightly different slopes m are obtained. 66 


The chemistry of carbocations has been intensively studied, and the literature is 
vast. We can do no more here than summarize some of the important features of 
the field. A comprehensive review in four volumes covers the area in detail. 67 

The nomenclature of positive carbon ions in general use up to the 1970s is 
not consistent with the naming of other types of positive ions. We follow Olah's 
suggestions inusing the, t erm carbocation 'mj^ss j' nf thp JQEmfrl y " spr * 
as_t he gene ric^ name fQ r_iQns-jtyith_£ositive charge on carbon. 68 There_are_two 
types of carbocation : the ruthenium ions, in which the pnskivg-xarbon Jias co- 
ordination number 3, a s in trimethylcarbenium ion (<-butyl cation) (18); and 

CH 3 

H 3 C 

/ C \ 

CH 3 


H x/V H 


63 (a) E. M. Kosower, J. Amer. Chem. Soc., 80, 3253, 3261, 3267 (1958); (b) E. M. Kosower, An 
Introduction to Physical Organic Chemistry, Wiley, New York, 1968, p. 295; solvation is discussed in 
detail beginning on p. 260. 

64 S. G. Smith, A. H. Fainberg, and S. Winstein, J. Amer. Chem. Soc, 83, 618 (1961). 

66 K. Dimroth, C. Reichardt, T. Siepmann, and F. Bohlmann, Justus Liebigs Ann. Chem., 661, 1 

66 A. H. Fainberg and S. Winstein, J. Amer. Chem. Soc., 79, 1597, 1602, 1608 (1957). 

67 (a) G. A. Olah and P. v. R. Schleyer, Eds., Carbonium Ions, Wiley-Interscience, New York, Vol. I, 
1968; Vol. II, 1970; Vol. Ill, 1972; Vol. IV, 1973. Other reviews: (b) D. Bethell and V. Gold, 
Carbonium Ions, Academic Press, London, 1967; (c) N. C. Deno, Prog. Phys. Org. Chem., 2, 129 (1964). 
66 G. A. Olah, J. Amer. Chem. Soc, 94, 808 (1972). 

234 Unimolecular Substitutions and Related Reactions 

the carbonium ions, 'j^_whjllh thfLjg^tryr ^r)-..-.^ ™- carb ons has 
nurn5grjT^r _5, as in the bridged structure , 19. The former structures, for many 
years designated classical ions, have ordinary two-electron bonds; the latter, 
known earlier as nonclassical ions, have a three-center, two-electron bond. 69 
Carbenium ions derived from alkenes by protonation may also be called alkenium 

The Existence of Carbocations 

Most carbocations are too reactive to be directly observable in ordinary solvents, 
and until relatively recently evidence has been obtained indirectly, primarily 
through the study of reaction kinetics and trapping processes, experiments dis- 
cussed in Sections 5.1, 5.2, and 5.4. Nevertheless, a few types of compounds have 
long been known to produce observable concentrations of positive ions relatively 
easily. The triarylmethyl derivatives were the first of this type to be investigated; 
the halides ionize readily in non-nucleophilic solvents such as sulfur dioxide, 70 
and the alcohols yield solutions of the ions in concentrated sulfuric acid. Early 
observations by the freezing-point depression technique (see Section 3.2, p. 130) 
established that each mole of triphenyl carbinol yields 4 moles of ions in sulfuric 
acid, the reaction presumably being by way of Equation 5.14. 71 Results in 
methane-sulfonic acid are similar. 72 

K i 

£OH + 2H 2 S0 4 >- C + + H 3 + + 2HS0 4 - (5.14) 

*\ A 

The cryoscopic method is also applicable to other triarylmethyl systems, to 
some diarymethyl and allylic ions, and, when ortho substituents are present, to 
aryl acylium ions (20) (Equation 5.15); 73 unfortunately, side reactions frustrate 
most attempts to generate carbocations in sulfuric acid. 

CH 3 — (' V-C— OH + 2H 2 S0 4 >• CH 3 — « V- + C=0 + H 3 + + 2HS0 4 " 

CH 3 CH 3 


More recently, development of the superacid solvent systems has permitted 
the preparation at low temperature of stable solutions of carbocations of many 
structural types. The solvents ordinarily used consist of the strong Lewis acid 
antimony pentafluoride with or without an added protonic acid, usually hydro- 

69 See note 68. 

70 N. N. Lichtin, Prog. Phys. Org. Chem., 1, 75 (1963). 

71 (a) A. Hantzsch, Z. Physik. Chem., 61, 257 (1907); (b) L. P. Hammett and A.J. Deyrup, J. Amur. 
Chem. Soc, 55, 1900 (1933). 

72 R. A. Craig, A. B. Garrett, and M. S. Newman, J. Amur. Chem. Soc, 72, 163 (1950). 

73 (a) H. P. Treffers and L. P. Hammett, J. Amer. Chem. Soc, 59, 1708 (1937); (b) M. S. Newman 
and N. C. Deno, J. Amer. Chem. Soc, 73, 3644 (1951); (c) N. C. Deno, H. G. Richey, Jr., J. D. 
Hodge, and M. J. Wisotsky, J. Amer. Chem. Soc, 84, 1498 (1962). 

Carbocations 235 

fluoric or fluorosulfuric acid. A substance of very low basicity such as S0 2 , 
S0 2 C1F, or S0 2 F 2 serves as diluent when required. As we have seen in Section 
3.2 (p. 134), these solvent systems are considerably more acidic than concentrated 
sulfuric acid as measured by the H acidity function. 74 Olah and his co-workers 
have made extensive contributions to this field. 75 The ready availability of solu- 
tions of many types of carbocations has made possible spectroscopic observations 
of a greatly expanded variety of structures. Nuclear magnetic resonance, both 
proton and 13 C, has been fruitful and has yielded information not only about 
structure but also about rearrangement processes; other methods, particularly 
infrared and Raman spectroscopy, have proved informative as well. X-Ray 
photoelectron spectroscopy (electron spectroscopy for chemical analysis, ESCA), 
which measures binding energies of Is electrons of the carbon atoms, yields in- 
formation about derealization of charge within the ion. 76 

Structures of Carbocations 

The sajientjeaturejrfthe structure of the cajJ3emurn_ions is jhdrjreferenceJhr 
coplanarity of the cationic carbon . and the three ..attached atoms.,... Structural 
theory, in its simple st f orm^jhe_principle of minimum electron-pair interaction 
(see Section 1.1, p. 8), predicts a .planar ^Jiybridized structure. Analogy with 
the boranes is in agreement: Planar 77 (CH 3 ) 3 B is isoelectronic with (CH 3 ) 3 C + , 
which ought therefore to be planar also. More sophisticated theoretical computa- 
tions agree with these simple arguments. 78 We have seen in Section 5.2 that the 
indirect evidence from rates of formation of bridgehead ions supports the idea of 
preferred planarity. Spectroscopic investigation of ions in strong acid solutions 
furnishes more direct evidence. Olah and his collaborators have recorded the 
infrared and Raman spectra of (CH 3 ) 3 C + ; the close similarity to spectra of 
(CH 3 ) 3 B confirms planarity of the ion. 79 

In allylic systems, favorable overlap of the p orbitals of the 77 system should 
require a coplanar arrangement of the three sp 2 carbons and their five substituent 
atoms; evidence that such a structure is indeed preferred comes, for example, 
from proton magnetic resonance observations that demonstrate barriers to bond 
rotation in the isomeric dimethylallyl ions 21, 22, and 23. These ions form stereo- 
specifically from the three dimethylcyclopropyl chlorides (Section 12.2), and 
barriers to rotation about the partial double bonds are sufficiently high to prevent 
interconversion at low temperature. At — 10°C, 21, the least stable isomer, 

74 R. J. Gillespie and T. E. Peel, Advan. Phys. Org. Chem., 9, 1 (1971). See Figure 3.3, p. 136. 

76 For reviews see (a) G. A. Olah and J. A. Olah in Carbonium Ions, Olah and Schleyer, Eds., Vol. II, 

p. 715; (b) R.J. Gillespie, Accts. Chem. Res., 1, 202 (1968). 

76 See the following reviews in Olah and Schleyer, Eds., Carbonium Ions, Vol. I : (a) electronic spectra, 
G. A. Olah, C. U. Pittman, Jr., and M. C. R. Symons, p. 153; (b) vibrational spectra, J. C. Evans, 
p. 223; (c) NMR spectra, G. K. Fraenkel and D. G. Farnum, p. 237; a review of applications of all 
the spectroscopic techniques to carbocation structures and reactions is (d) G. A. Olah, Angew. 
Chem. Int. Ed., 12, 173 (1973). 

77 H. A. Levy and L. O. Brockway, J. Amer. Chem. Soc, 59, 2085 (1937). 

78 See, for example: (a) J. E. Williams, Jr., R. Sustmann, L. C. Allen, and P. v. R. Schleyer, J. 
Amer. Chem. Soc, 91, 1037 (1969); (b) L. Radom, J. A. Pople, V. Buss, and P. v. R. Schleyer, J. 
Amer. Chem. Soc, 94, 31 1 (1972); (c) L. Radom, P. C. Hariharan, J. A. Pople, and P. v. R. Schleyer, 
J. Amer. Chem. Soc, 95, 6531 (1973) ; for a review, see (d) V. Buss, P. v. R. Schleyer, and L. C. Allen, 
Top. Stereochem., 7, 253 (1973). 

79 G. A. Olah, J. R. DeMember, A. Commeyras, and J. L. Bribes, J. Amer. Chem. Soc, 93, 459 (1971). 

236 Unimolecular Substitutions and Related Reactions 

changes with a half-life of about 10 min to the more stable cis,trans isomer, 22, 
and this in turn at + 35°C converts to 23. 80 

CH 3 

Similar considerations might be expected to apply to the triarylmethyl ions. 
The most favorable charge derealization would be obtained if the rings were all 
coplanar. But inspection of a model shows that a completely planar triphenyl- 
methyl ion can be made only at the expense of unacceptable crowding of the 
ortho hydrogens. 81 Triphenylmethyl ions are sufficiently stable to be isolated as 
salts in the crystalline state. In the solid perchlorate, the actual structure, 
although coplanar about the central cationic carbon, has the rings twisted out of 
this plane by an angle of about 32°. 82 In solution, nuclear magnetic resonance 
evidence, obtained with ring-fluorinated derivatives, suggests a similar structure, 
with a barrier to rotation of all three rings to the enantiomeric conformation 
(24 ^ 25) of about 9 kcal mole- 1 . 83 

AH* x 9 kcal mole- 1 


Carbocations with trivalent carbon may have carbon with coordination 
number 2. Acyl ions have already been mentioned; the vinyl cations, or car- 
bynium ions (26), have been detected as intermediates in addition of electro- 
philes to acetylenes and allenes and in solvolysis reactions with the highly reactive 
trifluoromethanesulfonate (triflate) leaving group. 84 Vinyl cations are expected 

80 P. v. R. Schleyer, T. M. Su, M. Saunders, and J. C. Rosenfeld, J. Amer. Chem. Soc, 91, 5174 

81 G. N. Lewis and M. Calvin, Chem. Rev., 25, 273 (1939). 

82 A. H. Gomes de Mesquita, C. H. MacGillavry, and K. Eriks, Acta Cryst., 18, 437 (1965). 

83 I. I. Schuster, A. K. Colter, and R.J. Kurland, J. Amer. Chem. Soc, 90, 4679 (1968). 

84 (a) P. J. Stang and R. Summerville, J. Amer. Chem. Soc, 91, 4600 (1969) ; (b) R. H. Summerville 
and P. v. R. Schleyer, J. Amer. Chem. Soc, 94, 3629 (1972); (c) T. C. Clarke, D. R. Kelsey, and 
R. G. Bergman, J. Amer. Chem. Soc, 94, 3626 (1972); (d) T. C. Clarke and R. G. Bergman, J. Amer. 
Chem. Soc, 94, 3627 (1972); (e) R. H. Summerville, C. A. Senkler, P. v. R. Schleyer, T. E. Dueber, 
and P.J. Stang, J. Amer. Chem. Soc, 96, 1100 (1974); (f) R. H. Summerville and P. v. R. Schleyer, 
J. Amer. Chem. Soc, 96, 1 1 10 (1974). Forreviews, see: (g) G. Modena and U. Tonellato, Advan. Phys. 
Org. Chem., 9, 185 (1971); (h) M. Hanack, Accts. Chem. Res., 3, 209 (1970). 

Mechanisms Intermediate Between S^l and Sjv2 237 

on the basis of detailed molecular orbital calculations to be linear if R x and R 2 
are the same, 85 but will probably not be exactly linear if R^ # R 2 - 86 

W hen the electr ojiS-0-f_a bond wi^in_th£JOR-b«t-rexDQved from_the_sit£i_of 
binding o f t h e l ea vi n g rronp 'JlLCI^t-J^tb_thc..r.h^^d-_££I!J£Ix,Lbg charge is 
distribute d over . several rarhnns, eac h of which w ill th en .have, coordination 
number^-or-f). Equations 5.16, 5.17, and 5.18 illustrate the formation of some 
ions of this type. Intensive research into the properties of these carbonium ions 

+ x- 

+ x- 



+ x- 


dates from the proposal by Winstein and Trifan in 1949 of the process shown in 
Equation 5.17 to account for solvolysis rates and stereochemistry in the bicyclo- 
[2.2.1]heptyl system. 87 The existence of the bridged structures has been a matter 
of controversy; 88 although some objections remain, 89 the weight of the evidence, 
including direct spectroscopic observation, now appears to have established their 
importance. 90 Because the carbonium ions arise in rearranging systems, we 
reserve more detailed discussion to Chapter 6. 

Formation and Reactions of Carbocations 

It is appropriate to summarize at this point the chemistry of carbocations. Table 
5.6 lists the principal means of generating these intermediates and their most 
important reactions. 


Up to this point we have confined our discussion of nucleophilic substitution to 
those reactions that appear to follow either an extreme S w 2 process (Chapter 4) or 
the limiting S w l path. There is a middle ground; many substitutions have some 
of the characteristics of each extreme but belong to neither. 

85 W. A. Latham, W.J. Hehre, and J. A. Pople, J. Amer. Chem. Soc, 93, 808 (1971). 

86 See note 84(f). 

87 S. Winstein and D. S. Trifan, J. Amer. Chem. Soc, 71, 2953 (1949). 

88 (a) P. D. Bartlett, Nonclassical Ions, W. A. Benjamin, Menlo Park, Calif., 1965; (b) H. C. Brown, 
Accts. Chem. Res., 6, 377 (1973); (c) D. Lenoir, P. Mison, E. Hyson, P. v. R. Schleyer, M. Saunders, 
P. Vogel, and L. A. Telkowski, J. Amer. Chem. Soc, 96, 2157 (1974); (d) G. D. Sargent, in Carbonium 
Ions, Olah and Schleyer, Eds., Vol. Ill, p. 1099. 

89 See note 88(b). 

80 See note 76(d), p. 235. 

238 Unimolecular Substitutions and Related Reactions 
Table 5.6 Formation and Reactions of Carbocations 

„ _, ,_ , • „ R — x > R + + x " 

Bond heterosis' R _ x + y R+ + x 

Addition to C=C" 

\ / A \ +/ 

/>=q + A > yp-\ 

Addition to C=O c 

A" A" 

\ \+ / \ +/ 

C=0 + A > C— O i ► ^0=0 

Reactions Regenerating Carbocations 
Hydrogen transfer" 1 

R X H + R 2 + > R x + + R 2 H- 

Rearrangement 6 

R i\ +/ R 2 R i\ + / R i 

^C-C -^ /C -C-R 2 

Ri K 2 

Ri R 


Addition" R+ + C=C >■ ,-C— C 

Fragmentation* ^C— C > R+ + C=C 

Reactions Destroying Carbocations 
Combination with Lewis base" 

R + + Y:" > RY 

Elimination" .C—C >- C=C + H + 

° Chapter 5. 

6 Chapter 7. 

" Chapter 8. 

" C. D. Nenitzescu, in Carbonium Ions, G. A. Olah and P. v. R. Schleyer, Eds., Wiley-Interscience, 

New York, 1970, Vol. II, p. 463; see also D. M. Brouwer and H. Hogeveen, Prog. Phys. Org. Chem., 

9, 179 (1972), who also review the following less commonly encountered electrophilic substitution 


R— H + H + > R + + H 2 

Ri— R 2 + H+ > Ri + R 2 — H 

Ri + + R 2 — R 3 >" Ri— R 2 + R 3 + 

e Chapter 6. 

Mechanisms Intermediate Between S N 1 and S N 2 239 

Solvolysis Mechanisms 

The problem of how to classify and account for this intermediate behavior 
continues to plague chemists interested in mechanism. The greatest difficulty 
arises for solvolysis, because the kinetic behavior with respect to solvent cannot 
be determined ; we shall be concerned here primarily with reactions of this type. 

An obvious possibility is that in some cases S w 2 and limiting S w l processes 
occur simultaneously. This idea does not seem to have been particularly fruit- 
ful. 91 Most discussions of the problem assume that there is a range of mechanism 
possible between the extremes, and that even in intermediate cases some particu- 
lar mechanism prevails. 92 

Three central themes are important in the mechanistic investigations. The 
first possibility is that there is an experimentally detectable distinction between 
cases in which a particular solvent molecule assists departure of the leaving 
group by forming a covalent bond to carbon at the transition state, and cases in 
which the solvent stabilizes the transition state and resulting ion pair only by 
nonspecific electrostatic solvation interactions. 93 This hypothesis allows for a 
range of behavior by postulating that bonding to the leaving group, and, in the 
solvent-assisted cases, to solvent, may be strong or weak, and by allowing the 
intervention of ion-pair intermediates. Figure 5.6 summarizes the argument in 
the form of reaction coordinate diagrams. 

The second alternative is that there is only one mechanism; specific bonding 
to some nucleophile always assists the breaking of the C — X bond, even if only 
slightly. S w 2 behavior arises from a "tight" transition state with both entering 
and leaving groups close and strongly interacting; S w l behavior is the result of a 
"loose" transition state, C — X bond nearly completely broken, and S — C bond 
only just starting to form. 94 Again, the initial product can be an ion pair. We 
outline this proposal in Figure 5.7. Comparison of Figures 5.6 and 5.7 will show 
that the only real distinction between alternatives 1 and 2 is in their description 
of the S w l process. 

Finally, a third idea, not a separate mechanism but a concept that can be 
applied to either of the other two, is that an ion pair is always formed first, so that 
even the "pure" S w 2 reaction has an intermediate. This possibility is shown in 
Figure 5.8. 

The tools used in investigating the mechanistic problem are those we have 

91 For a contrary view, see (a) G. Kohnstam, A. Queen, and B. Shillaker, Proc. Chem. Soc, 157 (1959); 
(b) B.J. Gregory, G. Kohnstam, M. Paddon-Row, and A. Queen, Chem. Commun., 1032 (1970); and 
for a refutation of their interpretation, (c) R. A. Sneen and J. W. Larsen, J. Amer. Chem. Soc, 91, 603 1 
(1969); (d) R. A. Sneen and H. M. Robbins, J. Amer. Chem. Soc, 94, 7868 (1972). 

92 The concepts associated with mechanism are statistical; a mechanism is an average path for a 
large number of molecules. On a molecular level, individual molecules follow different paths 
across the potential energy surface. (Refer to the discussion in Section 2.6, p. 99). By a "single 
mechanism" we mean a valley across the potential energy surface with a high point lower than the 
high points of other valleys by an energy large compared to kT. Two simultaneous mechanisms 
would occur if there were two valleys leading from reactant to product with high points of nearly the 
same energy but separated from each other by hills high compared to k T. 

93 (a) C. K. Ingold, Structure and Mechanism in Organic Chemistry, 2nd ed., Cornell University Press, 
Ithaca, N.Y., 1969, chap. VII; (b) W. v. E. Doering and H. H. Zeiss, J. Amer. Chem. Soc, 75, 4733 

94 (a) E. R. Thornton, J. Amer. Chem. Soc, 89, 2915 (1967); (b) G. J. Frisone and E. R. Thornton, 
J. Amer. Chem. Soc, 90, 1211 (1968). 

240 Unimolecular Substitutions and Related Reactions 

Reaction coordinate 

Reaction coordinate 

Figure 5.6 Distinct mechanisms, (a) S N 2. (b) Ionization to an ion pair with nucleophilic 
participation by solvent, (c) Limiting S N 1. 

discussed in previous sections. Stereochemistry, effect on rate and product distri- 
bution of added salts, influence of structure and of leaving group on kinetics and 
products, sensitivity to solvent ionizing power and nucleophilicity, and isotope 
effects are all brought to bear. Despite this broad range of available methods, the 
ambiguities remain and there is still room for much experimental innovation. 

Solvent-Assisted Ionization 

Investigations reported by Schleyer and a number of co-workers have contri- 
buted significantly to clarification of some of the points in question. A study of 

Mechanisms Intermediate Between S N 1 and S N 2 241 

H * 

Reaction coordinate 

6 + | 8- 

H /,\ 


/ 1 
f + 1 

SOH + .C- 


H / \ 






-c . + X" 

Reaction coordinate 

Reaction coordinate 
Figure 5.7 Single mechanism, (a) S N 2. (b) Intermediate, (c) S w l. 

rearrangements occurring during solvolysis of tosylates bearing substituted 
phenyl groups on the /3-carbon (27) led them to suspect that nucleophilic assis- 

242 Unimolecular Substitutions and Related Reactions 

Reaction coordinate 

Reaction coordinate 

Figure 5.8 All reactions by way of ion pairs, (a) S„2, rate-determining attack on ion pair. 
(b) S N 1, rate-determining ion-pair formation. 

tance to ionization by solvent (Figure 5.6b) is more general than had previously 
been thought. 95 (These rearrangement experiments are discussed in Section 6.1.) 

Their approach in looking into the problem further was to find structures in 
which specific covalent bonding to the back side of the carbon undergoing 
substitution is difficult or impossible. As models for reactions at tertiary carbon 
they chose bridgehead substitutions. We have seen in Section 5.2 that rates in 
these systems are retarded, in some cases by many powers of ten, because of the 
increase in strain upon ionization. But the important point in the present context 
is that it is impossible for a solvent molecule to approach from the back side of a 
bridgehead carbon; the only possibilities are frontside attack, known to be 
strongly disfavored (Section 4.2), or limiting S w l solvolysis with nonspecific 

If /-butyl chloride solvolyzes by a mechanism like that depicted in Figure 
5.6c, without any significant nucleophilic assistance at the transition state, the 
sensitivity to changes of solvent nucleophilicity ought to be the same as for the 
bridgehead systems. This is the result found when the reactions off-butyl chloride 
(Equation 5.19) and adamantyl bromide (Equation 5.20) were compared. 86 The 

(CH 3 ) 3 C— CI + SOH 

Br + SOH 

os + h + -i- cr 

OS + H + + Br- 



85 D. J. Raber, J. M. Harris, and P. v. R. Schleyer, J. Amer. Chem. Soc, 93, 4829 (1971), and refer- 
ences cited therein. 

86 D. J. Raber, R. C. Bingham, J. M. Harris, J. L. Fry, and P. v. R. Schleyer, J. Amer. Chem. Soc, 
92, 5977 (1970). 

Mechanisms Intermediate Between S N l and S N 2 243 

correlation between Y and rate of Reaction 5.20 is excellent over a wide variety of 
solvents of varying nucleophilicity ; if i-butyl chloride were subject to nucleo- 
philic assistance, the Y values would reflect this fact and would not correlate 
adamantyl rates for solvents of different nucleophilicity. For very strongly 
ionizing solvents such as trifluoroethanol, trifluoroacetic acid, and hexafluoro-2- 
propanol, the correlation fails. 97 The reason proposed is that in these solvents the 
J-butyl substrates are undergoing elimination by attack of solvent on a proton. 
The adamantyl systems can neither solvolyze with nucleophilic assistance nor 
eliminate, and it has therefore been proposed that 1 -adamantyl (or 2-adamantyl, 
see below) tosylate be the standard for the Y scale. 98 This revised Y scale mea- 
sures solvent ionizing power only and does not include any contribution from 
solvent nucleophilicity. 

In order to extend this line of argument to secondary systems, Schleyer and 
his collaborators chose the 2-adamantyl structure (28). They reasoned that the 

H H 



axial hydrogens in this rigid molecule would block backside approach of a 
nucleophile. Indeed, they found that 2-adamantyl tosylate solvolysis rates corre- 
lated with those of 1 -adamantyl, showing the same lack of sensitivity to solvent 
nucleophilicity. Open-chain secondary tosylates, for example isopropyl, proved 
to be markedly sensitive to nucleophilicity." These compounds react at different 
rates in solvents of the same Y but different nucleophilicity; therefore the solvent 
must be assisting the departure of the leaving group by nucleophilic attack, as 
suggested in Figure 5.6a or 5.6b. 

Use of other methods has contributed further to the emerging picture of 
solvolysis of most secondary systems as being solvent-assisted. For example, the 
solvolysis rate acceleration on substituting a-hydrogen by CH 3 in 2-adamantyl 
bromide is 10 7 ' 5 , much larger than that found for other secondary-tertiary pairs 
such as isopropyl-i-butyl. In molecules less hindered than 2-adamantyl, the 
secondary substrate is accelerated by nucleophilic attack of solvent. 100 Rate 
accelerations and product distributions found on adding azide ion to solvolysis 
mixtures (Problem 4) also provide confirmatory evidence for these conclu- 

97 (a) J. M. Harris, D.J. Raber, W. C. Neal, Jr., and M. D. Dukes, Tetrahedron Lett., 2331 (1974); 
(b) F. L. Schadt, P. v. R. Schleyer, and T. W. Bentley, Tetrahedron Lett., 2335 (1974). 

98 See note 97. 

88 (a) J. L. Fry, C. J. Lancelot, L. K. M. Lam, J. M. Harris, R. C. Bingham, D. J. Raber, R. E. 

Hall, and P. v. R. Schleyer, J. Amer. Chem. Soc, 92, 2538 (1970); (b) P. v. R. Schleyer, J. L. Fry, 

L. K. M. Lam, and C.J. Lancelot, J. Amer. Chem. Soc, 92, 2542 (1970). 

100 J. L. Fry, J. M. Harris, R. C. Bingham, and P. v. R. Schleyer, J. Amer. Chem. Soc, 92, 2540 


244 Unimolecular Substitutions and Related Reactions 

sions. 101 Evidently, earlier arguments in the literature based on the assumption 
that secondary systems are limiting or close to it must be reevaluated in the light 
of these findings. It also seems quite clear that, despite earlier reports, 102 primary 
systems do not follow a limiting mechanism, even in acidic solvents. 

As we shall see in more detail in Chapter 6, there are structures in which an 
i nternal nucleo phile, in the form of a neighboring group such as phenyl, assists 
the ionization. In these instances, t he n eighb oring g ro up ta kes u p th e space at 
theside xif-the_ reacting car bon opposite the leaving group and_so blocks_solv.ent 
particip^tJQ^^while^a^jhfi_sam£- time partly-^efeving the-deyglopi ng ele ctron 
.defici ency and __sp rerinr.ingJJTe^jTej^ljjf^ucj^^ hy^solvent. For 

molecules of this kind, then, secondary and even primary substrates can solvolyze 
without solvent participation, by a mechanism we may call S N l with internal 
assistance. This process may occur in competition with a path like that for ordinary 
primary and secondary substrates, in which solvent participates and the internal 
group does not. 103 

Returning, then, to the two alternatives for solvolysis mechanisms with 
which we began this section, it appears that it is indeed possible to construct 
systems that solvolyze without nucleophilic assistance from solvent. For solvent- 
assisted reactions, the two alternatives are essentially equivalent; we can there- 
fore choose the first alternative as being more consistent with current informa- 

The Ion-Pair Mechanism 

The results we have cited do not bear on the ion-pair question. It is still possible 
that the reactions occurring with participation of nucleophile are attacks on a 
reversibly formed ion pair rather than on the covalent substrate. Sneen and 
Larsen found that 2-octyl methanesulfonate reacts in aqueous dioxane containing 
added azide ion to yield a mixture of 2-octyl alcohol and 2-octyl azide. 104 The 
water and azide ion are competing, as we would expect on the basis of the dis- 
cussion above. But the ratio of the rate of disappearance of the methanesulfonate 
in the presence of azide to the rate in the absence of azide was that expected 
if there were an intermediate that could react in any one of three ways : return to 
substrate, combination with water, or combination with azide. (The derivation 
of the rate expressions is left to the reader in Problem 15.) Sneen and Larsen pro- 
posed that the intermediate is an ion pair. This finding, in a system that would 
have been expected to react by an S^-like process, led them to propose that all 
nucleophilic substitutions, Sjv2 and S^l alike, react through ion pairs. The charac- 
teristic Sjv2 kinetic behavior would be the consequence of rate-determining attack 
by nucleophile on ion pair rather than on covalent substrate (Figure 5.8). 
Earlier, Swain and Kreevoy had suggested the possibility of rate-determining 
attack by methanol on ion pairs from triphenylmethyl chloride in benzene sol- 

101 J. M. Harris, D.J. Raber, R. E. Hall, and P. v. R. Schleyer, J. Amer. Chem. Soc, 92, 5729 (1970). 

102 See G. K. Ingold, Structure and Mechanism in Organic Chemistry, p. 436. 

103 (a) F. L. Schadt and P. v. R. Schleyer, J. Amer. Chem. Soc, 95, 7860 (1973); (b) G. A. Dafforn 
and A. Streitwieser, Jr., Tetrahedron Lett., 3159 (1970); (c) P. C. Myhre and E. Evans, J. Amer. 
Chem. Soc, 91, 5641 (1969). 

104 (a) R. A. Sneen and J. W. Larsen, J. Amer. Chem. Soc, 91, 362, 6031 (1969); (b) R. A. Sneen, 
Accts. Chem. Res., 6, 46 (1973). 

Mechanisms Intermediate Between S#l and S#2 245 

vent. 105 Shiner and his co-workers have also found evidence for rate-determining 
attack on ion pairs. 106 

In analyzing their data, Sneen and Larsen had to correct for salt effects, 
since they were comparing rate with azide present to rate without. 107 Schleyer 
and co-workers have criticized Sneen's conclusions by pointing out the uncer- 
tainties involved in such corrections, 108 and Sneen has replied, justifying his 
earlier conclusions and presenting similar evidence for a-phenylethyl systems, 109 
and for an allylic system. 110 The question is far from settled, and will continue to 
be a subject of investigation. 111 

Solvent Nucleophilicity 

A point of key importance in study of solvolysis is the nucleophilicity of the sol- 
vent. Whereas the Y and other scales have been available for measuring ionizing 
power for some years, there has been no satisfactory scale for nucleophilicity. 
Swain, Mosely, and Bown attempted to set up an equation for correlation 
of solvolysis rates that included both nucleophilicity and ionizing power; 112 
their system did not prove particularly helpful for understanding mechanism. 113 
The Swain-Scott equation, discussed in Chapter 4 (p. 185), was not evaluated for 

For lack of a better system, the ratio of rate in an ethanol-water mixture of 
the same Y value as acetic acid to rate in the much less nucleophilic acetic acid, 
(^e<;oh/^acoh)y> has served as a measure of sensitivity to solvent nucleophilicity. 
More recently, the problem has received renewed attention, and two groups have 
proposed possible approaches. 114 Of the two proposals, that of Bentley, Schadt, 
and Schleyer is easier to apply. Their scheme defines the solvent nucleophilicity, 
N, by Equation 5.21, where k is the solvolysis rate constant of methyl tosylate in 

N = log ( — ) - 0.3Y (5.21) 

\ *0/CH 3 OT3 

the solvent of interest, k is the solvolysis rate constant of methyl tosylate in the 
reference solvent, and the term — 0.3Y corrects for susceptibility to ionizing 
power. (The value 0.3 is m for methyl tosylate in the Winstein-Grunwald mY 
correlation for the very non-nucleophilic solvents acetic acid and formic acid.) 
Methyl tosylate solvolysis thus serves as the standard reaction for determining 
nucleophilicity, just as /-butyl chloride solvolysis (now replaced by 2-adamantyl 
tosylate solvolysis) does for finding Y. 

105 C. G. Swain and M. M. Kreevoy, J. Amer. Chem. Soc., 77, 1122 (1955). 

106 (a) V.J. Shiner, Jr., R. D. Fisher, and W. Dowd, J. Amer. Chem. Soc, 91, 7748 (1969); (b) V.J. 
Shiner, Jr., S. R. Hartshorn, and P. C. Vogel, J. Org. Chem., 38, 3604 (1973). 

107 See note 104(a). 

108 D.J. Raber, J. M. Harris, R. E. Hall, and P. v. R. Schleyer, J. Amer. Chem. Soc, 93, 4821 (1971). 

109 R. A. Sneen and H. M. Robbins, J. Amer. Chem. Soc, 94, 7868 (1972). 

110 R. A. Sneen and W. A. Bradley, J. Amer. Chem. Soc, 94, 6975 (1972). 

111 See, for example, W. T. Bentley, S. H. Liggero, M. A. Imhoff, and P. v. R. Schleyer, J. Amer. 
Chem. Soc, 96, 1970 (1974); (b) F. G. Bordwell and G. A. Pagani, J. Amer. Chem. Soc, 97, 118 (1975), 
and following papers. 

112 C. G. Swain, R. B. Mosely, and D. E. Bown, J. Amer. Chem. Soc, 77, 3731 (1955). 

113 S. Winstein, A. H. Fainberg, and E. Grunwald, J. Amer. Chem. Soc, 79, 4146 (1957). 

114 (a) P. E. Peterson and F.J. Waller, J. Amer. Chem. Soc, 94, 991 (1972); (b) T. W. Bentley, F. L. 
Schadt, and P. v. R. Schleyer, J. Amer. Chem. Soc, 94, 992 (1972). 

246 Unimolecular Substitutions and Related Reactions 

Application of the Reacting Bond Rules . 

It may be useful at this point to analyze the reaction coordinate in greater detail 
than we have done so far. We shall be making use of the reacting bond rules 
(Section 2.6, p. 104). Briefly summarized, the rules predict that (1) the effect of 
structural changes on location of the transition state with respect to the reaction 
coordinate should follow the Hammond postulate, that is, the easier a process the 
less advanced it will be at the transition state; and (2) the effect of structural 
change on location of the transition state with respect to a bound vibration will 
be opposite to the Hammond behavior, that is, the easier the process the more 
advanced it will be at the transition state. The discussion to follow is based on 
that of Thornton, 115 but is extended through reaction coordinate diagrams of the 
kind proposed by More O'Ferrall 116 and developed by Jencks. 117 

We want to consider a simplified nucleophilic substitution scheme consisting 
of the entering nucleophile, N, the carbon undergoing substitution, C, and the 
leaving group, X. An S N 2 reaction will have a transition state with both N and 
X partially bonded to C (29). The transition state may be tighter (30) or looser 
(31) ; it may also be unsymmetrical, with bond making to N more advanced (32) 

N-C-X N--C-X N—C •• -X 

29 30 31 

or less advanced (33) than bond breaking. An S^l reaction will have the C — X 

N-C--X N---C--X 

32 33 

bond partly broken, but no bonding to N, at the transition state of the ionization 
step (34). We shall represent the solvated ion pair that is the intermediate first 

N C----X N C+ X" 

34 35 

formed on ionization of C — X by 35 ; here N would be a solvating solvent mole- 
cule. We shall suppose that N does not move appreciably closer to C during the 
ionization, although we know this assumption to be an oversimplification, as is 
our neglect of other kinds of ion pairs. 

There are two structural parameters of interest in this scheme : the N — C 
distance and the C — X distance. We construct in Figure 5.9 a diagram of the 
potential energy surface as a function of these two parameters for an S^ process. 
The horizontal plane represents the two coordinates, so that at the back left- 
hand corner are the reactants, N + C — X. Coming forward to the front of the 
diagram represents increasing the C — X distance, so that the left front corner is 
ion pair 35, with N still in its original position but the C — X bond broken. 
Going from left to right represents decreasing the N — C distance, so that at the 
right front is product, + N — C + X~. At the back right is a hypothetical penta- 
coordinate state, with both N and X bonded to C. The height above the plane at 
each point represents the free energy for that particular combination of C — X 

115 E. R. Thornton, J. Amer. Chem. Soc, 89, 2915 (1967). 

116 R. A. More O'Ferrall, J. Chem. Soc. B, 274 (1970). 

117 W. P. Jencks, Chem. Rev., 72, 705 (1972). 

Mechanisms Intermediate Between S w l and S w 2 247 

N + C + + X' 


N---C distance 

decrease " 

Figure 5.9 A hypothetical free-energy surface for an S w 2 reaction. Reaction starts at the 
back left-hand corner and proceeds along the heavy line over the surface, with 
simultaneous approach of N and departure of X, to the products at the front 
right-hand corner. The transition state is marked by *. 

N + C-X 

N+C + + X" 


N-C distance 


Figure 5.10 In the limiting S w l process, the most favorable path is, first, rate-determining 
breaking of the C — X bond by passing over the transition state * 1 to the inter- 
mediate, N + C + + X~; then, proceeding in another step over a second 
barrier, * 2 , to products. 

248 Unimolecular Substitutions and Related Reactions 

N +C-X 

N — C-X 

N + C + + X 

C distance 

■ increase 

decrease ■ 

Figure 5.11 Projection of the S N 2 reaction coordinate (solid line). The transition state is 
indicated by *; in this example it is symmetric with respect to N--C bond 
making and C--X bond breaking (Structure 29). Energy minima are desig- 
nated by o. The motions are as follows: 

N-^^C X -► «- N 

«- N C X -» N -» 


Electron supply to C favors _Li and shifts the transition state to *', and the 
reaction then follows the dashed curve. 

C -s 




and N — C distances. The curve up over the saddle point at the center of the dia- 
gram represents the lowest energy pathway for the S^2 reaction, with the transi- 
tion state indicated by *. Figure 5.10 is a similar diagram for the limiting S^l 

In order to study these diagrams further, we look directly down from 
above and project the reaction coordinate onto the horizontal plane. 118 Since we 
need to retain the essential features of the potential energy, we indicate maxima 
of energy along the reaction coordinate by * and minima by °. Figure 5.1 1 is the 
projection of the S#2 path, and Figure 5.12 is the projection of the S^l path. 

Now we ask what the effect will be on the S#2 process of electron donation 
to carbon. The motion along the reaction coordinate, R 1} is 36; R 2 is its reverse, 
37. Motion perpendicular to the reaction coordinate is the vibration represented 
by 38 and 39 ; 38 represents a displacement toward the lower left of the diagram 

N->-^C X- 
Motion Ri 

-N C^^-X 
Motion R 2 

See notes 116, 117. 

Mechanisms Intermediate Between S N \ and S w 2 249 

Figure 5.12 Projection of the limiting S N 1 reaction coordinate. Transition state of the rate- 
determining step is *j. The central minimum, o,, is the solvated ion pair. 

N C X-+ 

N-+ C 

Motion J_j 




and 39 is a displacement toward the upper right. These four motions we have 
indicated in Figure 5.1 1. Greater electron supply to C (for example from a more 
electron-releasing substituent) will make N less eager to bond and will allow X 
to depart more easily; since part of motion R x (or R 2 ) is helped and part is 
hindered, the position of the transition state along the reaction coordinate will be 
little affected. The same change, however, assists J_ x and makes J_ 2 less favor- 
able; the transition state will therefore shift in the direction of _|_ l5 to *'. The new 
reaction coordinate, the dashed line in Figure 5.11 brings the system to a transi- 
tion state that is still symmetric with respect to bond making and breaking, but is 
looser; that is, the bond to N is less formed and that to X is more broken at the 
transition state than before the structural change. Electron withdrawal at C will 
have the opposite effect. 

If the structure is changed further, so as to make electron density even more 
available to C, the curve will eventually move all the way to the edge and will 
follow the line in Figure 5.12. The transition between S w 2 and S w l is perhaps 
most easily seen by starting from S w l, Figure 5.12. Suppose that we make C + a 
less good cation by electron withdrawal from C. At the ion-pair intermediate, 
Oj, all motions are bound vibrations. If C + is made a worse cation, N and X~ 
will tend to draw closer and the shift will be toward the upper right, to °' f) 
Figure 5.13. At the same time, o' t will be raised in energy compared with o {} 
because the carbocation is less well stabilized. The transition state * 1 will also 
move. Motion along the reaction coordinate, R a , is C — X breaking only, and it is 
hindered by making C + a poorer ion, so the transition state moves in the direction 
R a . But motion J_ 6 , Figure 5.13, is approach of N; it is a bound vibration and is 
assisted by making C + a poorer ion, and so the transition state should also move in 
direction J_ 6 . Since motion along the reaction coordinate is expected to dominate 
when both kinds occur (rule 3, Section 2.6, p. 104), we expect the resultant 

250 Unimolecular Substitutions and Related Reactions 

Figure 5.13 The effect on the location of the intermediate, ° ( , of electron withdrawal at 
C + . Motions R u R 2> _L 1( and _L 2 are the same as in Figure 5.11, but all are 
bound vibrations. The intermediate will shift in the direction of _L 2 to °[. At 
the same time, the transition state * 1 will shift to *{. The new reaction co- 
ordinate is given by the dashed curve. 

change to *[ in Figure 5.13, and the new reaction coordinate shown by the dashed 

If the process just described is continued, * 1 moves ever closer to o 4> while 
° ( increases in energy and the curve moves toward the center of the diagram. 
When minimum o 4 disappears and only * 1 remains (* x will also at that point 
have merged with * 2 , Figure 5.12), the mechanism is S w 2. We leave it as an exer- 
cise for the reader to work out predictions of how the curves should change with 
the nature of the entering and leaving groups. 

Sneen's ion-pair scheme can also be shown with these two-dimensional 
diagrams. According to his mechanism, all substitutions follow the path shown in 
Figure 5.12; the distinction between S w l and S w 2 behavior depends on whether 
*! or * 2 is higher, and variation in behavior depends on the relative positions 
along the curve, and the energies, of * 1} ° ; , and * 2 . 


We may define a unimolecular electrophilic substitution, S E 1, by Equations 5.22 
and 5.23. The electrophilic substitutions have not been as thoroughly studied as 

RX ^=: R:" + X + (5.22) 

R:- + Y + > RY (5.23) 

Unimolecular Electrophilic Substitutions — Carbanions 251 

have the nucleophilic, and details of mechanism are not as well denned. Never- 
theless, there are a number of transformations that can be profitably considered in 
terms of the S £ l process. 119 

In Section 4.5 we discussed reactions in which electrophilic substitution of a 
metal ion takes place by a bimolecular pathway. The unimolecular substitution 
is less common, although there are some examples in cases where the carbanion 
is well stabilized. 120 For our purposes here the most important S B 1 reactions are 
those in which the leaving group is a proton or a neutral carbon molecule. 

Proton Leaving Group 

Cleavage of a carbon-hydrogen bond to yield a carbanion and proton is a 
Brensted acid-base reaction (Equations 5.24 and 5.25). The mechanism is not 

RH + B: ^^ R:" + BH+ (5.24) 

R:" + Y + > RY (5.25) 

strictly speaking a unimolecular one, because there are two molecules taking part 
in the ionization step. It is, however, analogous to an acid-catalyzed nucleophilic 
substitution, in which a Lewis acid helps to pull off the leaving group. Those 
reactions are ordinarily included in the S N 1 category. We may therefore consider 
Reactions 5.24-5.25 in the present context. 

The most elementary example of the electrophilic substitution with hydro- 
gen leaving group is the exchange of one proton for another, a process that can be 
studied by isotopic labeling. We have considered in Section 3.3 the equilibrium 
aspects of C — H acidity ; data were given there that allow a rough assessment of 
relative stabilities of various carbanion structures (Table 3.1, p. 146). The 
parallel between rates of proton removal and anion stability as measured by the 
acid dissociation constant was also considered there. In general, the more highly 
stabilized the anion the more rapidly a given base will produce it by proton 

The stereochemical outcome of a substitution by way of a carbanion depends 
on the geometrical preferences of the anion and on its degree of association with 
other species present in the medium. Elementary consideration of carbanion 
structure leads to the conclusion that :CH 3 ~ and simple alkyl homologs should be 
pyramidal. The isoelectronic ammonia and amines undergo fast inversion; the 
same might be expected for carbanions 40 ^ 41. 121 If this change takes place 
rapidly, an anion generated from a chiral precursor would lose its configuration 

C Y^" 

40 41 

118 For a review of electrophilic substitution and the carbanion field, see D. J. Cram, Fundamentals 
of Carbanion Chemistry, Academic Press, New York, 1965. 

120 See, for example: (a) B.J. Gregory and C. K. Ingold, J. Chem. Soc. B, 276 (1969); (b) D. Dodd 
and M. D. Johnson, J. Chem. Soc. B, 1071 (1969) ; (c) D. Dodd, C. K. Ingold, and M. D. Johnson, 
J. Chem. Soc. B, 1076 (1969). 

121 A. Rauk, L. C. Allen, and K. Mislow, Angew. Chem. Int. Ed., 9, 400 (1970) review theoretical 
and experimental aspects of pyramidal inversion. 

252 Unimolecular Substitutions and Related Reactions 

and give racemic products on reaction with an electrophile. Attempts to prepare 
optically active Grignard reagents have been unsuccessful, except in the case of a 
cyclopropyl derivative such as 42, where the increase in strain associated with the 
planar transition state (I strain 122 ) provides a sufficiently high barrier to inver- 
sion to maintain the stereochemistry. 123 The lithio-, and even sodio-derivatives 
of the cyclopropyl system also show sufficient stereochemical stability to give 
optically active products. 124 There is a certain amount of covalent character in 
the carbon— metal bonds, although it must be quite small in the organosodium 
compounds. The highly covalent organomercurials are readily prepared in 
optically active form without any special structural requirements. 

Most of the work on stereochemistry of carbanions free of specific bonding 
to metals has been done with molecules that include a stabilizing group. Exam- 
ples are shown in Structures 43, 44, and 45. In these cases, because of the stabiliza- 
tion attained by favorable conjugation with the tt electron systems, the ions are 

MgX .<£ : q< 

42 43 44 

H 3 C 


probably planar. 125 The situation for these structures is much like that of the 
carbocations, and we may expect ion-pairing phenomena to exert a strong in- 
fluence on the stereochemistry. Indeed, the stereochemical consequences of 
generating anions at chiral centers in conjugation with tt systems depend strongly 
on the base and solvent. 126 

In the deuterated 9-methylfluorenyl system (46), Cram and co-workers 
found retention of configuration in tetrahydrofuran with ammonia or a primary 
amine as base. 127 Streitwieser has obtained similar results with benzyl systems in 
cyclohexylamine with cyclohexylamide as base. 128 Cram's proposed mechanism 
is shown in Scheme 6. In dimethylsulfoxide, the exchange and racemization 

122 (a) H. C. Brown and M. Gerstein, J. Amer. Chem. Soc, 72, 2926 (1950); (b) H. U. Brown, R. S. 
Fletcher, and R. B. Johannesen, J. Amer. Chem. Soc, 73, 212 (1951). 

123 H. M. Walborsky and A. E. Young, J. Amer. Chem. Soc, 86, 3288 (1964). 

124 (a) H. M. Walborsky, F. J. Impastato, and A. E. Young, J. Amer. Chem. Soc, 86, 3283 (1964); 
(b) J. B. Pierce and H. M. Walborsky, J. Org. Chem., 33, 1962 (1968). 

126 A fluorine substituent, however, has the opposite effect on geometry. Pyramidal ions are stabilized 
by fluorine and planar ions destabilized; conjugation with the filled p orbitals on fluorine is un- 
favorable. See A. Streitwieser, Jr., and F. Mares, J. Amer. Chem. Soc, 90, 2444 (1968). Chlorine, 
bromine, and iodine apparently stabilize an adjacent carbanion more than does fluorine, presumably 
because the destabilizing p orbital overlap is less effective with the larger halogens (see Section 5.2, 
p. 227). J. Hine, N. W. Burske, M. Hine, and P. B. Langford, J. Amer. Chem. Soc, 79, 1406 (1957). 

126 See Cram, Fundamentals of Carbanion Chemistry, chap. Ill, for a summary of results and discussion 
of mechanisms. 

127 (a) D. J. Cram and L. Gosser, J. Amer. Chem. Soc, 85, 3890 (1963); (b) D. J. Cram and L. 
Gosser, J. Amer. Chem. Soc, 86, 5445 (1964). 

128 A. Streitwieser, Jr., and J. H. Hammons, Prog. Phys. Org. Chem., 3, 41 (1965). 

Unimolecular Electrophilic Substitutions — Garbanions 253 

Scheme 6 

H 3 C 


N + 
H H H 

H R C 

NH 2 D 


rates are equal; the anions must in this case become racemic before reprotona- 
tion. The more polar solvent presumably allows the ion pairs to dissociate, or at 
least to last long enough to lose chirality. 129 In a fairly acidic protic solvent 
such as methanol, inversion occurs by the process indicated in Scheme 7. 130 

Scheme 7 

„0— CH 3 



CH r O- 









O— CH, 

H 3 C 

Finally, in certain cases, such as in Structure 47, in which the ion pair can easily 
lose its chirality without dissociating, Cram has identified a process that causes 
racemization to be faster than exchange. 131 More than one of these processes 
can occur simultaneously. 132 

129 See note 127. 

130 D.J. Cram and L. Gosser, J. Amer. Chem. Soc., 86, 5457 (1964). 

131 K. C. Chu and D.J. Cram, J. Amer. Chem. Soc, 94, 3521 (1972). 

132 J. N. Roitman and D. J. Cram, J. Amer. Chem. Soc, 93, 2225 (1971). 

254 Unimolecular Substitutions and Related Reactions 

Anions stabilized by adjacent carbonyl groups (44) usually give racemiza- 
tion no matter what the solvent. The charge is distributed between carbon and 
oxygen; the hard proton acid prefers the hard end of the ambident base and adds 
to the oxygen. 133 An enol results, and it lasts long enough before changing to 
the more stable keto form for its environment to become symmetric. 134 Cyclo- 
propyl and vinyl anions, for example 48 and 49, have a greater tendency to 
maintain their configuration than do ions without these special structural 
features. 135 

^ C=N 



Reprotonation is, of course, not the only possible fate of carbanions. The 
variety of their reactions makes them highly useful intermediates in synthesis. 136 

Carbon Leaving Groups 

A number of reactions of the general type shown in Equation 5.26 lead to 
carbanions by loss of a carbon group. These processes occur when R: ~ is a 
stabilized carbanion ; they can also be considered as the reverse of nucleophilic 
additions to carbonyl (Chapter 8) . 

Cram and co-workers have investigated these reactions with ketone leaving 
groups (R l5 R 2 = alkyl or aryl) and find that, as with the deprotonation route, 

R x* - ^ - 

R--C— 0:-M + >- R:"M + + C=Q (5.26) 

Ri R 2 

the stereochemical consequences depend on the conditions. In a relatively non- 
polar and weakly basic solvent such as i-butyl alcohol, the metal ion is closely 
associated with the leaving group and with a solvent molecule and guides a 
proton donor to the side from which the leaving group departed. The result is 
retention (Scheme 8). 137 In better-ionizing solvents, the ion pairs can dissociate, 

133 (a) M. Eigen, Angew. Chem. Int. Ed., 3, 1 (1964); (b) R. G. Pearson, Survey Prog. Chem., 5, 1 (1969); 
see Section 3.5 for discussion of the hard-soft principle. 

134 D. J. Cram, B. Rickborn, C. A. Kingsbury, and P. Haberfield, J. Amer. Chem. Soc., 83, 3678 

135 (a) H. M. Walborsky and J. M. Motes, J. Amer. Chem. Soc, 92, 2445 (1970); (b) J. M. Motes and 
H. M. Walborsky, J. Amer. Chem. Soc, 92, 3697 (1970); (c) H. M. Walborsky and L. M. Turner, 
J. Amer. Chem. Soc, 94, 2273 (1972). 

136 See, for example, (a) H. O. House, Modern Synthetic Reactions, 2nd ed., W. A. Benjamin, Menlo 
Park, Calif., 1972; (b) D. C. Ayres, Carbanions in Synthesis, Oldbourne Press, London, 1966. 

137 (a) D.J. Cram, J. L. Mateos, F. Hauck, A. Langemann, K. R. Kopecky, W. D. Nielsen, and 
J. Allinger, J. Amer. Chem. Soc, 81, 5774 (1959); (b) J. N. Roitman and D.J. Cram, J. Amer. Chem. 
Soc, 93, 2231 (1971). 

Scheme 8 

Unimolecular Electrophilic Substitutions — Carbanions 255 

H— O— S 
6-"M + 

H— O— S 

■* C:--M + ---0=C. 

4 y 

^C— H + M+ + 0=C^ + SO- 
4 x 

and racemization results if the solvent is aprotic and inversion if the solvent can 
donate a proton from the back side. 138 

A variation of the general carbon leaving group scheme of Equation 5.26 
is decarboxylation (Equations 5.27 and 5.28). 139 In order for the fragmentation 

R— C 


-* R:" + C0 2 



R:" + SOH 

■+ RH+ SO- 


to occur readily, the carbanion must be stabilized. Structures 50-55 show some of 
the types of acids that decarboxylate easily. In many of these structures, a 












\o 2 





X 3 C— COOH 


mechanism is available for decarboxylation of the free acid as well as of the 
conjugate base. An intramolecular proton transfer (Equation 5.29) leads directly 
to the enol of the decarboxylated product. 140 



/ C ^ C% o 



c. . 

+ co 2 


In Chapter 8 we shall consider a number of other processes analogous to 
Equation 5.26 but in which the initial alkoxide is itself an intermediate arising 
from attack of a nucleophile on a carbonyl group. 

138 See note 137(a). 

139 For a review of decarboxylation, see B. R. Brown, Quart. Rev. (London), 5, 131 (1951). 

140 F. H. Westheimer and W. A. Jones, J. Amer. Chem. Soc, 63, 3283 (1941). 

256 Unimolecular Substitutions and Related Reactions 


We consider in this section a third reactive intermediate, the carbene. 141 A 
carhgne is a molecule containmg^adivalent carhonjhat hears an unshared pair o f 
electrons, (Structure 56)|15arbenes may be considered as the conjugate bases of 


X Y X— N: 

56 57 

X X 

Y— C+ . C: + H + (5.30) 

H Y 

carbocations VEquation 5.30), although most known carbenes do not in practice 
arise in this way; 142 the y are als ojejated to carbanions through jjijOLclirnination 
(Equation 5.31), a route that is experimentally practicable. 

X X 

Y— C:- > C: + Z:" (5.31) 

Z X Y 

Carbenes are highly reactive, have short lifetimes, and undergo charac- 
teristic chemical changes, the most important of which are listed with examples in 
Table 5.7. Monovalent nitrogen intermediates (57), called nitrenes, are also 
known; their chemistry is in many ways similar to that of carbenes. 143 

Formation of Carbenes 

Hine and his co-workers showed in the 1950s by kinetic and trapping ex- 
periments that dichloromethylene, : CC1 2 , is an intermediate in the reaction of 
haloforms with base in aqueous solution. 144 Scheme 9 depicts for chloroform the 
mechanism they proposed. If the first step is a rapid equilibrium and k 2 is rate- 
determining, the observed second-order kinetics are consistent with the mech- 
anism, 145 as are a number of other results. 146 

141 The term carbene is used here as a generic designation; individual carbenes are named as substi- 
tuted methylenes. For reviews of carbene chemistry, see: (a) D. Bethell, Advan. Phys. Org. Chem., 7, 
153 (1969); (b) G. L. Closs, Top. Stereochem., 3, 193 (1968); (c) W. Kirmse, Carbene Chemistry, 2nd 
ed., Academic Press, New York, 1971 ; (d) J. Hine, Divalent Carbon, Ronald Press, New York, 1964; 
(e) M.Jones and R. A. Moss, Eds., Carbenes, Wiley, New York, 1973, Vol. I. 

142 Certain types of carbocations can be deprotonated, with formation of typical carbene products. 
See R. A. Olofson, S. W. Walinsky, J. P. Marino, and J. L. Jernow, J. Arner. Chem. Soc, 90, 6554 

143 Nitrene chemistry is discussed in Nitrenes, W. Lwowski, Ed., Wiley-Interscience, New York, 1970. 

144 (a) J. Hine, J. Amer. Chem. Soc, 72, 2438 (1950); (b) J. Hine and A. M. Dowel], Jr., J. Amer. 
Chem. Soc, 76, 2688 (1954); (c) J. Hine, A. M. Dowell, Jr., and J. E. Singley, Jr., J. Amer. Chem. 
Soc, 78, 479 (1956). 

145 See note 144(a). 

146 (a) J. Hine, N. W. Burske, M. Hine, and P. B. Langford, J. Amer. Chem. Soc, 79, 1406 (1957), and 
references to earlier work cited therein; (b) E. D. Bergmann, D. Ginsberg, and D. Lavie, J. Amer. 
Chem. Soc, 72, 5012 (1950) ; (c) R. Lombard and R. Boesch, Bull. Soc Chim. France, 733 (1953); and 
(d) J. Hine and P. B. Langford, J. Amer. Chem. Soc, 79, 5497 (1957). 

Carbenes 257 

Table 5.7 Characteristic Reactions of Carbenes 


x • \ ^ ' 

Insertion :CXY + ^C— H >■ ^.C— C— H 


w H 

^C— C— X > — C C— X 



Addition :CXY + C=C > — C C— 

/ \ / \ 

Dimerization 2 :CXY > XYC=CXY 

Rearrangement R— C— C— X > C=C 

I 7 X R 

Scheme 9 

HCC1 3 + OH" . :CC1 3 - + H 2 

:CC1 3 - — ^-> :CC1 2 + Cl" 

H a O, OH- 
several steps 

:CC1 2 > — -► > CO + HCOO- + Cl" 


The ce- elimination me thod jsjnainly appli cable to the^ aljomethjjgnes. A 
closely related method of obtaining intermediates of the carbene type is through 
organometallic derivatives of general structure 58, where X is a halogen and M is 
a metal, usually Li, Zn, or Sn. These compounds, when heated in the presence of 

R x X 


R 2 M 


appropriate substrates, yield typical carbene products. 147 In many of these cases, 
howeyer^JLkjhougM.jJia.Llhe free carbene : CRjR^s not involved, but thatjhje 
reaction^ takes place with the or gan ometallic 58 dire ctl y- T h ese reactions a re 
te rmed c a r hemid tp_ .distinguish them from_those of free carbenes. The trihalo- 
methylmercury compounds, however, are an exception. 148 

147 See note 141(a). 

14a D. Seyferth, J. Y. Mui, and J. M. Burlitch, J. Amer. Chem. Soc, 89, 4953 (1967). 

258 Unimolecular Substitutions and Related Reactions 

The second important route to carbenes Js. by decomposition of _diazo_ 
compounds (59) according to Equation 5.32. 149 

R K + •• - Rl v r. + 

~C=N=N: •< ► J.C— N=N: 

R 2 R 2 


R., A R ^ 

:CN 2 — -> C: + :N=N: (5.32) 

^ or hv S 

R R 2 

R K 

C : > products 

Structure of Carbenes 

A carbene carbon uses two of its four valence orbital s for bondi ng to the attached 
groups. XT the two remaining orbitals are of nearly equal energy, the two un- 
shared electrons should prefer to go one into each with spins parallel (Hund's 
rule) ; if the energies are sufficiently different, the electrons will pair and occupy 
the orbital of lower energy. A_sJto^ctur£jyit h two unpaired electr ons is said to jae. 
\ji_&JlipleLjiate, a situation well known from spectroscopfc~oEiservations of excited 
atoms and molecules, but relatively rare in ground-state chemistry. 150 

Herzberg provided the first definitive evidence on the geometry of : CH 2 
through his observation of absorption spectra of both the lowest-energy triplet and 
the lowest-energy singlet. 151 The precise geometry of the triplet could not be 
determined, but Herzberg originally concluded that it is linear or nearly so ; the 
spectra did furnish an accurate measurement of the structure of the higher- 
energy singlet and showed the H — C — H angle to be 102.4°. Structural informa- 
tion is also available for a number of halomethylenes from absorption spectra. 152 
Electron paramagnetic resonance spectroscopy (epr) is a second technique that 
has yielded information on carbene structures. 153 Similar in principle to nuclear 
magnetic resonance, epr detects energy changes accompanying changes in 
electron spin states in a magnetic field. Triplet spectra are characteristic and 
easily identified. 154 Wasserman and co-workers observed ground-state CH 2 by 

149 Photochemical reactions, indicated in reaction schemes by the symbol hv, are considered in 
Chapter 13. For the present, it is sufficient to note that absorption of light transforms a molecule to 
an excited state, which, in the case of diazo compounds, has sufficient energy for rupture of the 
C — N bond. Generation of carbenes from diazo compounds is reviewed by W. J. Baron, M. R. 
DeCamp, M. E. Hendrick, M. Jones, Jr., R. H. Levin, and M. B. Sohn, in Jones and Moss, Eds., 
Carbenes, Vol. I, p. 1. 
160 An important exception is 2 , which has a triplet ground state. 

151 (a) G. Herzberg and J. Shoosmith, Nature, 183, 1801 (1959); (b) G. Herzberg, Proc. Roy. Soc, 
A262, 291 (1961); (c) G. Herzberg and J. W. C.Johns, Proc. Roy. Soc, A295, 107 (1966). 

152 A summary of structural results may be found in Bethel, Advan. Phys. Org. Chem., 7, 153 (1969). 

153 Epr spectroscopy is discussed in a number of sources; for a brief introduction see D. J. Pasto and 
C. R. Johnson, Organic Structure Determination, Prentice-Hall, Englewood Cliffs, N.J., 1969, chap. 6. 

154 A. Carrington and A. D. McLachlan, Introduction to Magnetic Resonance, Harper & Row, New 
York, 1967, chapter 8. 

Carbenes 259 

electron paramagnetic resonance and concluded, contrary to Herzberg's original 
determination, that the triplet is nonlinear, with a H — C — H angle of about 
136°. 155 Herzberg reinterpreted the ultraviolet data and found that a nonlinear 
structure is consistent with the spectrum. 156 Thepicture_ that emerges fo r other 
carbenes is that halomethy lenes are groimd^stat e singlets with bond angles in The 
rangp^fflfl^tTO^^wr^^^^mf^hylerifj arylmethy lenes, a.nrj_ probably jjlsn^lkyl- 
methyle nes 157 ar e gro und-state triplets with bond angles 130-180° and have 
excited singlet _states with angles of 100-110°. Accurate quantum mechanical 
calculations reproduce^ the experimental results well for : CH 2 , : CHF, and 
: CF 2 . 158 Structures 60 and 61 show the probable orbital occupancies for singlet 
and triplet carbenes, respectively. 



60 61 

Reactions of Carbenes 

The first caxbenare action to be c onsideredis- insertion - (Equation 5.33). It was first 

R i x R i\ H 

R 2 — C— H + :CH 2 > R 2 — C— C— H (5.33) 

R-3 R-3 

reported in 1942 by Meerwein and co-workers, 159 but its importance was not 
recognized until Doering investigated the reaction and noted that in the liquid 
phase : CH 2 generated by photolysis of diazomethane attacks the various types 
of C — H bonds of hydrocarbons with no discrimination. 160 More extensive 
results of Richardson, Simmons, and Dvoretsky have confirmed this finding. 161 
In the gas phase, the reaction is more selective, and when measures are taken to 
increase the lifetime of the : CH 2 intermediates by addition of an inert gas, so 
that more of the initially formed unselective singlet has time to decay to the some- 
what less reactive triplet ground state, the insertion becomes more selective still. 162 
Table 5.8 presents representative experimental results. Insertion is r-nmmon for 

166 E. Wasserman, V.J. Kuck, R. S. Hutton, and W. A. Yager, J. Amer. Chem. Soc, 92, 7491 (1970). 

166 G. Herzberg and J. W. C.Johns, J. Chem. Phys., 54, 2276 (1971). 

167 (a) See note 155; (b) C. A. Hutchinson, Jr., and B. E. Kohler, J. Chem. Phys., 51, 3327 (1969); 
(c) R. Hoffmann, G. D. Zeiss, and G. W. Van Dine, J. Amer. Chem. Soc, 90, 1485 (1968). 

158 (a) J. F. Harrison and L. C. Allen, J. Amer. Chem. Soc, 91, 807 (1969) ; (b) C. F. Bender, H. F. 
Schaefer III, D. F. Franceschetti, and L. C. Allen, J. Amer. Chem. Soc, 94, 6888 (1972) ; (c) M. J. S. 
Dewar, R. C. Haddon, and P. K. Weiner, J. Amer. Chem. Soc, 96, 253 (1974); (d) J. F. Harrison, 
J. Amer. Chem. Soc, 93, 4112 (1971). 
169 H. Meerwein, H. Rathjen, and H. Werner, Chem. Ber., 75, 1610 (1942). 

160 W. v. E. Doering, R. G. Buttery, R. G. Laughlin, and N. Chaudhuri, J. Amer. Chem. Soc, 78, 
3224 (1956). 

161 D. B. Richardson, M. C. Simmons, and I. Dvoretzky, J. Amer. Chem. Soc, 82, 5001 (1960); 83, 
1934 (1961). 

162 (a) H. M. Frey and G. B. Kistiakowsky, J. Amer. Chem. Soc, 79, 6373 (1957); (b) H. M. Frey, 
J. Amer. Chem. Soc, 80, 5005 (1958). 

> £ 
v 11 
■5 "" 

rt cN 


3 _ 


U T3 


« .a 

<j £ 

" c 

JS "^ 

►5 f 


o o JP 
H | « 









Tf CO 

— . to 




o in in in in 
— r^ cm r^ cm 

— i ID CM ID CM 

— — CM 

CO — < CM -* CM 







« H <J 

a o o 

Carbenes 261 

jacthylene and cnrbon-suhsliluted-methylenes and can occur either inter- or 
intram ol e cularly s 

\ yh P n th* rarhpn p j s in the ..triplet-statftj-a h ydrogen -abstraction to. yield a 
ra dical pair (Equation 5.34) seems a reasonable possibility, far the insertion 

:CH Z + \l— H ^ \> + CH 3 > C— CH 3 (5.34) 

mechanism. Th e singlet-state carben es, hnwpver ; in se rt _i ntn thp f! — H h nad 
with retention of configurajdoJOLr-and-a-isrngie^ste p proc ess is like ly. 163 The attack 
of the singlet carbene on the C — H bond could occur either through the occupied 
hybrid (62) or through the vacant p orbital (63) ; the latter possibility, which 

62 63 

would be electrophilic S E 2 substitution, is in better accord with the strongly 
electrophilic character of carbenes and with the frontside attack required by the 
stereochemistry. Theoretical calculations of Hoffmann and co-workers suggest 
that attack is initially mainly at the hydrogen end of the C — H bond (64), and 
that transfer of the hydrogen to the incoming CH 2 runs ahead of C — C bond 
making. 164 This proposal is similar to one by DeMore and Benson. 165 Dihalo- 
carbenes do not insert as readily as does :CH 2 ; 166 carbenoids usually do not 
insert. 167 

A second c haracteristic reaction of carbenes is addition to olefins to yield 
gyxloprp panes. S inglgt^carbe nes might j~eaj^t_j^j;ithex.n^ 
philesj_triplets may_be expect ed to behave likeirep radicals. The data in Table 
5.9, showing the increase in rate of addition on substitution of electron-donating 

163 (a) Kirmse, Carbene Chemistry, p. 220; (b) P. S. Skell and R. C. Woodworth, J. Amer. Chem. Soc, 78, 
4496 (1956) (Structures I and II in this paper are reversed. See p. 6427.) ; (c) W. v. E. Doering and 
H. Prinzbach, Tetrahedron, 6, 24 (1959); (d) C. D. Gutsche, G. L. Bachman, W. Udell, and S. 
Bauerlein, J. Amer. Chem. Soc, 93, 5172 (1971). 

164 R. C. Dobson, D. M. Hays, and R. Hoffmann, J. Amer- Chem. Soc, 93, 6188 (1971). See also 
note 158(b), p. 259. 

166 (a) W. B. DeMore and S. W. Benson, Advan. Photochem., 1, 219 (1964); for further discussion 
of the insertion pathway, see (b) E. A. Hill, J. Org. Chem., 37, 4008 (1972). 

166 V. Franzen and R. Edens, Justus Uebigs Ann. Chan., 729, 33 (1969). 

167 L. Friedman, R.J. Honour, and J. G. Berger, J. Amer. Chem. Soc, 92, 4640 (1970), and references 
cited therein. 

Table 5.9 Relative Reactivities of Carbenes with Olefins 





CF a 
CC1 2 
CC1 2 
CBr 2 
ICH 2 ZnI 



















° From F 2 C || , hv. R. A. Mitsch, J. Amer. Chem. Soc, 87, 758 (1965). 

6 From HCC1 3 or HCBr 3 , base. W. v. E. Doering and W. A. Henderson, Jr., J. Amer. Chem. Soc, 80, 5274 (1958). 
" From ^HgCCl 2 Br. D. Seyferth and J. M. Burlitch, J. Amer. Chem. Soc, 86, 2730 (1964). 
" E. P. Blanchard and H. E. Simmons, J. Amer. Chem. Soc, 86, 1337 (1964). 

Carbenes 263 

alkyl groups in the olefin, demonstrate that the methylenes and carbenoids are in 
practice strong electrophiles. Reactivity of carbenoids is lower with the highly 
substituted olefins, a result of steric hindrance considered to be evidence that 
they are not free carbenes. 168 

A structure with unshared pairs of electrons adjacent to the car bene center 
(65) should be much less electrophilic. Although systems of this type have not 
been thoroughly investigated, the available evidence indicates that they have 
reduced electrophilicity. 169 


v fi=3 


A second question posed by the olefin additions is one of stereochemistry. A 
concerted ring formation of the type shown in Equation 5.35 implies stereo- 
specific cis ad dition, a suggestion first made in 1956 by Skell and Woodworth. 170 

Ri. *>? ,R 3 /\ 

n ^c^c<, ► r-> c - c n:-r ( 5 - 35 ) 

With a triplet carbene, however, the spin state of one of the electrons must 
change before bonding can be completed ; if this process takes long enough for 
rotation to occur about bonds in the intermediate, a mixture of products should 
result (Scheme 10). 171 It should be pointed out that this argument is not without 
flaw; the singlet is not required to react stereospecifically simply because it can, 


Scheme 10 

1 I J 
^C— C^ + 1CH 2 - 

R R 

1 )CH 2 

■» -— P P 

a ^CH 2 
1 / 2 
i -~ P P 

R R 

R R 

R R 

CH 2 

-> R- 

R 1 ^ CH2 R ^i i- CH > 

R R k 

169 See note 167. 

189 (a) U. Schollkopf and E. Wiskott, Angew. Chem. Int. Ed., 2, 485 (1963); (b) D. Seebach, Angew. 
Chem. Int. Ed., 6, 443 (1967) ; see also (c) R. Gleiter and R. Hoffmann, J. Amer. Chem. Soc, 90, 5457 
(1968); (d) H.J. Schonherr and H. W. Wanzlick, Chem. Ber., 103, 1037 (1970). 

170 (a) See note 163(b); (b) R. Hoffmann, J. Amer. Chem. Soc, 90, 1475 (1968), argues on the basis 
of orbital symmetry that the approach cannot be symmetrical, and that the :CH 2 must initially be 
closer to one end of the olefin than to the other; the one-step stereospecific nature of the addition 
is not affected by this argument. 

171 R. Hoffmann, note 170(b), gives a more rigorous discussion of the additions and reaches the 
same conclusions regarding stereochemistry. 

Table 5.10 Stereochemistry of Addition of Carbenes to cis- and trans-2- Butene 




cis Addition 




Ground State 





to r\ 






500 mm pressure 
> 2000 mm; excess 











From e£HgCCl 2 Br 







From F 2 C | 








Pure olefin as solvent 
Olefin diluted 100:1 
with e-C 6 H 12 








Butadiene added 
Diluted with C 6 F„ 




I, m 

:CH 2 
:CH 2 

CH 2 
CBr 2 
CC1 2 

:CF 2 

:C(CN) 2 
:C(CN) 2 

° Parentheses indicate that reactive state is deduced from stereochemistry of olefin addition. 

" H. M. Frey, Proc. Roy. Soc, A251, 575 (1959). 

c H. M. Frey, J. Amer. Chim. Soc, 82, 5947 (1960). 

" P. S. Skell and R. C. Woodworth, J. Amer. Chem. Soc, 78, 4496, 6427 (1956). 

' P. S. Skell and A. Y. Garner, J. Amer. Chem. Soc, 78, 3409, 5430 (1956); W. v. E. Doering and P. LaFlamme, J. Amer. Chem. Soc, 78, 5447 (1956). It is 

possible that this a-elimination does not involve a free carbene. 

' D. Seyferth and J. M. Burlitch, J. Amer. Chem. Soc, 86, 2730 (1964). 

» R. A. Mitsch, J. Amer. Chem. Soc, 87, 758 (1965). 

* E. Wasserman, L. Barash, and W. A. Yager, J. Amer. Chem. Soc, 87, 2075 (1965). 
' E. Ciganek, J. Amer. Chem. Soc, 88, 1979 (1966). 

' R. W. Brandon, G. L. Closs, G. E. Davoust, C. A. Hutchison, Jr., B. E. Kohler, and R. Silbey, J. Chem. Phys., 43, 2006 (1965). 

* Butadiene is an effective scavenger for triplets. 

' M.Jones, Jr., and K. R. Rettig, J. Amer. Chem. Soc, 87, 4015 (1965). 
™ M.Jones, Jr., and K. R. Rettig, J. Amer. Chem. Soc, 87, 4013 (1965). 

Problems 265 

nor must the triplet necessarily add with loss of stereochemistry. 172 Table 5.10 
presents the data. It will be noted that, with the exception of dicyanomethylene, 
loss of stereochemistry is not complete in triplet additions. The rates of spin 
inversion and bond rotation must be of comparable magnitudes. We discuss this 
point further in Section 12.1. Stereochemistry of the concerted additions is also 
considered further in Section 12.1. Carbenoids add stereospecifically, 173 but 
since free carbenes are not involved, the singlet-triplet considerations do not 


^-l^Show that the simple limiting S N 1 mechanism predicts the kinetic behavior 
givenin Equation 5.4, p. 214. 

{2^Explain the rate ratio for compounds 1 and 2 estimated for limiting solvolysis. 

H 3 C 

H— C- 
H 3 C / 

(CH 3 ) 3 C 




(CH 3 ) 3 C 
1 2 

Relative rate 
(estimate): 1 10 5 

3. Explain the rate ratio for compounds 3 and 4 estimated for limiting S N 1 
solvolysis by correcting the cyclopropyl system for anchimeric assistance which 
occurs when the ring opens. 


H OTs 


3 4 

Relative rate 
(estimate): 1 10" 10 

4. Solvolysis rates of isopropyl tosylate and 2-adamantyl tosylate (28, p. 243) in 
80 percent ethanol are measured with and without added azide. Define rate enhance- 
ment, R.E., as the ratio of rate with azide to rate without, and designate by/ BN3 the 
fraction of alkyl azide in the product. Explain the significance of the fact that the iso- 
propyl results fit the equation 



— JR] 

while the 2-adamantyl results do not. 

/57) Explain why the carbene 5 does not react with cyclohexene in the manner of 
ordinary carbenes, but does react with dimethyl fumarate (6) and maleate (7) to yield 
spiropentanes (8). 






COOCH 3 <f> 




172 See note 141(b), p. 256 and note 171. 

173 G. L. Closs and L. E. Closs, Angew. Chem. Int. Ed., 1, 334 (1962). 

266 Unimolecular Substitutions and Related Reactions 

/6: Explain the relative rates of solvolysis of tosylates 9 and 10. 


Relative rate: 

CH 2 


Mi, Explain why the |3-keto acid 11 does not decarboxylate at 300°C, whereas 12 

does so readily below 100°C. 



H 3 C CH 3 

CH 3 



CH 3 





8. Use the reacting bond rule to predict the effect on position of transition state 
of electron supply at nucleophile and at leaving group in the example considered in the 
text, pp. 246-250. 

■O- Predict the products formed by reaction of ground-state carbon atoms with 
cw-2-butene and with /rcwu-2-butene. 

(fBl Propose a mechanism to account for the following result : 

CH a 


3 C— c= 

=N 2 

gas phase 

> 0= I3 C=C(CH 3 ) 2 + 0=C= 13 C(CH 3 

CH 3 

11. Using the reacting bond rules, analyze the change in location of the S N 2 
transition state expected when the nucleophile is replaced by a better one. Compare the 
prediction with Hoffmann's analysis of the £ Ts/^Br ratio (Section 4.3, p. 192). 

12. Show how reaction paths with transition states in which N---C bond making 
has progressed to a greater or lesser extent than C---X bond breaking are accommo- 
dated in a two-dimensional reaction coordinate diagram. 

'\13. Explain why 1-adamantyl and 2-adamantyl derivatives cannot undergo 
elimination during solvolysis. 

ftl Alcohols react with thionyl chloride to yield the unstable chlorosulfite ions 
(13), which react further to the alkyl chloride and S0 2 . (Rearrangement and elimina- 
tion can also occur.) In dioxane, the product is formed with retention of configuration 

R 3 '/- OH 




„ --C— O— SOC1 
R 3 / 
R 2 


Ra / 

R 2 





-C— Cl 



(14). If pyridinium hydrochloride is present, configuration is inverted (15). Explain. 

15. For each of the following possible mechanisms for competitive reaction of a 
substrate RX with solvent, S, and with added nucleophile, N, find the predicted ratio of 

References for Problems 267 

rate of disappearance of RX in the presence of N to rate of disappearance of RX in the 
absence of N. 

(a) RX . R + X- 

R + X- + S — ^-> RS+ + X- 

R + X" + N *" > RN+ + X 

(b) RX + S * 8 > RS+ + X- 

RX + N *" > RS + + X 


2. S. H. Liggero, J. J. Harper, P. v. R. Schleyer, A. P. Krapcho, and D. E. Horn, 

J. Amer. Chem. Soc., 92, 3789 (1970). 

3. P. v. R. Schleyer, F. W. Sliwinski, G. W. Van Dine, U. Schollkopf, J. Paust, and 

K. Fellenberger, J. Amer. Chem. Soc, 94, 125 (1972). 

4. J. M. Harris, D. J. Raber, R. E. Hall, and P. v. R. Schleyer, J. Amer. Chem. Soc, 92, 

5729 (1970). 

5. W. M.Jones, M. E. Stowe, E. E. Wells, Jr., and E. W. Lester, J. Amer. Chem. Soc, 90, 

1849 (1968). 

6. V. Buss, R. Gleiter, and P. v. R. Schleyer, J. Amer. Chem. Soc, 93, 3927 (1971). 

7. F. S. Fawcett, Chem. Rev., 47, 219 (1950). 

9. P. S. Skell and R. R. Engel, J. Amer. Chem. Soc, 87, 1 135 (1965). 
10. (a) I. G. Gsizmadia, J. Font, and O. P. Strausz, J. Amer. Chem. Soc, 90, 7360 (1968) ; 
(b) J. Fenwick, G. Frater, K. Ogi, and O. P. Strausz, J. Amer. Chem. Soc, 95, 
124 (1973); (c) I. G. Gsizmadia, H. E. Gunning, R. K. Gosavi, and O. P. 
Strausz, J. Amer. Chem. Soc, 95, 133 (1973). 

14. (a) D. J. Gram, J. Amer. Chem. Soc, 75, 332 (1953) ; (b) G. G. Lee and A. J. Fin- 

layson, Can. J. Chem., 39, 260 (1961) ; (c) G. G. Lee, J. W. Clayton, D. G. Lee, 
and A. J. Finlayson, Tetrahedron, 18, 1395 (1962); (d) C. E. Boozer and E. S. 
Lewis, J. Amer. Chem. Soc, 75, 3182 (1953). 

15. R. A. Sneen and J. W. Larsen, J. Amer. Chem. Soc, 91, 362 (1969). 

Chapter 6 



In this chapter we shall discuss intramolecular rearrangements to electron- 
deficient carbon, nitrogen, and oxygen. 


The intramolecular migration, shown in Equation 6.1, of a hydrogen, an alkyl, 
or an aryl group with its pair of electrons from a j8 carbon (migration origin) to the 
adjacent carbocationic center (migration terminus) is called a 1,2-shift (or in the case 
of migration of an alkyl or an aryl group, a Wagner-Meerwein shift) . 

J l„ II 

— C— C— ► — C— C— (6.1) 

M + + I 

R R 

The new carbocation thus formed can subsequently add to a Lewis base, lose a 
proton from an adjacent atom, or rearrange further. 

The first such rearrangement to be studied was that of pinacol (1) to 
pinacolone (2) in acid solution (Equation 6.2). 2 

1 For review articles, see: (a) J. L. Fry and G. J. Karabatsos, in Carbonium Ions, G. A. Olah and 
P. v. R. Schleyer, Eds., Wiley-Interscience, New York, 1970, Vol. II, p. 521; (b) C. J. Collins, 
Quart. Rev. (London), 14, 357 (1960) ; (c) D. M. Brouwer and H. Hogeveen, Prog. Phys. Org. Chem., 9, 
179 (1972); and (d) S. P. McManus, Organic Reactive Intermediates, Academic Press, New York, 

2 R. Fittig, Justus Liebigs Ann. Chem., 114, 54 (1860). 


1,2-Shifts in Carbenium Ions 269 
H3C' CHq H3C GHo H3C CHo 

II II II CH 3 ~ 

CH 3 — C— C— CH 3 " CH 3 — C— C— CH 3 : CH 3 — C— C— CH 3 —?->. (6.2) 


! H H 

CH 3 CH 3 

+ I -H+ ^ I 

CH 3 — C — C — CH 3 . GHo — C — C — CH 3 

n ^ I II I 

CO CH 3 O CH 3 



The name ^pjna rnl rea rrang ement" is now given to „Jiig_ general type c> f _re - 
a rrang e ment exemplified by_ JEquation 6.2 r jil which- the methyl -gioupi^on _the 
1 T 2-dioLmay _-be replaced bxjQther-aJkyir hydrogeru, or aryl groups. 

In the pinacol rearrangement the driving force to migration is the formation 
of a carbonyl group. The driving force to migration in solvolyses and similar 
reactions is usually the formation of a more stable carbocation. Since the energy 
differences between a tertiary and a secondary and between a secondary and a 
primary carbocation are ca. 16 kcal mole -1 each, 3 rearrangements converting a 
less to a more highly substituted carbocation are exothermic. Thus, for example, 
reaction of neopentyl iodide with silver nitrate gives entirely rearranged products 
(Equation 6.3). 4 

CH 3 CH 3 CH 3 


AgiNu 3 pu ,-i pu + ^ r-tr r> r-u r>xj > 

CH 3 — C— CH 2 — I 8 " 3 > CH 3 — C— CH 2 + , CH 3 — -C— CH 2 CH 3 , (6.3) 

I I H + 

CH 3 CH 3 

CH 3 CH 3 

CH 3 — C=CH— CH 3 + CH 3 — C— CH 2 — CH 3 

Similarly, the dehydration of 1-butanol leads to 2-butenes (Equation 6.4). 5,s 

H+ _ .__ _ _ ___ H- 


CH 3 CH 2 CH 2 CH 2 OH riTo* CH 3 CH 2 CH 2 CH 2 + , (6.4) 

CH 3 CH 2 CHCH 3 — 2^> CH 3 CH=CHCH 3 

Vinyl cations are less stable than their aliphatic counterparts. Therefore 
solvolysis of l-methyl-2,2-diphenylethenyl triflate (trifluoromethylsulfonate) 

3 (a) F. D. Lossing and G. P. Semeluk, Can. J. Chem., 48, 955 (1970) ; (b) L. Radom, J. A. Pople, and 
P. v. R. Schleyer, J. Amer. Chem. Soc, 94, 5935 (1972). 

4 F. C. Whitmore, E. L. Wittle, and A. H. Popkin, J. Amer. Chem. Soc, 61, 1586 (1939). 
6 F. C. Whitmore, J. Amer. Chem. Soc, 54, 3274 (1932). 

6 Although the reactions shown in Equations 6.3 and 6.4, and in some equations and schemes 
found later in this chapter depict a primary carbocation as an intermediate, it is not certain whether 
these highly unstable species exist in solution. Both reactions may involve migration concerted with 
departure of the leaving group. See (a) P. Ausloos, R. E. Rebbert, L. W. Sieck, and T. O. Tiernan, 
J. Amer. Chem. Soc, 94, 8939 (1972) and references therein; (b) P. C. Hariharan, L. Radom, J. A. 
Pople, and P. v. R. Schleyer, J. Amer. Chem. Soc, 96, 599 (1974). 

270 Intramolecular Rearrangements 

leads to the rearranged product phenyl 1 -phenylethyl ketone. 7 Apparently the 
mechani sm is that sho wn in Equation 6.5. A 1 ,2-shiftjcon vert s one v inyl cation to 
ariother^Jj^jhjiM^ejir^^ by conjugation with a benzene ring. 

<4 OTf d> d> 

V r / 80 °° EtOH , V— r *~ > A r r / H °°, , R ^ 

,/ C==C \ 2oo/ Ha o ' ,/ \ * *— y=<\ " (6>5) 

9 CH 3 9 CH 3 CH 3 

*\ A . , A 

C=C " i— C— CH 

HO CH 3 ^ CH 3 

Under the long-lived conditions of carbocations in superacid (Section 5.3, 
p. 235), 1,2-shifts interconverting ions of like stability also occur and are very 
rapid. For example, at — 180°C the five methyl groups of 2,3, 3-trimethylbutyl 
cation have only one peak in the nmr. This observation implies that the methyl 
shift in Equation 6.6 occurs at the rate of 75 x 10 3 sec ~ 1 with an activation barrier 
of <5 kcal mole" 1 . 8 

CH 3 H 3 C 

+•^-1 CH 3 ~ I + 

CH 3 — C— C— CH 3 , CH 3 — C— C— CH 3 (6.6) 

H 3 C CH 3 H 3 C GH 3 

Occasionally rearrangements from more stable to less stable carbocations 
occur, but only if ( 1 ) the energy difference between them is not too large or (2) 
the carbocation that rearranges has no other possible rapid reactions open to it. 9 
For example, in superacid medium, in the temperature range 0-40°C, the proton 
nmr spectrum of isopropyl cation indicates that the two types of protons are 
exchanging rapidly. The activation energy for the process was found to be 
16 kcal mole" 1 . In addition to other processes, the equilibrium shown in Equation 
6.7 apparently occurs. 10 In the superacid medium, no Lewis base is available 

S H H ** 

H H H H H H H H H H H 

either to add to the carbocation or to accept a proton from it in an elimination 
reaction, and in the absence of such competing reactions there is ample time for 
the endothermic 1,2-hydride shift to take place. 

1,2-Shifts have stereochemical as well as energetic requirements. Ijri_order 
for such rearrangements tojxxur, the C— Z (Z =g_ rnigxatLug group) bond at the 
nr!gral:ionI !cHgirrrrruit~ne^in. or,a1most itu. thejplane described by the vacant p 
orbitaiimjh^^diac^ntjcarbon ^ancLtheiCa^^C^ bond as in Figure 6.1 — that is, the 
dihe^ral_an^kjbeJween_Z ar^dj^^nir^^,od3itaLrnust be 0°. For example, 

7 M. A. Imhoff, R. H. Summerville, P. v. R. Schleyer, A. G. Martinez, M. Hanack, T. E. Dueber, 
and P. J. Stang, J. Amer. Chem. Soc, 92, 3802 (1970). 

8 G. A. Olah and J. Lukas, J. Amer. Chem. Soc, 89, 4739 (1967). 

8 For references to a number of such rearrangements, see (a) note 3(b) and (b) M. Saunders, P. 
Vogel, E. L. Hagen, and J. Rosenfeld, Accts. Chem. Res., 6, 53 (1973). 
10 See note 9(b). 

1,2-Shifts in Carbenium Ions 271 

R R 

Figure 6.1 The ideal relationship of the empty p orbital to the migrating group (Z) for a 

the apparent 1,2-hydride shift (Equation 6.8) in the 2-adamantyl cation (3) 
was shown to be entirely quenched in highly dilute solution. 11 Thus it must be 
an inter-, not an zrc/ramolecular reaction. Further, the apparent 1,2-methyl shift 
in the 2-methyladamantyl cation (4, Equation 6.9) has been shown by isotope 


labeling to occur by a complicated skeletal rearrangement. 12 In both these 
cases the C — Z bond and the vacant p orbital, which in 3 and 4 is perpendic- 
ular to the plane of the page, form a dihedral angle of 90 °. 13 In this worst of 
all possible stereochemical situations the simple 1,2-shift cannot occur, and 


rearrangement must take another pathway. 

The Timing of the Migration in Acyclic Alkyl Systems 

A CQinrnQrjLp henomenon in organjcjc hemistry , illustra tedju rther in Problems 6, 1 
and-4L2^i^thaj^ L ^rjQu^^jacent to the leaving group acts as_an intramolecular 
nuc leophile . This can occur if _thf neighboring group has an un shared pair of 
elecJxojis_pxjL_doj : ible Jaopjij ajs sJiQA^n, for example, in Equations 6.10 and 6.11. 
The cyclic structures 5 or 6 may sometimes be isolated, but more often are 
attacked by a nucleophile : The ring is opened and some (or all) of the product 
may be rearranged. 

11 P. v. R. Schleyer, L. K. M. Lam, D.J. Raber, J. L. Fry, M. A. McKervey, J. R. Alford, B. D. 
Cuddy, V. G. Keizer, H. W. Geluk, and J. L. M. A. Schlatman, J. Amer. Chem. Soc, 92, 5246 (1970). 

12 Z. Majerski, P. v. R. Schleyer, and A. P. Wolf, J. Amer. Chem. Soc, 92, 5731 (1970). 

13 (a) See notes 1 1 and 12 ; (b) D. M. Brouwer and H. Hogeveen, Rec. Trav. Chim. Pays-Bas, 89, 21 1 


272 Intramolecular Rearrangements 


I I 
-C— C— X 




I I 

-C— c- 

I I 




^ecauge_lheuefIeCtiv-e_XXUlC£ntratiQn nfjJ^jTejgJThmjrT g grnnp is veryjhjcrh_ (it is 

^a lways jn thejr nmediate vic initvof the reaction site) and because of the relatively 
small degree of reor^ajiizadori_r^uired _ to _j£ach_JJie--transilian_.state (and, 
therefore, small entropy change), reactions of this typeareoften f aster t han inter- 
molecular or unimolecular substitutions. The nucleophilic assistance of a neigh- 
boring group to departure oFaleaving group is called neighboring group participation 
or anchimeric assistance. 

Analogy with intramolecular nucleophilic substitution reactions raises two 
fundamental problems in the study of rearrangements. Thg_first is whethe r, wheg 

jlj ^bonj jrjrydrogen migratesjn arijJectron-dencient structure, it does so. only 
a fter the cationi c center_h as fully __formed jn a previous step, or whether it mi- 
g rates j inTiultarreousjy_with .departure^ of the leaving^group, thus ^providing 
anchimeric assistance. Such participation is conceivable even though carbon and 

Figure 6.2 Orbital picture of the transition state for a 1,2-shift in which migration is 
concerted with ionization of the leaving group. 

1,2-Shifts in Carbenium Ions 273 

hydrogen have no unshared pairs: The pair of electrons the migrating group 
takes with it from the /? to the a carbon is partially available to the a carbon at the 
transition state for the migration, as illustrated in Structure 7 and in Figure 6.2. 


\ •' "• / 

/ e <*;\ 


Winstein suggested that hyperconjugation and bridging might be descriptions of a 
single derealization phenomenon : In the former there is little movement of the 
participating group, and in bridging there is much. 14 This idea is illustrated in 
Figure 6.3. 

A second related, but distinct, question is whether there is an energy mini- 
mum on the reaction path when the migrating group is bonded to both migration 
origin and terminus — that is, whether there is a bridged intermediate (8). 



If t he migrating group does provide anchi meric assista nce, certain conse- 
quences should follow. One is kinetic: The ra t e should be faster than the rate of 
an exactly analogous, but unass isted, reaction. Anoth gria stereochemical^Neigh- 
boring-group participation is an in tramoi£ailar.S ) v2 displacement .arid therefore 
the migratiq nj grminus should he inverted hy the r earr angement. Or, looking at 
it another way, two closely related molecules may react by different paths if in 
one the neighboring group can attack the leaving group from the back side, 
but in the other it cannot adopt that position. Most experiments designed to deter- 
mine whether anchimeric assistance occurs or not have centered on the kinetics 



Hyperconjugation Bridging 

Figure 6.3 Illustration of the idea that bridging and hyperconjugation may be descriptions 
of a single derealization phenomenon. 

14 (a) S. Winstein, B. K. Morse, E. Grunwald, K. C. Schreiber, and J. Corse, J. Amer. Ckem. Soc, 74, 
1113 (1952). (b) For further discussion of this point, see D. E. Eaton and T. G. Traylor, J. Amer. Ckem. 
Soc, 96, 1226 (1974) and references therein. 

274 Intramolecular Rearrangements 

and/or stereochemistry of the reaction under consideration. Rate acceleration is 
often difficult to ascertain because of problems in predicting the rate of the non- 
assisted reaction. Inversion of configuration is, of course, experimentally ob- 
servable only in chiral systems, but in systems that are achiral the stereochemistry 
of the reaction can often be determined by isotope labeling. 

Experiments indicate that in open-chain and unstrained cyclic compounds, 
hydride and alkyl groups usually do not provide anchimeric assistance if the 
leaving group is on a secondary or tertiary carbon. 15 (For a discussion of partici- 
pation in strained cyclic systems, see Section 6.2.) Early evidence against neigh- 
boring-group participation by alkyl groups came from oxygen-exchange studies 
in the pinacol rearrangement. When pinacol was allowed to rearrange in acidic 
ls O-labeled water, recovered, unreacted pinacol was found to contain ls O. This 
result is consistent with formation of a carbocation that either rearranges to 
pinacolone or adds water to return to pinacol as shown in Equation 6.2. The 
possibility that ionization and rearrangement occur in the same step as shown in 
Equation 6.12 and that the 18 is incorporated during a reverse rearrangement 
of pinacolone to pinacol is excluded thus : The addition of pinacolone to the 

H 3 C CH 3 CH 3 

CH 3 — C— C— CH 3 . ' ' CH 3 — C— C— CH 3 (6.12) 

| | +H °° II I 

HO +OH +HO CH 3 


reaction system does not affect the rate of rearrangement, and therefore the re- 
arrangement cannot be reversible. 16 

Stereochemical evidence confirms that neither alkyl nor hydride provides 
anchimeric assistance in the pinacol rearrangement. Compounds 9 and 10 both 

Scheme 1 

15 As indicated in note 5, there is still controversy over the existence of primary carbocations in sol- 
ution. For cases when some participation by neighboring hydride or alkyl in the formation of 
secondary or tertiary carbocations has been suggested see, for example, (a) V.J. Shiner, Jr., and J. 
G.Jewett, J. Amer. Chem. Soc., 87, 1382 (1965); (b) note 13(a), p. 271; (c) S. Winstein and 
H. Marshall, J. Amer. Chem. Soc, 74, 1120 (1952). 

16 C. A. Bunton, T. Hadwick, D. R. Llewellyn, and Y. Pocker, Chem. Ind. (London), 547 (1956). 

1 ,2-Shifts in Carbcnium Ions 275 

give the same products, 11 and 12, in the same ratio (9:1) when they undergo the 
pinacol rearrangement with BF 3 -ether complex, as shown in Scheme l. 17 (Note 
that the hydroxy group lost here, as usual, is the one that gives the most stable 
carbocation. 18 ) If the migrating group provided anchimeric assistance, it would 
have to come in from the back side of the departing — + OH 2 . In Compound 9 the 
group that can come in from the back side is the hydride, and Compound 1 1 should 
be the principal product. Conversely, in Compound 10 it is the alkyl chain of the 
ring that can come in from the back side, and the chief product should be 
Compound 12. The fact that the products are formed in a constant ratio indicates 
that a common intermediate — presumably the planar carbocation — must be 
formed from both starting materials. 19 More direct stereochemical evidence has 
been provided by Kirmse and co-workers. Chiral (5)-2-methylbutan-l,2-diol (13) 
rearranges to racemic 2-methylbutanal (14) as shown in Equation 6.13. 20 

CH 3 CH 3 

C 2 H 5 — C— CH 2 OH -5^> C 2 H 5 — C— C^ (6.13) 

OH H " 

S R,S 

13 14 

(See also pp. 281-284.) 

Aryl Participation — The Phenonium Ion Controversy 21 

A question that has aroused considerable controversy in the past 25 years is 
whether aryl groups can provide anchimeric assistance and if so under what 
conditions. The controversy began in 1949 when Cram solvolyzed the L-threo 
and L-erythro isomers of 3-phenyl-2-butyl tosylate in acetic acid, l- TTzreo-tosylate 
gave 96 percent racemic threo-acetate (plus olefins) , whereas the L-erythro isomer 
gave 98 percent L-erythro-acetate. 22 To explain the experimental facts, Cram 
postulated that neighboring phenyl begins a backside migration to C a as the 
tosylate departs. At the first energy maximum both the tosylate and the phenyl 

17 P. L. Barili, G. Berti, B. Macchia, F. Macchia, and L. Monti, J. Chem. Soc C, 1168 (1970). 

16 (a) See note 1(b), p. 268, for examples and exceptions; for another exception see (b) W. M. 

Schubert and P. H. LeFevre, J. Amer. Chem. Soc, 94, 1639 (1972). 

19 Departure of the leaving group is apparently rate-determining when the first-formed carbocation 
is not particularly stabilized. This is shown by the fact that the rate of rearrangement of alkyl 
glycols is dependent on the concentration of 

R R 

I I 

R— C C— R 

I I 

+ OH 2 OH 
[J. F. Duncan and K. R. Lynn, J. Chem. Soc, 3512, 3519 (1956) ; J. B. Ley and C. A. Vernon, Chem. 
lnd. (London), 146 (1956).] That the rate-determining step can be the migration when the first- 
formed carbocation is particularly stable has been shown by Schubert and LeFevre [note 18(b)]. 
These workers subjected l,l-diphenyl-2-methyl-l,2-propanediol to the pinacol rearrangement and 
found that deuterium substitution in the migrating methyls caused the reaction to slow down. 

20 W. Kirmse, H. Arold, and B. Kornrumpf, Chem. Bet., 104, 1783 (1971). 

21 C. J. Lancelot, D. J. Cram, and P. v. R. Schleyer, in Carbonium Ions, G. A. Olah and P. v. R. 
Schleyer, Eds., Wiley-Interscience, New York, 1972, Vol. III. 

22 D.J. Cram, J. Amer. Chem. Soc, 71, 3863 (1949). 

276 Intramolecular Rearrangements 

groups are partially bonded to the a carbon. After heterolysis of the carbon- 
tosylate bond is complete, an intermediate phenonium ion is formed in which the 
phenyl is equally bonded to both the a and j8 carbons. The phenonium ion formed 
from the L-^wo-tosylate (Equation 6.14) has a plane of symmetry perpendicular 
to and bisecting the C a — C e bond and therefore must yield racemic products. 


H 3 C 



4> H 

CH 3 



H, OTs 

\ g a / 

c— c 

<£ CH 3 



AcO ,CH 3 


H 3 CT I^H 


The phenonium ion from the L-er^Aro-tosylate is chiral (Equation 6. 1 5) and can 
give chiral products. Examination of the two possible paths of attack of acetic 
acid (it must come from the opposite side from the bulky phenyl ring) in each of 
the intermediates confirms that the products expected from them are those that 
are observed experimentally. 

Cram provided further evidence for the existence of a phenonium ion inter- 
mediate by isolating starting tosylate after reaction had proceeded for 1.5 half- 
lives; he found that the L-^reo-tosylate was 94 percent racemized but the l- 
erythro-\.osy\3Xz was still optically pure. 23 These results can be easily understood u 
it is assumed that the starting material first forms a phenonium-tosylate intimate 
ion pair, which can either revert to starting materials or go on to products. The 
achiral ion pair from the fAreo-tosylate will return to racemic starting material 
whereas the chiral intermediate from the erythro isomer will return to opticalh 
active starting material. 

Winstein provided powerful support for the phenonium ion hypothesis ii 
1952. He followed the rate of solvolysis of *Areo-3-phenyl-2-butyl tosylate botl 
titrametrically, by titrating the toluenesulfbnic acid formed, and polarimetrically 

33 D.J. Cram, J. Amet. Chem. Soc, 74, 2129 (1952). 

1,2-Shifts in Carbenium Ions 277 

by watching the rate of loss of optical activity. He found that the polarimetric 
rate was five times the titrametric rate and concluded that the intermediate 
phenonium ion is formed rapidly but reverts back to starting materials four times 
more often than it goes on to products. That both solvolysis and racemization 
occur through a common intermediate seeemed most probable because of the 
similar sensitivity of the rates of both reactions to solvent polarity. 24 

The concept of an intermediate phenonium ion was, at first, controversial, 
and its chief detractor was H. C. Brown. 25 Although 3-phenyl-2-butyl tosylate 
showed the stereochemical behavior expected if an intermediate phenonium ion 
were formed, it did not, in his opinion, show the rate acceleration that should 
attend anchimeric assistance to ionization of the tosylate. 26 Brown said that the 
stereochemical results could be accounted for by invoking rapidly equilibrating 
open carbocations (15). According to his explanation, ionization of the tosylate 

HtC* C4H3 H3C4 LHg 

I I ^ I I 

H— C— C— H . H— C— C— H 

I + + J 

</> t 


occurs, for steric reasons, only when the phenyl and the tosylate are trans to each 
other. The phenyl then migrates rapidly back and forth, blocking solvent attack 
from the back side by the "windshield wiper effect." Rotation about the C a — C^ 
bond does not occur because (1) the rapid phenyl transfer hinders it and (2) the 
large phenyl group must remain trans to the large, departing, tosylate group. 
Solvent attack from the back side, relative to the tosylate, is blocked by the 
phenyl group. Eventually, solvent attacks the a or j8 carbon from the front side, 
giving the stereochemical results obtained by Cram and by Winstein. 

More recently, studies initiated by Schleyer 27 and completed by Brown and 
Schleyer 28 have convinced Brown of the existence of the phenonium ion. Sch- 
leyer, Brown, and their co-workers determined the rates and products of aceto- 

AcO JGH3 H ^CH 3 

H---C— C— H + C— C, 

H * C ' 1 A OA? (6.16) 



24 S. Winstein and K. C. Schreiber, J. Amer. Chem. Soc, 74, 2165 (1952). 

25 (a) H. C. Brown, Chem. Soc. (London), Spec. Publ., 16, 140 (1962) ; (b) H. C. Brown, K.J. Morgan, 
and F.J. Chloupek, J. Amer. Chem. Soc, 87, 2137 (1965). 

28 The solvolysis of 3-phenyl-2-butyl tosylate is only half as fast as that of 2-butyl tosylate. However, 
Winstein suggested that the inductive effect of the phenyl group should retard the rate by a factor of 
ten and that neighboring-group participation therefore has given a fivefold rate enhancement 
[see note 14(a), p. 273]. See p. 280 for the actual rate enhancement. 

27 (a) C. J. Lancelot and P. v. R. Schleyer, J. Amer. Chem. Soc, 91, 4291, 4296 (1969); (b) C.J. 
Lancelot, J.J. Harper, and P. v. R. Schleyer, J. Amer. Chem. Soc, 91, 4294 (1969); (c) P. v. R. 
Schleyer and C.J. Lancelot, J. Amer. Chem. Soc, 91, 4297 (1969). 

26 (a) H. C. Brown, C. J. Kim, C. J. Lancelot, and P. v. R. Schleyer, J. Amer. Chem. Soc, 92, 5244 
(1970); (b) H. C. Brown and C.J. Kim, J. Amer. Chem. Soc, 93, 5765 (1971). 

278 Intramolecular Rearrangements 

lysis of /Ara>-3-aryl-2-butyl brosylate (16) with a number of different X substituents. 
Their goal was to calculate from both product and kinetic data the amount of 
aryl participation in ionization and then to compare the results. If both methods 
gave the same answer, that would be convincing evidence for the phenonium 
ion. 29 

They analyzed the product data by assuming that all the threo-acetate 
formed arises from a phenonium ion and all the erythro-z.ceX.ate from backside 
assistance of the solvent to ionization. Then the percentage of aryl participation 
is synonymous with the percentage of ^ra>-acetate in the product. The product 
analyses for acetolysis at 75°C are in the sixth column of Table 6. 1 . 

The rate data were analyzed by assuming Equation 6.17. In this equation 
k t is the titrametric rate constant for product formation, k s is the solvent-assisted 
ionization constant, and Fk A is the fraction of the aryl-assisted rate constant that 
gives rise to product (as opposed to the fraction that gives starting material 
through internal return). 

k t = k s + Fk & (6.17) 

The constant k t is determined experimentally, and k s can be calculated by use of a 
Hammett plot as described below. Then Fk A can be calculated by simply sub- 
tracting k s from k t . If Fk A is the rate of formation of anchimerically assisted 
solvolysis product, it should lead to threo-acetaXe. The product arising from 
k s should lead to erythro-a.ceta.te. Therefore the fraction of ^reo-acetate ex- 
pected can be calculated by FkJ(Fk A + k s ) or Fkjk t . Column five of Table 6.1 
shows the calculated fraction of /Areo-acetate. 

In order to find k s for each compound, the logs of the k t 's for acetolysis of 16 
were determined and plotted against the Hammett a constants of the X sub- 
stituents (Figure 6.4). For electron-withdrawing X the plot is a straight line 
with a negative slope. This is just what would be expected from an aryl-non- 
assisted pathway in which a negative inductive effect from the phenyl ring de- 
creases the rate of ionization (cf. the effect of substituents on the ionization of 

Table 6.1 Rates and Products of Acetolysis of Substituted 
*Ar«0-3-PHENYL-2-BUTYL Brosylates (16) at 75.0°C 


k t x 10 5 

k s x 10 5 

F£ a x 10 5 

Fkjkt x 


Percent threo- 

X = 



/>— MeO 






p— Me 






m — Me 












p— CI 






m— CI 




m-CF 3 




/>-CF 3 




/>-N0 2 




m,m'-(CF 3 ) 2 




Source: H. C. Brown, C.J. Kim, C.J. Lancelot, and P. v. R. Schleyer, J. Amer. Chem. Soc, 92, 5244 
(1970). Reprinted by permission of the American Chemical Society. 

28 See note 28. 

1,2-Shifts in Carbenium Ions 279 

-2.0 - 

-3.0 - 









Figure 6.4 Logs of the rates of acetolysis of <Areo-3-aryl-2-butyl brosylates (16) at 75.0°C 
vs. the a constants of the X substituent. From H. C. Brown, C. J. Kim, C. J. 
Lancelot, and P. v. R. Schleyer, J. Amer. Chem. Soc, 92, 5244 (1970). Reprinted 
by permission of the American Chemical Society. 

benzoic acid, Section 2.2). Thus, for electron-withdrawing X, k s equals k t . The 
rates of solvolysis of 16 when X is electron-donating, however, are faster than 
would be predicted from simple inductive effects. The deviations are ascribed by 
Brown and Schleyer to anchimeric assistance: The extrapolation of the line 
correlating the a constants with the log of the rates when X is electron-with- 
drawing is taken as defining the k s contribution when X is electron-donating. 
For example, the />-methoxy substituent has a a constant of —0.27. On the 
extrapolated line this corresponds to log k s = —3.83 or k s = 1.49 x 10 -4 . 
Experimentally, k t is found to be 106.0 x 10 _4 , thus Fk A = 104.5 x 10 " 4 . 
Data for the other substituents are found in Table 6. 1 . 

The excellent correlation between the percentage of anchimeric assistance 
calculated from the rate (column 5) and product (column 6) data is compelling 
evidence that the above analyses are accurate and thus that separate, discrete 
pathways for solvolysis exist — one solvent-assisted and one aryl-assisted. 30 

Note that a very small rate enhancement corresponds to a large contribu- 
tion of anchimerically assisted component. 31 For example, the titrimetric rate 

30 The solvent-assisted mechanism for the solvolysis of secondary systems that have no neighboring 
groups has been confirmed; see Section 5.4, p. 243, and (a) D. J. Raber, J. M. Harris, and P. v. R. 
Schleyer, J. Amer. Chem. Soc, 93, 4829 (1971); (b) note 27(b). 

31 See note 27(c), p. 277. 

280 Intramolecular Rearrangements 

constant for solvolysis of 16 (X = H) is only 18.0/6.08 times faster than the 
solvolytic rate constant — a rate enhancement of about three. This corresponds to 
59 percent anchimeric assistance. 

Primary /3-aryl tosylates have also been shown to undergo solvolysis by two 
distinct pathways— aryl- and solvent-assisted. 32 Tertiary /J-aryl tosylates, how- 
ever, ionize to a stable carbocation and seem to require no assistance in isomeriza- 
tion. 33 

The unsubstituted phenonium ion, as well as other phenonium ions substi- 
tuted with electron-donating groups, have been recently observed as stable ions 
in superacid medium. 34 That the structure is actually 18 and not an unsym- 
metrically bridged ion (19) nor a nonclassical ion (20) (see Section 6.2) in which 
there are three-center bonds was shown by the nmr evidence. The ring carbon 
that is bonded to the aliphatic carbons was established by 13 C shifts to be tetra- 
hedral in nature; and 13 C and proton chemical shifts in the ring were similar to 
those of cations shown to have Structure 21. 



CH 2 ;CH 2 


vCH 2 




Stereochemistry 35 

The central carbon of the migrating group and the carbons of the migration 
terminus and of the migration origin all undergo bonding changes during a 
Wagner-Meerwein shift, and the stereochemistry at each may change. 

The orbital picture we have previously formulated (Figure 6.2) predicts 
that the stereochemistry of the migrating group will be retained during the migra- 
tion since, in this picture, the migrating group uses the same lobe of the same 
orbital to bond to both migration origin and migration terminus. Predominant 
retention is in fact observed, but some racemization may occur. For example, 
in the semipinacol rearrangement 36 of (35')-l-amino-2,3-dimethyl-2-pentanol 
(22), the product 23 that arises from migration of the 5-butyl group accounts for 
33 percent of the product. The chirality of the 5-butyl group in 23 is only 86-88 
percent retained. 37 Kirmse and co-workers have proposed that the pathway for 

32 J. M. Harris, F. L. Schadt, P. v. R. Schleyer, and C. J. Lancelot, J. Amer. Chem. Soc, 91, 7508 

33 H. C. Brown and C. J. Kim, J. Amer. Chem. Soc, 90, 2082 (1968). 

34 (a) G. A. Olah and R. D. Porter, J. Amer. Chem. Soc, 93, 6877 (1971) and references therein; 
(b) G. A. Olah, Angew. Chem. Int. Ed., 12, 173 (1973). 

35 D.J. Cram, in Steric Effects in Organic Chemistry, M. S. Newman, Ed., Wiley, New York, 1956. 

36 The semipinacol rearrangement is the rearrangement that ensues when a j8-amino alcohol is 
deaminated as in the following equation. See Problem 6.4. 

R' R R' R R' 

I I HNO, 11+ I 

R'— C— C— NH 2 ^-> R'— C— C— N=eN > R'— C— C— R + N 2 + H + 


37 W. Kirmse and W. Gruber, Chem. Ber., 106, 1365 (1973) ; W. Kirmse, W. Gruber, and J. Knist, 
Chem. Ber., 106, 1376 (1973). 

1,2-Shifts in Carbenium Ions 281 


2 HNO, 



(in 33% yield) 


86-88% retained 

racemization involves the cyclopropanol 24 as an intermediate. Their proposed 
mechanism is abbreviated in Equation 6. 1 9. 38 The intermediacy of 24 is sup- 
ported by the fact that deuterium is incorporated into 23 when the deamination 
is carried out in D a O. 

OH l\| 



+ OH 


-> 23 



The stereochemistry at the migration terminus depends on the relative 
timing of the leaving group's departure and the 1,2-shift. In the 



Cg C a 


system, if Z begins to migrate before X has completely departed, the migration 
terminus, C a , will be inverted. We have already seen in Cram's work that phenyl 
migration with neighboring-group participation leads to an inverted migration 
terminus. If, however, X departs before Z begins to move, either retention or 
inversion can occur at C a . If the lifetime of the carbocation is very short, retention 
will result if Z was cis to the leaving group in the unreacted starting material 
(Equation 6.20) and inversion will result if Z was trans (Equation 6.21). 




R 2 

- ^ 



- - 



If the C a carbocation has a long lifetime and there is free rotation about the 
C a — C bond, the relative amounts of retention and inversion will depend on 

38 Kirmse and co-workers suggest that 24 is formed and destroyed via a protonated cyclopropane 
(see Section 6.2, p. 310). 

282 Intramolecular Rearrangements 

whether the transition state leading to retention or inversion is more stable. If 
they are of equal energy, racemization should result; we have already seen an 
example of this in Equation 6.13. 

Deamination of amines often gives rise to "hot," short-lived carbocations 
(Section 5.2, p. 226). Deamination of ( + )-l,l-diphenyl-2-amino-l-propanol 
specifically labeled with 14 C in one of the two phenyl groups (25) gives a-phenyl- 
propiophenone as product, 88 percent of it inverted and 12 percent retained. All 
the inverted ketone comes from migration of the 14 C-labeled phenyl and all the 
retained from migration of the unlabeled phenyl group (Equation 6.22). 39 This 

H 3 C X H *{ H 3 C X y H 

*f/f ^^ H3C A H + A (6-22) 

C NH 2 (/ j£* 

ho / \ o^ ^ d* V 

25 88% 12% 

behavior can be understood if we look at the ground state of 25. The most stable 
of the three staggered rotamers of 25 is 25a (in this conformation each of the 
large phenyl groups has one small proton next to it), and therefore most of the 
amine molecules adopt this conformation. When the free carbocation is formed 
from 25a there is not time for rotation about the C^ — C a bond before a phenyl 
group migrates. The labeled phenyl is backside to the original amine group, and 

HCXI-^ ^M, OH ^\Xx^* 

H 3 C I N H H 3 C T H H 3 C T H 

<f>* 4> OH 

25a 25b 25c 

migration of it gives inversion. The unlabeled phenyl is frontside, and its migra- 
tion gives retention. 

The first-formed carbocation from the deamination of threo- 1 -amino- 1- 
phenyl-2-/>-tolyl-2-propanol (26) is stabilized by resonance and longer lived than 
the carbocation formed from the deamination of 25. In rotamers 26b and 26c the 
bulky phenyl and/>-tolyl groups are next to each other, and thus again the ground 
state amine will be almost entirely in the conformation represented by rotamer 
26a. The carbocation formed from 26a presumably has time to rotate about the 

H 3 C V/N ^ CH: 

NH 2 
HO. I ^CH, 


CH 3 

B. M. Benjamin, H.J. Schaeffer, and C.J. Collins, J. Amer. Chem. Soc, 79, 6160 (1957). 

] ,2-Shifts in Carbenium Ions 283 

C a — C bond before the migration because, although the product of tolyl migra- 
tion is formed in > 80 percent yield, 58 percent of it is retained and 42 percent 
inverted. Scheme 2 shows the probable reason for the predominance of the re- 
tained product. In the transition state for it (27) the two large groups (phenyl 
and methyl) are trans to each other but in the transition state for inversion (28) 
they are cis. 40 

Scheme 2 

H / 
H 3 C C 

J^ NH 2 

/.-tolyl OH 


H 3 C X 
/.-tolyl OH 

H 3 C -C 



/.-tolyl OH 


HO /C \CH 3 


/.-tolyl— C 






C— CH 3 




The absence of neighboring-group participation in deamination reactions seems 
to be a fairly general phenomenon in the chemistry of these "hot" ions, although 
when the neighboring group is as reactive as />-methoxyphenyl some participa- 
tion may occur. 41 

When the steric effects in the transition states for retention and inversion 
are of equal energy, attack of a migrating group on a hot carbocation occurs 
preferentially from the back side. For example, (i?)-l-amino-2-methylbutanol-l 
29, is deaminated in aqueous HC10 4 to afford 2-methylbutanal, 14, (16 percent) 
with 30 percent inversion of configuration at C a . 42 

40 B. M. Benjamin and C.J. Collins, J. Amer. Chem. Soc, 83, 3662 (1961). 

41 P. I. Pollak and D. Y. Curtin, J. Amer. Chem. Soc, 72, 961 (1950). 

42 See note 20, p. 275. 

284 Intramolecular Rearrangements 

HNO a 

CH 3 — C— C' 

C 2 H 5 

30% inversion 


C 2 H 5 
CH 3 »-j— CH 2 OH hrio'* CH 3 — C— C; (6.23) 

NH 2 


(Comparison of Equations 6.23 and 6.13 shows how the stereochemistry at C a 
may depend on the lifetime of the carbocation.) 

The stereochemistry at the migration origin cannot always be studied 
because, as in the pinacol and semipinacol rearrangements and as in Wagner- 
Meerwein shifts where migration is followed by loss of a proton, the migration 
origin often becomes trigonal in the product. When it is tetrahedral in the product 
its stereochemistry varies and is not yet fully understood. If the nucleophile 
attacks before the migrating group has fully departed, then it must come in from 
the back side and give inversion at the migration origin. We saw a dramatic 
example of this in Cram's work on the solvolysis of 3-phenyl-2-butyl tosylate, 
in which solvent attacks the phenonium ion directly and the migration origin, 
C B , is almost entirely inverted. If the migrating group has completely departed 
from the migration origin before the nucleophile attacks and there is time for 
rotation about the C a — C^ bond, then racemization should result. (If there is not 
time for free rotation, attack from one side might be less hindered than attack 
from the other.) Racemization at C B occurs, for example, in the deamination of 
(5')-l-amino-2-cyclohexylbutane (30), which affords, among other products, 
racemic 2-cyclohexylbutan-2-ol (31 ). 43 

CeHn ^ n " 

H--^-CH 2 NH 2 -§££> HO-C-CH3 (6.24) 

C2Hs C 2 H 5 

5 R,S 

30 31 

A number of cases have been found in which 1,2-hydride shifts occur with 
retention at C B . For example, (5)-6-(aminomethyl)-2-methyloctane (32) is 
deaminated in aqueous perchloric acid to give 2,6-dimethyloctan-6-ol in 35 per- 
cent yield. This product is formed with 41 percent retention at C^. No fully 
satisfactory explanation for the retention has been proposed. 44 

A CH 2 NH 2 




Migratory Aptitudes 

The relative ease with which alkyl and aryl groups migrate is called their 
migratory aptitude. Unfortunately, migratory aptitudes are not absolute quantities; 
values determined in one reaction under one set of conditions may differ enor- 

" W. Kirmse and W. Gruber, Chem. Ber., 104, 1789 (1971). 
44 W. Kirmse and H. Arold, Chem. Ber., 104, 1800 (1971). 

1 ,2-Shifts in Carbenium Ions 285 

mously from values in another reaction or even in the same reaction under other 

Both "intermolecular" and intramolecular migratory aptitudes have been 
studied in the pinacol rearrangement. For determination of the latter, a pinacol 
in which the /? carbon is substituted with two different R groups is used, and the 
product is analyzed to see in what proportion the two groups have migrated. 
It is necessary to use symmetrical pinacols, (33) and compare the migration of R x 
and R 2 . If unsymmetrical pinacols (34) are used, the group with the higher mi- 
gratory aptitude may not be able to migrate. For example, if l,l-dimethyl-2,2- 
diphenylethylene glycol is treated with H 2 S0 4 in acetic anhydride, only methyl 

R 2 R 2 Ri R2 

Ri — C — C — Ri Ri — C — C — Ro 



33 34 

migration occurs. 45 This does not mean that methyl has the higher migratory 
aptitude, but simply that the more stable diphenyl-substituted cation (35) is 
formed in preference to the dimethyl-substituted cation (36), as shown in 
Equation 6.26. In 35 only methyl migration is possible. 

> CH 3 — C— C~<£ 
HO CH 3 
CH 3 — C— t~<j> ' 35 + (6.26) 

By analyzing the products often symmetrical glycols of the type of Structure 
33 Bachmann determined the following migratory aptitudes relative to phenyl : 
/>-ethoxyphenyl, 500; anisyl, 500; /Kolyl, 15.7; />-biphenyl, 11.5; m-tolyl, 1.95; 
m-methoxyphenyl, 1 .6 ; phenyl, 1 .0 ; />-chlorophenyl, 0.66 ; wz-chlorophenyl, 0. 46 

"Intermolecular" migratory aptitudes in the pinacol rearrangement have 
been determined by comparing the rates of rearrangement of different pinacols, 
each with four identical substituents of the type 37. 

Ri— C— C— Ri 

I I 


46 Ramart-Lucas and M. F. Salmon-Legagneur, Compt. Rend., 188, 1301 (1929). 
46 W. E. Bachmann and J. W. Ferguson, J. Amer. Chem. Soc, 56, 2081 (1934). 

286 Intramolecular Rearrangements 

The migratory aptitudes obtained in this way were />-anisyl, 880; p-tolyl, 40; 
phenyl, 1 ; />-chlorophenyl, 0. 47 Depovere points out that the larger values for 
the migratory aptitudes of />-anisyl and p-to\yl here as compared to Bachmann's 
data are due to the twofold role of the electron-donating groups in 37 : They 
migrate better from the /3 carbon and they facilitate ionization at the a carbon. 

We have already mentioned that migratory aptitudes are dependent on the 
reaction and on the conditions under which the reaction is carried out. An 
example of the latter type of variation is that in the pinacol rearrangement of 
triphenylethylene glycol, the phenyl/hydrogen migration ratio may vary by a 
factor of 180 (from 7.33 to 0.41) when the catalyst is changed from concentrated 
sulfuric acid to HC1 in water/dioxane. 48 

A striking example of the former type of variation can be gained from a 
comparison of the migratory aptitudes in the pinacol rearrangement (see above) 
with those in adeamination reaction. For example, the semipinacol rearrangement 
of 38 gives the following migratory aptitudes :/>-anisyl, 1.5; p-tolyl, 1.3; phenyl, 1; 
/>-chlorophenyl, 0.9. 49 


(f>~ C— CH 2 NH 2 

Generally, deamination reactions show a lower selectivity than pinacol and 
Wagner-Meerwein rearrangements. This has been explained in two ways. First, 
the "hot" carbocation theory says that carbocations formed from deamination 
are of extremely high energy and therefore lacking in discrimination. 50 Huisgen, 
on the other hand, has proposed that in deamination, because the energy of 
ionization is very low, the absolute differences in the activation energies for the 
possible subsequent reactions are small. This follows if one assumes a constant 
ratio between the activation energies of the various steps on the reaction path. 51 
(See also Section 5.2, p. 226.) 

A novel method of measuring migratory aptitudes has been published by 
Shubin and co-workers. 52 They studied the temperature at which the two methyls 
of 39 became equivalent in superacid solution in the nmr and found the following 
results for various substituents X : H, 70°C ; CH 3 , - 1 00°C ; CI, - 55°C ; F, - 70°C ; 
CF 3 , 0°C. 

47 P. Depovere and R. Devis, Bull. Soc Chim. France, 479 (1969). 

" C.J. Collins, J, Amer. Chem. Soc, 77, 5517 (1955). 

49 D. Y. Curtin and M. C. Crew, J. Amer. Chem. Soc., 76, 3719 (1954). 

60 D. Semenow, C.-H. Shih, and W. G. Young, J. Amer. Chem. Soc, 80, 5472 (1958). 

61 R. Huisgen and C. Riichardt, Justus Liebigs Ann. Chem., 601, 1 (1956). 

62 V. G. Shubin, D. V. Korchagina, G. I. Borodkin, B. G. Derendjaev, and V. A. Koptyug, J. 
Chem. Soc, D, 696 (1970). 

1,2-Shifts in Carbenium Ions 287 

Memory Effects 53 

Heretofore we have been concerned mainly with single rearrangements. Multiple 
rearrangements also occur, in which the carbocation formed after the initial 
migration rearranges again (and again) before products are formed. Some of 
these consecutive rearrangements are remarkable in that presumably identical 
carbocations, which arise by rearrangement from different starting materials, 
retain a memory of their antecedent and give different second rearrangements. 
For example, deamination ofsyn- and araft-2-norbornenyl-7-carbinyl amines 
(40 and 41) both give twice-rearranged products (Equations 6.27 and 6.28). 
The first rearrangement in both deaminations is a ring expansion to give 42. 




-> HO 


If 42 is symmetrical, as would be expected if a flat carbocation were formed, both 
reactions should go on to give the same products. But they do not. 54 

The cause of the memory effect is not well understood. Berson has suggested 
that the symmetrical ion 42 is not the first-formed cation in both reactions, but 
that twisted cations that can rearrange further before they undergo the readjust- 
ments that convert them to 42 are formed first. In this view 40 would first form 43, 
in which the a bond is better able to migrate than the it bond, whereas 41 would 
first form 44, in which the 77 bond is better situated for migration. 55 

63 For a review, see J. A. Berson, Angew. Chem. Int. Ed., 7, 779 (1968). 

54 J. A. Berson, J. J. Gajewski, and D. S. Donald, J. Amer. Chem. Soc., 91, 5550 (1969). 

65 See (a) note 53; (b) note 54; (c) J. A. Berson, J. M. McKenna, and H. Junge, J. Amer. Chem. 

Soc.,93, 1296 (1971). 

288 Intramolecular Rearrangements 


Collins, on the other hand, has proposed that the memory effect can be 
explained, at least for some systems, by "counter-ion control" : The leaving group 
stays near the site of ionization and thereby influences the future steric course of 
the reaction. 56 

6.2 CARBONIUM IONS 57 - 60 

In this section we shall discuss carbocations in which at least o ne carbon^through 
a th ree-c enter bond (see Section 5.3) is coordinated to four_jo£-fiv^-atoms. By 
Olah's tarminology these are "carb onium jom^juTopposed to tricoordinated 
"carbenium ions." 61 By older terminology the more highly coordinated carboca- 
tions are called "nonclassical carbonium ions" to differentiate them from the 
tricoordinated "classical carbonium ions." 

Homoallylic Carbonium Ions 62 

In 1946 Shoppee noted that the reaction of 3-)3-cholesteryl chloride with acetate 
ion proceeds entirely with retention of configuration (Equation 6.29). Substi- 
tutions on the analogous saturated compound proceed with the expected 

56 C. J. Collins, I. T. Glover, M. D. Eckart, V. F. Raaen, B. M. Benjamin, and B. S. Benjaminov, 
J. Amer. Chem. Soc, 94, 899 (1972). 

67 For a review on the general subject, see P. D. Bartlett, Nonclassical Ions, W. A. Benjamin, Menlo 
Park, Calif., 1965. 

66 For reviews of homoallylic and small-ring participation, see: (a) R. Breslow, in Molecular Re- 
arrangements, P. Mayo, Ed., Wiley- Interscience, New York, 1963, Vol. 1, p. 233; (b) M. Hanack and 
H.-J. Schneider, Angew. Chem., Int. Ed., 6, 666 (1967); (c) R. R. Story and B. C. Clark, in Carbonium 
Ions, G. A. Olah and P. v. R. Schleyer, Eds., Wiley-Interscience, New York, 1972, Vol. Ill, p. 1007; 
(d) K. B. Wiberg, B. A. Hess, and A. J. Ashe, in Carbonium Ions, Olah and Schleyer, Eds., Vol. Ill, 
p. 1295; (e) H. G. Rickey, in Carbonium Ions, Olah and Schleyer, Eds., Vol. Ill, p. 1201. 

59 For reviews of bicyclic carbonium ions, see: (a) J. A. Berson in Molecular Rearrangements, P. Mayo, 
Ed., N.Y., Vol. I, p. Ill; (b) G. D. Sargent, Quart. Rev. (London), 20, p. 301 (1966); (c) G. D. 
Sargent, in Carbonium Ions, Olah and Schleyer, Eds., Vol. Ill, p. 1099. 

60 For an opposing view, see (a) note 25(a), p. 277; (b) H. C. Brown, Chem. & Eng. News, 45, 
Feb. 13, p. 87 (1967); (c) H. C. Brown, Accts. Chem. Res., 6, 377 (1973); (d) E. N. Peters and H. C. 
Brown, J. Amer. Chem. Soc, 96, 263, 265 (1974); (e) H. C. Brown, M. Ravindranathan, and E. N. 
Peters, J. Amer. Chem. Soc, 96, 7351 (1974). 

61 G. A. Olah, J. Amer. Chem. Soc, 94, 808 (1972). 

62 See note 58. 

CH 3 

Carbonium Ions 289 

CH 3 



inversion. Shoppee postulated some sort of assistance from the 5,6-double bond 
to explain these results. 63 

Winstein investigated the kinetics and products of 3-/3-cholesteryl substitutions 
further. He found that under certain conditions 3-/S-cholesteryl tosylate (or 
chloride) is acetolyzed to the cholesteryl z'-acetate (Equation 6.30), and that this 
reaction is 100 times faster than the solvolysis of cyclohexyl tosylate. Moreover, 

CH 3 


CH 3 C— OH 

if the conditions are slightly varied, the t-acetate undergoes rearrangement to 
form 3-/3-cholesteryl acetate, also at an enhanced rate. 64 Rate enhancement for 
Reaction 6.30 might be explained if solvolysis of the tosylate leads immediately 
to the rearranged ion 45, and if this ion is for some reason particularly stable. 
Its formation would then be the driving force for the reaction. However, this 
explanation cannot be correct. If the driving force for acceleration of Reaction 
6.30 is the formation of cation 45, then the reverse ring opening of the t-acetate 
should not have a comparable driving force, but it does. Winstein suggested that 
a stabilized intermediate was common to both reactions and was responsible for 
their accelerated rates. 

But what is the nature of the intermediate ? A n bond between the empty p 
orbital on C 3 and the p orbital on C 5 could not impart such stability, because n 
overlap falls off rapidly with distance. Winstein suggested that the empty p 
orbital on C 3 overlaps in an end-on, or a, fashion with the p orbital on C 5 , while 
at the same time the 5,6-7? bond is maintained, resulting in a two-electron, 

63 C. W. Shoppee, J. Chem. Soc., 1147 (1946). 

04 S. Winstein and R. Adams, J. Amer. Chem. Soc, 70, 838 (1948). 

290 Intramolecular Rearrangements 

Figure 6.5 Orbital picture of homoallylic participation in the cholesteryl system. 



Figure 6.6 (a) Orbital picture of the transition state of solvolysis of e*o-5-norbornenyl 
halides. (b) Orbital picture of the transition state of solvolysis of endo-5-nor- 
bornenyl halides. 

three-center bond. 65 This structure is. shown in an orbital representation in 
Figure 6.5 and in a dotted-line representation 66 in Structure 46. 

Intermediate 46 is responsible for the retention of configuration observed 
by Shoppee. The 5,6-double bond that has displaced the leaving group from the 
back side now shields this side from attack by the entering group, thus leaving 
the front side as the only available route to substitution. 

Because p ositiy£xhaiu^-is-d£lQi^iiz£d-b,y^/> orbital one-^arbpjLatQm further 
removed than the allylir position, the kind of bond in g show n in 46 j§. rallpH 
homoallylicjt he homo is for homologous) participation. In this interm ediate both C 3 
and C R arec ooHina^^ tr > fo u r atoms and thus it is a carbonium ion. 

The work on the cholesterol system stimulated investigation of other 
examples of homoallylic participation. Roberts found that exo-5- and endo-5- 
bicyclo[2.2.1]heptenyl (i.e., exo-5- and enrfo-5-norbornenyl) halides (47 and 48) 
both solvolyze in aqueous ethanol to give the same product (49) ; the exo compound 
(47) solvolyzes about ten times more rapidly than the endo compound (48). 
Roberts pointed out that backside homoallylic participation in ionization was 
possible in 47 but not in 48 (see Figure 6.6) . Once 48 has ionized it can, in a second 

65 M. Simonetta and S. Winstein, J. Amer. Ckem. Soc, 76, 18 (1954). 

66 In this book we shall use the convention that a dotted line means a partial bond. Thus in Struc- 
ture 46 there is a partial bond between C 3 and C 5 and a partial double bond between C 5 and C e . 
For another convention see note 61, p. 288. 

Carbonium Ions 291 

step, form either the rearrange jenium ion 50 or the same carbonium ion 

formed in the solvolysis of 47. Thus both compounds give the same product. 67 





A much more spectacular driving force was found in the acetolysis ofanti-7- 
norbornenyl tosylate (51). This compound solvolyzes 10 11 times faster than the 
saturated analog and gives as the sole product the anti-acetate, 52. 68 Winstein 
attributed the enormously accelerated rate to powerful anchimeric assistance of 
both p orbitals of the 2,3-double bond. 



Carbon-7 is located on a plane that bisects the 2,3-bond and is in fact homoallylic 
to both sides of the double bond. Therefore a developing p orbital on it is in a 
position to overlap equally with each of the p orbitals of the double bond as is 
shown in Figure 6.7. No attack of solvent at C 2 or C 3 occurs in this system to give 
a three-membered ring analogous to i-cholesteryl derivatives and to 49 because 
the resulting carbon skeleton would be too strained. The fact that the pro duct is 
100 percent aw^ '^ac.elat£j^^xesult-xi£jLh£_bac k side of C 7 being hindered by the 
three-c enter bond thaH sjully Jormed m JheJ&termediate carboni um ion. 

Figures 6.6a and 6.7 show two kinds of homoallylic participation. We shall 
see below (p. 296) that other structures have also been proposed for this type of 
delocalized bonding. 

There are strict geometrical requirements for homoallylic participation. 
For example, Bartlett and Rice found no indication of homoallylic participation 
on solvolysis of 53 in aqueous acids. Apparently the strain energy of bonding is 
greater than the stabilization so obtained. 69 


Figure 6.7 Transition state for solvolysis of arcft-7-norbornenyl tosylate. 

97 J. D. Roberts, W. Bennett, and R. Armstrong, J. Amer. Chem. Soc, 72, 3329 (1950). 

98 (a) S. Winstein, M. Shatavsky, C. Norton, and R. B. Woodward, J. Amer. Chem. Soc, 77, 4183 
(1955); (b) S. Winstein and M. Shatavsky, J. Amer. Chem. Soc, 78, 592 (1956). 

69 P. D. Bartlett and M. R. Rice, J. Org. Chem., 28, 3351 (1963). 

292 Intramolecular Rearrangements 


The importance _jo r homoallylic participation of the exact. position nf the p 
orbitals of the double bong^in relation t o the dev eloping p nrhital at the- fortiori 
site Ts~also shown by the rate change attendant on puckering of the five-mem- 
bered ring in the series, 54, 55, and 56. 70 In the lower homologs of these bi- 

-x ,-x 

Relative rate: 

cycloalkenes the nve-membered ring is more puckered than in the higher homo- 
logs, and backside participation is facilitated. 

Electron demand at the incipient carbocation is also important in deter- 
mining whether or not homoa^ lic'^pal^cipaTioh '" "tak" e s~pl ace. Gassman and 
Fentiman have pfottecTthe logs of the rates of solvolysis of both 57 and 58 in 
dioxane-water vs. the Hammett a + constants of the X substituents. They 


(OPNB =p-nitrobenzoate) 


found that for all X's the logs of the rates of solvolysis of 57 fall on a straight 
line, as would be expected if the variations in rate were due to the electron- 
donating ability of X alone (see Section 2.2). The logs of the rates of 58 when X 
is a />-N,N-dimethyl or a /i-methoxy group fall on the same straight line, signify- 
ing that the mechanism of ionization is the same as that of 57. However, the logs 
of the rates of ionization of 58 when X is hydrogen, />-trifluoromethyl, or 3,5- 
bis-(trifluoromethyl) deviate from the line and are much larger than would be 
expected from the Hammett correlation. 71 Apparently, when _ X_is e\e-rtrcr\- 
donating, participation of the double boncHsrno t req uired for ionization :_The_ 
ca rbenium ion is more stable than the carbonium io n . However ^ when_X is 
ele ctron-withdrawing, t he-j^rheniurnjon is destabilized and the_c^b.ojnLiuinJ.on 
becomes the favored inte rmediate. 

Do uble~bonds _ fur ther removed from the incipient carbocation than the 
homoallyli c position c arLAlsQ -assist-in -ionization-jf the-geornetry^pf the_^ystem._ 
allows it L For example frawj-5-decen-l-yl ^-nitrobenzoate (59) solvolyzes 1500 
times faster than the corresponding saturated compound in aqueous acetone. 
The product is trans,trans-l-decalo\ (60). If after 12 half-lives the product is iso- 

70 B. A. Hess, Jr., J. Amer. Chem. Soc, 91, 5657 (1969) and references therein. 

71 P. G. Gassman and A. F. Fentiman, Jr., J. Amer. Chem. Soc, 92, 2549 (1970). 

Carbonium Ions 293 

lated, a ^-nitrobenzoate derivative is found which has the structure 61. Further- 
more, if the original /i-nitrobenzoate has ls O in the carbonyl carbon, it is found 
incompletely scrambled in 61. These facts lead us to conclude that the rearrange- 
ment occurs in an intimate ion pair of which the ion 62 is the cation. 72 









The Cyclopropylcarbinyl Cation 

In 1951 Roberts observed that most cationic reactions of cyclopropylcarbinyl and 
of cyclobutyl derivatives give the same products in nearly the same ratio. 73 For 
example, cyclopropylcarbinyl and cyclobutyl amines on deamination form the 
products shown in Equation 6.31. 74 Moreover, when allylcarbinyl tosylate (63) 

CH 2 NH 2 + NaN0 2 

CH 2 OH + 




NH 2 

+ NaN0 2 




is solvolyzed in 98 percent formic acid, the products shown in Equation 6.31 are 
again formed, and their ratio is similar to that of Equation 6.31. 



If solvolysis of 63 is carried out in more nucleophilic solvents (formic acid is 
strongly ionizing but weakly nucleophilic), predominant S N 2 reaction is ob- 
served. 75 

When cyclopropylcarbinyl amine labeled with 14 C in the 4-position is 
deaminated, the label is found to be scrambled in the products so that the three 
methylene groups have almost — but not quite — achieved equivalence. The 

72 H. L. Goering and W. D. Closson, J. Amer. Chem. Soc., 83, 3511 (1961). 

73 J. D. Roberts and R. H. Mazur, J. Amer. Chem. Soc, 73, 2509 (1951). 

74 R. H. Mazur, W. N. White, D. A. Semenow, C. C. Lee, M. S. Silver, and J. D. Roberts, J. Amer. 
Chem. Soc, 81, 4390 (1959). 

75 K. L. Servis and J. D. Roberts, J. Amer. Chem. Soc, 86, 3773 (1964). 

294 Intramolecular Rearrangements 

results are shown in Equation 6.32, in which the numbers at the carbons of the 
products refer to the percent 14 C found at that position in that product. 76 

CH 2 NH 2 



25.1 35.8 


CH 2 OH + ^V^\ OH 
53.2 33.4 &' 


A set of rapidly equilibrating carbenium ions might account for the rearrange- 
ments and the label scrambling; but this cannot be the correct explanation, for 
cyclopropylcarbinyl, cyclobutyl, and allylcarbinyl systems all solvolyze much 
more rapidly than would be expected from model compounds. Thus, for example, 
the rate of solvolysis of cyclopropylcarbinyl tosylate is 10 e times that of the solvent- 
assisted solvolysis of isobutyl tosylate. 77 Cyclobutyl tosylate solvolyzes 1 1 times 

CH 2 — OTs 

CH 2 — OTs 

Relative rate: 10 6 1 

more rapidly than cyclohexyl tosylate. 78 And allylcarbinyl tosylate in 98 percent 




Relative rate: 


HCOOH solvolyzes 3.7 times faster than its saturated analog, in spite of the 
electron-withdrawing effect of the double bond. 79 



Relative rate: 


Roberts suggested that a set of charge-delocalize d, rapidly ejprilibxating 
carb onium ions , which he called bicgclobutonium ions, are the fi rst-for med ions from 
aUjhj-eejystemSj, .In_Schenie 3 are sho wn the bi c y ln hntrmiiim i" n<! farmpH frnm 
the d eamina tion of 1 4 C-lab eled cyclopropylcarbinyl amine^Equation_6.32). 
According to Roberts,_thgre jwoaGTbe t wo equivalent fir s t-forme j^cax b"""'" -1 
ions: A three-center bond could be formed from the developing em pty or -bital 
on C^ ancT either orb ltals on C, and C B (path a) or orbitals on C, and C 2 (path 
b). Once the se carbonium- . ions-were.ibrmEd. 1 ..they couldJ^mnverti^le^aSy-of 
the^olher-carbonium iojiiin Scheme^. Equilibration arrows should be shown 
between all the structures, but their inclusion would further confuse this already 
conceptually difficult scheme. Figure 6.8 shows an orbital representation of 
bicyclobutonium ion (64). 

76 See note 74, p. 293. 

77 D. D. Roberts, J. Org. Chem., 29, 294 (1964); 30, 23 (1965). 

78 H. C. Brown and G. Ham, J. Amer. Chem. Soc, 78, 2735 (1956). 

79 See note 75, p. 293. 

Carbonium Ions 295 

Figure 6.8 Orbital representation of the bicyclobutonium ion. From R. H. Mazur, W. N. 
White, D. A. Semonow, C. C. Lee, M. S. Silver, and J. D. Roberts, J. Amer. 
Chem. Soc, 81, 4390 (1959). Reprinted by permission of the American Chemical 

Scheme 3 

Positive charge in each of the bicylobutonium ions would be distributed 
between the three carbon atoms of the three-center bond. For example, the 
positive charge on carbonium ion 64 would be delocalized over C 4 , C 1; and C 3 . 
If water attacked this ion at C 4 , unrearranged cyclopropylcarbinol would be 
obtained; if water attacked at C 1; cyclobutanol would be the product; and if it 
attacked at C 3 , allylcarbinol would be formed (Scheme 4) . Addition of water to 

Scheme 4 


^ + H 2 



each of the bicyclobutonium ions would give the same three products, but the 
14 C label would be scrambled differently in each. 

296 Intramolecular Rearrangements 

Note that if the bicyclobutonium ion were formed directly upon ionization 
of an allylcarbinyl derivative, it would be a case of homoallylic participation in 
an acyclic system. In fact, the bicyclobutonium ion is similar to the carbonium ion 
proposed by Winstein for homoallylic participation in the 7-norbornenyl system — 
cf. Figures 6.7 and 6.8 and Structures 65 and 66. The difference between them is 
that 66 is more symmetrical. 

65 66 

Since Roberts' work, a _great_dea l of evi dence, both experimental and 
theoretical, has accumulated that indka^ej_tnaI_lh£jbicyxlohutonium ion is not 
the first-formed ion upon solvolysis of unstrained cyclopropylcarbinyl systems. 
Instead, the structure of the ion apparently is the bisected cyclopropylcarbinyl 
cation, which is_shown in _ajatted-hne^brmulatien in 67 -and- iiL_arL or bital dia- 
gram fn FijjureJLS. (See also Section 10.6.) 


A comparison of Figures 6.8 and 6.9 shows that the bisected cyclopropyl- 
carbinyl cation differs from the bicyclobutonium ion in several ways. For example, 
in the b isected . cyclopropylcarbinyl cation, the carbinyL carban— (€»-}- and 4ts 
subs tituents li e above or b elow the„jmg in_ajplane tha t is perpendicular- to~the 
plane of the ring and bisects Cj^ndjiieJ^-— C 3 bond. The vacant ^jorbiialJs 
paraUel_ to jthe plane o f the ring an dto t he C 2 — "C^T>ond.~By n overlap _witfa _the 
C^CJ)pnding prbitals of the cyclopropane ring, which, becausejaf angle strain, 
have an abnormal amount_of^ character, 80 the positive charge at C 4 is de- 
localized to all three ring carbons. In the bicyclobutonium ion, C 4 is not equi- 

Figure 6.9 Orbital representation of the bisected cyclopropylcarbinyl cation. 

80 (a) D. Peters, Tetrahedron, 19, 1539 (1963); (b) M. Randi and A. Maksic, Theor. Chim. Acta, 3, 59 
(1965); (c) A. D. Walsh, Trans. Faraday Soc, 45, 179 (1949); (d) L. I. Ingraham, in Steric Effects in 
Organic Chemistry, M. S. Newman, Ed., Wiley, New York, 1956, chap. 11; (e) C. A. Coulson and 
W. E. Moffitt, Phil. Mag., 40, 1 (1949) ; (f ) R. Hoffmann and R. B. Davidson, J. Amer. Chem. Soc, 93, 
5699 (1971). 

Carbonium Ions 297 

distant from C 2 and from C 3 ; the vacant p orbital on C 4 is almost perpendicular 
to the plane of the ring. Furthermore, positive charge at C 4 in a single bicyclo- 
butonium ion can be delocalized to C x and to either C 2 or C 3 but not to both. 
Some of the evidence for the bisected cyclopropylcarbinyl cation follows. 
That the charge can be delocalized to both C 2 and C 3 simultaneously has been 
shown by the work of Schleyer and Van Dine. 81 These workers studied the sol- 
volysis of cyclopropylcarbinyl 3,5-dinitrobenzoates and found that methyl 
substituents accelerated the rate by an amount dependent only on the number of 
such substituents and not on their position. Thus 68, 69, and 70 react at almost 
the same rate. If the transition state for ionization were similar to the bicyclo- 
butonium ion, two methyl groups at C 2 should accelerate the rate more than one 
at C 2 and one at C 3 . A symmetrical transition state for ionization similar to the 
bisected cyclopropylcarbinyl cation (67) in which the charge is delocalized over 
all four carbon atoms best explains the results. 

CH 3 CH 3 

/\ CH 2 ODNB A\ CH 2 ODNB 

H,C-f-^ CH 2 ODNB H ^ C \[^y Ly 

CH 3 CH 3 

68 69 70 

That maximum acceleration occurs when the vacant p orbital is parallel 
to the plane of the cyclopropyl ring can be seen from the solvolysis of spiro [cyclo- 
propane- 1,2 '-adamantyl] chloride (71). The carbocation formed by departure 
of CI - is unable to adopt the geometry of the bisected cyclopropylcarbinyl 
cation, but can orient its empty p orbital properly to form the bicyclobutonium 
ion. This compound solvolyzes 10 3 times more slowly than 1-adamantyl chloride. 82 
On the other hand, 72 solvolyzes 10 5 times faster than 73. The cation from 72 
does have its p orbital parallel to the plane of the ring as in the bisected cyclo- 
propylcarbinyl cation. 83 

Other structures have also been suggested as intermediates in cyclopropyl- 
carbinyl and cyclo butyl solvolyses. 84 Winstein has pointed out that the nature of 
the intermediate cation may differ with the geometrical requirements of the 

81 P. v. R. Schleyer and G. W. Van Dine, J. Amer. Chem. Soc, 88, 2321 (1966). 

82 B. R. Ree and J. C. Martin, J. Amer. Chem. Soc, 92, 1660 (1970); V. Buss, R. Gleiter, P. v. R. 
Schleyer, J. Amer. Chem. Soc, 93, 3927 (1971) and references therein. 

83 Y. E. Rhodes and V. G. DiFate, J. Amer. Chem. Soc, 94, 7582 (1972). 

84 (a) Z. Majerski, S. Borcic, and D. E. Sunko, J. Chem. Soc D, 1636 (1970); (b) C. D. Poulter, 
E. C. Friedrich, and S. Winstein, J. Amer. Chem. Soc, 92, 4274 (1970); (c) C. D. Poulter and S. 
Winstein, J. Amer. Chem. Soc, 92, 4282 (1970); (d) Z. Majerski and P. v. R. Schleyer, J. Amer. 
Chem. Soc, 93, 665 ( 1971) ; (e) J. E. Baldwin and W. D. Foglesong, J. Amer. Chem. Soc, 90, 4303, 431 1 

298 Intramolecular Rearrangements 

starting material. 85 Indeed, Figure 6.10 presents the results of CNDO calcula- 
tions on the barrier to rotation of the carbinyl group. 86 It appears that a 30° 
rotation from the symmetrical structure (a = 0°, see 74) leads to only a small 
decrease in stabilization. 




Is the cyclopropylcarbinyl system also the first-formed ion in solvolysis of 
cyclobutyl derivatives? The evidence is conflicting. Majerski, Borcic, and 
Sunko studied the reactions shown in Equations 6.33 and 6.34 and found that 
when the starting material is the cyclopropylcarbinyl methanesulfonate, the label 
scrambling is less complete in the cyclopropylcarbinol than in the cyclobutanol; 
similarly, cyclobutyl methanesulfonate gives less label scrambling in the cyclo- 
butanol than in the cyclopropylcarbinol. 87 (In Equation 6.33, the numbers 
show the distribution of the CD 2 group. In Equation 6.34, they show the distri- 
bution of the CH 2 group.) 

CD 2 OMs 

H a O 








24% 38% 


yield too low 
for analysis 





H a O 

D 2 






52% 24% 


yield too low 
for analysis 


This would make it appear that cyclopropyl and cyclobutyl derivatives each 
solvolyze to give ions that are similar in structure to the starting material. Solvent 
capture may occur at this stage. If it does not, the first-formed ion rearranges. 

On the other hand, there is now a good deal of evidence that the solvolysis 
of most cyclobutyl derivatives does lead directly to the cyclopropylcarbinyl 
cation. For example, orbital symmetry considerations (Section 1 1.3) indicate that 
the conversion of cyclobutyl cations into cyclopropylcarbinyl cations should 
occur by disrotatory ring opening as shown in Figure 6.11; but any steric factors 
that would hinder such a process decelerate most cyclobutyl solvolyses. Thus 

86 See note 84(b). 

86 K. B. Wiberg and J. G. Pfeiffer, J. Amur. Chem. Soc, 92, 553 (1970). 

87 See note 84(a), p. 297. 

Carbonium Ions 299 

Relative energy 
(kcal mode - ) 

Angle of rotation 
Figure 6.10 Change in energy of the cyclopropylcarbinyl cation as the cationic center is 
rotated. From K. B. Wiberg and J. G. Pfeiffer, J. Amer. Chem. Soc, 92, 553 
(1970). Reprinted by permission of the American Chemical Society. 

both 75 and 76 solvolyze in acetone/water to give 3-cyclopentenol (77), but 75 
solvolyzes 10 7 times faster than 76. 88 In 75, to overlap with the back side of the 
developing p orbital, the orbitals of the bond being broken must turn in such a 
way as to move the bridgehead hydrogens away from each other. In 76, however, 
the same process would require that the bridgehead hydrogens move toward 
each other. This is energetically unfavorable. 













Cyclobutyl cations certainly do exist if they are especially stabilized. For 
example, 1-phenylcyclo butyl cation shows no tendency to rearrange in superacid 
solution. 89 

If two different C 4 H 7 + ions may exist, which is the more stable ? The fact 
that most cyclobutyl derivatives seem to solvolyze directly to the cyclopropyl- 
carbinyl cation strongly suggests that that ion is the more stabilized. Nuclear 
magnetic resonance studies, however, give conflicting information. The spectrum 
of the unsubstituted cyclopropylcarbinyl cation in superacid solution is most 

+ X~ 

Figure 6.11 Orbital symmetry allowed (disrotatory) opening of a cyclobutyl cation. Note 
that the orbitals of the C — C bond being broken overlap with the back side of 
the orbital used for bonding to the departing group. 

68 (a) K. B. Wiberg, V. Z. Williams, Jr., and L. E. Friedrich, J. Amer. Chem. Soc, 90, 5338 (1968); 

(b) J. Amer. Chem. Soc, 92, 564 (1970). 

89 G. A. Olah, C. L. Jeuell, D. P. Kelly, and R. D. Porter, J. Amer. Chem. Soc, 94, 146 (1972). 

300 Intramolecular Rearrangements 

consistent with it being a set of equilibrating bicyclobutonium ions. 90 The 
spectrum of the cation derived from 1-methylcyclobutyl chloride is best explained 
if the cyclobutyl cation is in rapid equilibrium with the corresponding cyclo- 
propylcarbinyl cation and the equilibrium favors the former, as shown in 
Equation 6.35. 91 


The nmr spectrum of the 4,4-dimethylcyclopropylcarbinyl cation in super- 
acid is only in agreement with the bisected structure of the ion (78). In Structure 
78 the two methyl groups are not equivalent — one is cis to the cyclopropyl ring 


and the other is trans. Indeed, the nmr spectrum shows two different peaks due 
to methyl groups separated by 0.54 ppm, which do not coalesce up to — 30°C, 
at which temperature ring opening occurs. 92 

Molecular orbital calculations suggest that for the parent ion and for 
methylated ions, 78 and 79, the bisected cyclopropylcarbinyl structure is the 
structure of lowest energy. 93 They also predict that the cyclopropylcarbinyl- 


-CH 3 


cyclopropylcarbinyl conversions, which we know must occur from label scram- 
bling experiments (Equation 6.32) and other rearrangements, have as a transition 
state a puckered cyclobutyl cation. 94 Figure 6.12 shows the proposed reaction 
coordinate diagram for the parent system and the gem-dimethyl system. The most 
stable cation in the latter system, in agreement with Olah's work, is that which is 
stabilized by having the £«m-dimethyl group on the same carbon as the positive 

The Norbornyl Cation 95 

In discussing the cyclopropylcarbinyl cation before the norbornyl cation we have, 
chronologically, put the cart before the horse. The first experimentally docu- 
mented example of anchimeric assistance by a C — C a bond was announced by 
Winstein and Trifan in 1949. 96 These workers studied the solvolysis of exo- and 

90 See note 89, but see also W. J. Hehre and P. C. Hiberty, J. Amer. Chem. Soc, 96, 302 (1974). 

91 M. Saunders and J. Rosenfeld, J. Amer. Chem. Soc, 92, 2548 (1970). 

92 (a) See note 34, p. 280; (b) C. U. Pittman, Jr., and G. A. Olah, J. Amer. Chem. Soc., 87, 2998 

83 (a) See note 58(e), p. 288; (b) W.J. Hehre and P. C. Hiberty, J. Amer. Chem. Soc, 96, 302 (1974). 

94 See note 93(b). 

95 See note 59(c), p. 288. 

96 S. Winstein and D. S. Trifan, J. Amer. Chem. Soc, 71, 2953 (1949). 

Carbonium Ions 301 


v^ ^ + v 

^ ^ 



Figure 6.12 (a) Rearrangement in the cyclopropylcarbinyl system, (b) Rearrangement in 
the dimethyl cyclopropylcarbinyl system. From W. J. Hehre and P. C. Hib- 
berty, J. Amer. Chem. Soc, 96, 302 (1974). Reprinted by permission of the 
American Chemical Society. 

endo-2-noThomyl arenesulfonates (80 and 81, respectively) and found that the 
reactions had these interesting characteristics: (1) the exo compound solvolyzes 
350 times more rapidly than the endo compound; (2) both exo and endo starting 
materials give exclusively ( > 99.9 percent) exo product as shown in Equation 
6.36; (3) chiral exo starting material gives entirely racemic product, but the 
product from endo starting material retains some chirality; and (4) chiral exo 
starting material, recovered before complete reaction, is partially racemized. 
The ratio of polarimetric and titrametric rate constants in acetic acid is 4.6. 
Since recovered, unreacted endo starting material is not racemized, the rate of 
ionization of 80 relative to the rate of ionization of 81 in acetic acid is not 350 
but 350 x 4.6 or 1550. 97 

97 (a) See note 96; (b) S. Winstein and D. Trifan, J. Amer. Chem. Soc, 74, 1147, 1154 (1952); (c) S. 
Winstein, E. Clippinger, R. Howe, and E. Vogelfanger, J. Amer. Chem. Soc, 87, 376 (1965). 

302 Intramolecular Rearrangements 

Figure 6.13 Orbital picture of the norbornyl cation. 



1 >^OS0 2 Ar 




Winstein pointed out that th ese observations are all cons isten t j f , in th e 
so lvolysis of 80. the 1 .6-bond assists in the ionization _and^hjL^^'ngr^bQmonium' ' 
ion, shown in 82 and Figure 6.13. is the fi rst^foroiecHnterrnediate. 

E quati on 6.37 shpws_ theresonan ce structures implied by 8 Z_The_driving force 


for the_rearra 

enLarQuld be the relief of skeletal strain. 

The explanations, in terms of 82, of the observed differences between the 
exo and endo brosylates (80 and 81) follow. 

Rate In the 6*ro-norbornyl arenesulfonates, the C x — C 6 bond is in the 
trans-periplanar orientation to the leaving group and therefore in the optimum 
position to provide anchimeric assistance. The Cj — C 6 bond is not properly 
oriented for anchimeric assistance in the m/o-norbornyl arenesulfonate ; and 
although the C ± — C 7 bond is not badly oriented, the rearranged ion (83) re- 

Carbonium Ions 303 

suiting from participation of this bond is more highly strained than the starting 
material. .Thus, according to WinstHn thf* ftWft-n n rh o rnyl rim 'v atiy_e_i irst io nizes 

to _thj^rhargr-Wali'7pH rarhpninm inn (ft4) Onrp frirmpt^thuLinrL ran rearrange 



to t he more s ta ble-ear bonium ion (82), 98 Figure 6.14 shows the proposed reaction 
coordinate diagrams for solvolysis of the exo- and ercdo-norbornyl sulfonates. 

Product The product from solvent attack on the carbonium io n_ 82 rn nst 
be from the exo direction since the endo side would b e hinder ed by the three- 
center e^HjoEcL^ 

Stereochemistry The norbornonium ion has a plane of symmetry. This 
can perhaps be seen most readily if 82 is rotated about the C ± — C 4 axis, as shown 
in Equation 6.38. Thus chiral starting material should give racemic product if the 
intermediate 82 lies on the reaction path : Solvent attack at C 2 yields product of 
retained configuration, but attack at the equivalent site, C 1} yields inverted 
product. If the chiral norbornenium ion (84) were the intermediate, solvent 
attack could occur only at C 2 and retained product would be obtained. 100 As 
we have already seen, the product from chiral exo starting material is entirely 
racemic. The exo-norbornyl derivatives obtained from endo starting material 



Figure 6.14 (a) Probable reaction coordinate diagram for the solvolysis of exo-2-norbornyl 
derivatives, (b) Probable reaction coordinate diagram for solvolysis of endo-2- 
norbornyl derivatives. 

68 See note 96, p. 300, and note 97, p. 301. 
99 See note 96, p. 300, and note 97, p. 301. 
100 See note 96, p. 300, and note 97, p. 301. 

304 Intramolecular Rearrangements 





are about 87 percent racemized in strongly nucleophilic solvents. Thus most of 

the product is indeed forme d by the reac tion^ 

some solve nt m ust also att ack__Cg~before 

rearrange. T ess rmrleop hilir solven ts give a greater extent of racemization. 1 ° 1 

Isomerization of starting material Partial racemization of recovered 
exo starting material is consistent with the hypothesis that anorbornonium ion is 
formed immediately on ionization if it is further postulated that an intimate ion 
pair is the first ionic species on the reaction path. Internal return from the 
achiral norbornonium-arenesulfonate intimate ion pair must give racemized 
starting material. 102 

If the norbornyl cation is formed on solvolysis of exo-norbornyl derivatives, 
C 2 should become equivalent to C 2 and C 7 to C 3 . In a most elegant tracer 
experiment, Roberts and Lee synthesized «xo-2-norbornyl-[2,3- 14 C] brosylate 
(85), solvolyzed it in acetic acid, and degraded the product. Equation 6.39 shows 
the product distribution expected if the symmetrical carbonium ion (82) were 
formed. The label was found not only at C ls C 2 , C 3 , and C 7 , but also at C 5 and 





by attack at a by attack at b 

50% 50% 

C 6 . To account for this Roberts suggested that 6,2- or 6,1 -hydride shifts occur 
in the carbonium ion simultaneously with the rearrangement of Equation 6.39 
as shown in Equation 6.40. 103 

Although cationic reactions of 2-^o-norbornyl arenesulfonates have char- 
acteristics that would be associated with a charge-delocalized carbonium ion 
intermediate — driving force, stereospecific product formation, rearranged pro- 
ducts, internal return to rearranged starting material, and special chiral character- 
istics — a storm of controversy has raged over its existence. Its opponents, of whom 
H. C. Brown is the chief, have maintained that the postulation of a bridged 
carbonium ion intermediate is not necessary to explain the characteristics of the 

101 See note 97, p. 301. 

102 See note 97, p. 301. 

103 J. D. Roberts and C. C. Lee, J. Amer. Chem. Soc., 73, 5009 (1951) ; (b) J. D. Roberts, C. C. Lee, 
and W. H. Saunders, Jr., J. Amer. Chem. Soc, 76, 4501 (1954). 

Carbonium Ions 305 

norbornyl system. He has argued that the k ex Jk end0 rate ratio in solvolyses of 
norbornyl derivatives is large, not because k exo is particularly great but because 
^endo 1S particularly small. In his view a 2-endo substituent experiences steric 

by attack at d 



by attack at c 

hindrance to ionization by the three endo protons. He suggests, furthermore, 
that the peculiar U-shaped structure of the C 6 — C 1 — C 2 segment hinders endo 
approach of a nucleophile to the classical 2-norbornyl cation and thus exo 
product is formed. Finally, he proposes that the skeletal rearrangements and loss 
of chirality are consistent with rapid 1 ,2-Wagner-Meewein shifts as shown in 
Equation 6.41. 104 


Note that the two carbenium ions in Equation 6.41 are mirror images of one 
another. The carbonium ion (82) would then be a transition state for Equation 
6.41, not a stabilized intermediate. 

The investigation of the 2-norbornyl cation has been intensive and detailed. 
Sargent says, it "may well be the most thoroughly investigated yet least thoroughly 
understood reactive intermediate known to organic chemists. Seldom, if ever, 
has a single species been the subject of so many ingenious experiments conceived 
by so many eminent investigators utilizing such a variety of sophisticated meth- 
ods. Despite the intensity of this effort, the structure of the 2-norbornyl cation 
remains an enigma." 105 However, most workers in the field now agree that when 
a secondary e*o-norbornyl derivative is solvolyzed, the bridged carbonium ion is 
formed as an intermediate. We shall only touch on the controversy momentarily 
and give examples of experiments carried out to clarify one of its aspects — is the 
large exo/endo rate ratio due to a remarkably large (assisted) exo rate or a 
remarkably small (hindered) endo rate? For more detailed presentations, the 
reader is referred to the references cited in notes 59. and 60, p. 288. 

A number of cases of steric deceleration of solvolysis have been reported. 
For example, the nonbonded strain in 87 is approximately 1.9 kcal mole -1 
greater than that in 86. Assuming that the strain is fully relieved in the transition 
state for ionization, one would predict that the rate of solvolysis of the endo- 
tosylate (87) should exceed that of the e#o-tosylate (86) by a factor of ~25. 

104 See note 60, p. 288. 
106 See note 59(c), p. 288. 

306 Intramolecular Rearrangements 

The exo compound actually solvolyzes 5.7 times faster than the endo compound. 
Since there is no obvious route for a bond participation here, it appears that there 
must be an increase in nonbonded strain in the transition state of 87 of RTln 5.7 
or ~1 kcal mole -1 . 106 

As Sargent has pointed out, experiments and examination of molecular 
models both indicate that this system should offer more extreme steric hindrance 
to endo ionization than the norbornyl system does. One kcal mole -1 , then, is 
an upper limit for the increase in nonbonded interaction experienced by the 
leaving group in going from the ground to the transition state in endo-2-nor- 
bornyl tosylate. 107 But 1 kcal mole -1 cannot be responsible for the exo/endo 
ionization rate ratio of 1550 reported by Winstein and Trifan, a ratio since 
corroborated by hundreds of other studies. 

More recently Nordlander and co-workers adopted a different approach to 
determine whether endo ionization of 2-norbornyl derivatives is hindered. 108 
They solvolyzed exo- and endo-2-norbomyl tosylate in the strongly ionizing 
but very weakly nucleophilic solvent, trifluoroacetic acid, and found the exo/ 
endo rate ratio to be 1 120. They then compared the rates of solvolysis of endo-2- 
norbornyl tosylate and of 2-adamantyl tosylate in two solvents — trifluoroacetic 
acid and much more nucleophilic acetic acid. Using an analysis suggested by 
Schleyer, 109 they reasoned that if ionization of eWo-2-norbornyl tosylate is 
sterically hindered, its rate should show a large dependence on the nucleophili- 
city of the solvent. But 2-adamantyl tosylate cannot solvolyze with solvent assis- 
tance (see Section 5.4, p. 243). Thus the ratio of the rate of solvolysis of endo-2- 
norbornyl tosylate to the rate of solvolysis of 2-adamantyl tosylate should be much 
larger in acetic acid than in trifluoroacetic acid. In fact, the ratio is 30 times 
greater in acetic acid than in trifluoroacetic acid. If the rates of solvolyses of 
<rara5-2-methylcyclopentyl tosylate (88) and 2-adamantyl tosylate are compared 
in the same two solvents, the ratio of rates is 31 times greater in acetic acid. 
Thus enrfo-2-norbornyl tosylate seems to be acting normally — that is, like other 
secondary tosylates with a branch in the j8 position. 

H 3 C 


106 H. C. Brown, I. Rothberg, P. v. R. Schleyer, M. M. Donaldson, and J. J. Harper, Proc. Nat. 
Acad. Sci. U.S., 56, 1653 (1967). 

107 See note 59(c), p. 288. 

108 J. E. Nordlander, R. R. Gruetzmacher, W.J. Kelly, and S. P. Jindal, J. Amer. Chem. Soc., 96, 181 

109 P. v. R. Schleyer, J. L. Fry, L. K. M. Lam, and C. J. Lancelot, J. Amer. Chem. Soc, 92, 2542 

Carbonium Ions 307 

There are abundant examples that show that classical nonbridged 2- 
norbornenium ions certainly do exist if there is an alkyl or other electron-releasing 
group on C 2 . 110 For example, optically active 89 solvolyses with partial retention 
of configuration. Thus the carbenium ion must be formed in spite of the fact that 
C 8 is an excellent bridging group. 111 

When 2-norbornyl fluoride is dissolved in superacid solution, a carbo- 
cation is obtained as shown in Equation 6.42. This ion has been examined by a 
number of physical methods, and the data are consistent with its structure being 
the bridged ion, 82. 112 For example, the ion has been examined by ESCA 




(electron spectroscopy for chemical analysis). By this method one can determine 
the energy required to remove inner shell electrons from around the nucleus. 
A sample is exposed to high-energy X-rays of known wavelength, which cause 
electrons to be ejected from the molecule. The energy conservation expression 
for the photoemission process can be expressed by 

E hv = E Mn + E b + E„ (6.43) 

where E hv , E kin , and E b are the X-ray energy, the kinetic energy of the electron 
emitted, and the binding energy of the electron emitted, respectively. E^ is a 
constant for a given system and can be determined. An electron multiplier de- 
tector counts the emitted electrons, and an electron energy analyzer determines 
the kinetic energies of the emitted electrons. Thus E b can be determined from 
Equation 6.43. 113 

The energy required to remove a Is electron from a hydrocarbon is almost a 
constant. For example, by ESCA one cannot distinguish between benzene and 
neopentane. In classical, nonresonance-stabilized carbocations, the positive 
charge is usually centered on a single atom, and thus more energy must be applied 
to remove an electron from this atom than from its uncharged neighbors. Figure 
6.15 shows the carbon Is electron spectrum for the £-butyl cation. The positive 
carbon is well separated from the carbons of the methyl groups. Figure 6.16 

110 For a study of how electron-releasing a 2-substituent must be for a 2-norbornyl derivative to 
ionize to the unbridged derivative, see D. G. Farnum and A. D. Wolf, J. Amer. Chem. Soc, 96, 5166 

111 H. L. Goering, C.-S. Chan, and J. V. Clevenger, J. Amer. Chem. Soc, 96, 7602 (1974). 

112 G. A. Olah, G. Liang, G. D. Mateescu, and J. L. Riemenschneider, J. Amer. Chem. Soc, 95, 8698 
(1973) and references therein. 

113 For a reivew of ESCA studies, see J. M. Hollander and W. L. Jolly, Accts. Chem. Res., 3, 193 

308 Intramolecular Rearrangements 

counts sec 







1195 1200 

~~ i r~ 

~~ 1 




-£ 6 (eV) 

Figure 6.15 Carbon Is electron spectrum (ESCA) of the <-butyl cation. From G. A. Olah, 
Angew. Chem. Int. Ed., 12, 173 (1973). Reproduced by permission of Verlag 
Chemie, GMBH. 

shows the carbon Is electron spectrum for the 2-methylnorbornyl cation 
and the norbornyl cation. The former is a classical ion (see p. 307) and has a 
spectrum similar to that of the i-butyl cation. The electron spectrum of the nor- 
bornyl cation, by comparison, has no high binding center. Olah says, "Since in 
electron spectroscopy the time scale of the measured ionization processes is of the 
order of 10 ~ 16 sec, definite ionic species can be characterized regardless of 
possible intra and intermolecular interactions (e.g., Wagner-Meerwein rearrange- 
ments, hydrogen shifts, proton exchange, etc.), which have no effect. Thus, 
ESCA spectroscopy gives an indisputable, direct answer to the long debated 
question of the 'nonclassical' nature of the norbornyl cation independent of any 
equilibration process." 114 

The nmr and Raman spectra of the parent norbornyl cation in superacid is 
also most consistent with the bridged structure 82. 115 The nmr spectra of a num- 

114 See note 34(b), p. 280. 

115 See note 112, p. 307. 

Carbonium Ions 309 

202 - 

2064 - 






Figure 6.16 Carbon Is electron spectrum (ESCA) of (a) the 2-methylnorbornyl cation and 
(b) the norbornyl cation. From G. A. Olah, Angew. Chem. Int. Ed., 12, 173 
(1973). Reproduced by permission of Verlag Chemie, GMBH. 

ber of stabilized 2-norbornyl cations in superacid have also been determined. 
For example, 90 and 91 have both been characterized as rapidly equilibrating 
carbenium ions by *H and 13 C nmr spectroscopy. 116 

/>xicH 3 


The Bicyclo[2.2.2]octyl System 

Since «co-2-norbornyl arenesulfonates apparently do solvolyze with anchi- 
meric assistance, the less strained 2-bicyclo[2.2.2]octyl derivatives (92) are of 
interest. In this system no comparison of the rates of exo and endo derivatives 
can be made, since a substituent exo to one bridge is eiida to the" otherT Stereo- 
chemical studies are, however, possible. If the carbonium ion (93) were formed 
from chiral 92 by participation of the C ± — C 6 bond, it would be chiral. Scheme 5 
shows that attack at C 2 of 93 should give retained bicyclo[2.2.2.]octyl solvolysis 
products (92a), and attack at C ± should give chiral ^o-2-bicyclo[3.2.1]octyl 

1 G. A. Olah and G. Liang, J. Amer. Chem. Soc, 96, 189, 195 (1974). 

310 Intramolecular Rearrangements 

derivatives (94). The carbenium ion (95) derived from 92, on the other hand, is 
achiral, and once it is formed it can only give rise to racemic products. 
Scheme 5 


. A/° s + 


> racemic products 



Two laboratories, those of Walborsky and of Goering, simultaneously 
investigated the stereochemistry of solvolysis of optically active bicyclo[2.2.2]- 
octyl arenesulfonates, and both found that the product consists of only two 
compounds: 2-bicyclo[2.2.2]octyl and exo-2-bicyclo[3.2.1] derivatives. The [2.2.2] 
system is largely retained although there is some attendant racemization, and the 
[3.2.1] system is also chiral but again partially racemized. Roth grou ps concluded 
that ionization at C 2 is assisted by the Cj — C 6 bond jmrj "" tW rhp product is 
forrne^jr^njy_b^soTvent ¥ttacTT^jthejnterrr^^aJ:jajcarboniuni_ion(93)--SeBie- 
^Tea kage" of the carbomum ion to ^h^jymjnetrical carbenium ion (95) does, 
however^ s eem to ta ke place, and from this, the racemized produciS-aFe-formed, 117 

Protonated Gyclopropanes 118 

Deamination of l-aminopropane-l- 14 C gives unscrambled 2-propanol and 
partially scrambled 1-propanol as shown in Equation 6.44. (The numbers at 
the carbons of the 1-propanol indicate the percentage of 14 C found at each 
position.) 119 The 2-propanol almost surely arises from a 1,2-hydride shift. 

CH 3 CH 2 14 CH 2 NH 2 HN ° 2 > CH 3 CH— 14 CH 3 + CH 3 — CH 2 — CH 2 OH (6.44) 

^ 1.9 2.2 95.9 

The label at C 3 of the primary alcohol could arise from a 1,3-hydride shift, but 
no simple hydride shift can bring about the label at C 2 . 

Aboderin and Baird suggested the mechanism of Scheme 6 for the label 
scrambling in Equation 6.44. 120 In each of the edge-protonated cyclopropanes (96a- 

117 (a) H. M. Walborsky, M. E. Baum, and A. A. Youssef, J. Amer. Chem. Soc, 83, 988 (1961); 
(b) H. L. Goering and M. F. Sloan, J. Amer. Chem. Soc, 83, 1397 (1961). 

118 See note 1(a), p. 268 and note 9(a), p. 270. 

119 (a) C. C. Lee and J. E. Kruger, J. Amer. Chem. Soc, 87, 3986 (1965); (b) C. C. Lee and J. E. 
Kruger, Tetrahedron, 23, 2539 (1967). 

120 (a) See note 6, p. 269; (b) A. A. Aboderin and R. L. Baird, J. Amer. Chem. Soc, 86, 2300 (1964). 

Carbonium Ions 311 

96c), two carbons are tetracoordinated ; the third participant in the three-center 
bond is hydrogen. Figure 6.17 shows an orbital diagram of Structure 96a. 

Scheme 6 

CH 3 CH 2 *CH 2 OH 


*CH 3 CH 2 CH 2 OH 

H a O 

CH 3 CH 2 *CH 2 OH 
CH 3 CH*CH 3 

CH 3 CH 2 *CH 2 OH 

*CH 3 CH 2 CH 2 OH 

H a o 

CH 3 *CH 2 CH 2 OH 

In the product-determining step of Scheme 6, the nucleophilic oxygen of water 
attacks one of the carbons; this carbon then withdraws its orbital from the three- 
center bond and an ordinary a bond is formed between the remaining carbon 
and the hydrogen. 

Another mechanism, that shown in Scheme 7, has also been suggested for 
the label scrambling of Equation 6.44. In each of the comer-protonated cyclo- 
propanes (96a-97c), all three participants in the three-center bond are carbon. 

Figure 6.17 Orbital picture of edge-protonated cyclopropane. 

312 Intramolecular Rearrangements 

Structures 96a-96c would be the transition states for the interconversions of 
Structures 97a-97c. 

Scheme 7 

CH 3 CH 2 *CH 2 OH 
CH 3 *CH 2 CH 2 OH 

H 3 

H , H 


H— C.t * 


H ^ H 






H a O 

CH 3 *CH 2 CH 2 OH 


H,, /H 

X C— C 


CH 3 CH 2 *CH 2 OH *CH 3 CH 2 CH 2 OH 

Ab initio molecular orbital calculations carried out by Pople, Schleyer, and 
co-workers predict that the most stable form of G 3 H 7 + is the 2-propyl cation 98. 
The second most stable structure they found to be the corner-protonated cyclo- 


propane, 97. The calculations suggest that 97 lies at an energy minimum and 
thus is an intermediate, not merely a transition state, but that 96 is probably 
not an intermediate. Figure 6.18 shows some of the structures and their calcu- 
lated relative energies. 121 

A number of other reactions have been postulated to involve protonated 
cyclopropanes as intermediates. 122 For example, nmr studies of the sec-h\x\.y\ 
cation in superacid show that from — 100 to — 40°C a process, with an activation 
energy of 7 kcal mole -1 , occurs that scrambles all the protons. The activation 
energy is too low for the scrambling to occur by the mechanism shown in Equa- 



121 P. C. Hariharan, L. Radoni, J. A. Pople, P. v. R. Schleyer, J. Amer. Chem. Soc, 96, 599 (1974). 

122 For a recent example, see: C. H. DePuy, A. H. Andrist, and P. C. Funfschilling, J. Amer. Chem. 
Soc, 96, 948 (1974). 

Carbonium Ions 313 

20 r 




(kcal mole -1 ) 

10 - 

H H 

C H 

H^ 94 ;v 


+ ' 


H H 



I +.-H 

96 C^-- 

Figure 6.18 Relative energies of various C 3 H 7 + ions. Data from P. C. Hariharan, L. Radom 
J. A. Pople, and P. v. R. Schleyer, J. Amer. Chem. Soc, 96, 599 (1974). Re- 
printed by permission of the American Chemical Society. 

tion 6.45 (see p. 270). Saunders suggests that the most probable mechanism is 
that shown in Scheme 8. 123 

1,3-Hydride shifts can take place directly, without the intervention of a 
carbonium ion intermediate, if the geometry of the system is favorable. For 
example, in the solvolysis of cyclohexyl-2,6-d 2 tosylate in 97 percent acetic acid, 
1,3-hydride shifts have been reported to account for 33 percent of the product. 124 
If this is so, it must be because the reaction is made facile by the proximity of the 
3-axial hydrogen to the empty p orbital. 

123 See note 9(b), p. 270. 

124 Y. G. Bundel, V. A. Savin, A. A. Lubovich, and O. A. Reutov, Proc. Acad. Soi. USSR Chem. Sect. 
(in English), 165, 1180 (1965). 

314 Intramolecular Rearrangements 

Scheme 8 



H H 


H H H 





H 3 C 








/ 3 I\ 

H H H 

Hydride shifts of higher order than 1,3 occur if (1) the migration origin and 
the migration terminus are close together and (2) the geometry of the system 
allows overlap of the orbitals of hydrogen and of the migration terminus. Be- 
cause of the proximity requirement such shifts are rare in acyclic systems 125 in 
nucleophilic solvents, 126 but in reactions of medium ring (7-12 carbon atoms) 

Scheme 9 







126 For a summary of these, see J. L. Fry and G.J. Karabatsos, in Olah and Schleyer, Eds., Carbonium 
Ions, Vol. II, pp. 555-557. 

126 Saunders and Stofko have observed 1,3- 1,4-, and 1,5-intramolecular shifts from tertiary to 
tertiary center in superacid and have calculated the activation barriers to be 8.5, 12-13, and 6-7 
kcal mole" 1 , respectively. (M. Saunders and J. J. Stofko, Jr., J. Amer. Chem. Soc, 95, 252 (1973)). 

Carbonium Ions 315 

carbocations, 1,3-, 1,4-, 1,5- and 1,6-hydride shifts occur readily. 127 "Trans- 
annular shifts" were first noted when unexpected products were found 128, 129 in 
the peroxyformic acid oxidation of medium-ring alkenes. For example, cyclo- 
octene gave, in addition to minor amounts of the expected trans-l, 2-dio\, cyclo- 
octane-ay- 1,4-diol and 3- and 4-cyclooctene-ols. Either a 1,3- or 1,5-hydride 
shift could bring about formation of the 1,4-diol and of the unsaturated alcohols 
(see Scheme 9) . That both orders of hydride shift take place in this reaction 
was shown by Cope and co-workers, who treated 5,6-d 2 -cyclooctene oxide (102) 
with 90 percent formic acid and, by determining the position of deuterium in the 

products, ascertained that 1,5-migration accounted for 94 percent of the forma- 
tion of 3-cycloocten-l-ol and 61 percent of the 1,4-diol. 130 

The fact that only trans-\,2- and or-l,4-glycols are obtained implies that 
they cannot actually be formed by the simplified mechanism in Scheme 9. The 
carbenium ions 99-101 should give a mixture of cis and trans glycols. However, 
the reaction can be neither entirely concerted, as shown for a 1,5-hydride shift 
in Equation 6.46, nor involve initial formation of a carbonium ion, as shown in 
Equation 6.47 : The k H /k D isotope effects are too small for C — H bond breaking 



RoA / 









to be involved in the rate-determining step. 131 The mechanism is probably 
similar to that shown in Equation 6.48, in which the slow step is breaking of the 
C — O bond (although some stereochemical-preserving attraction remains). 

127 For reviews, see: (a) V. Prelog and J. G. Traynham, in Molecular Rearrangements, P. Mayo, Ed., 
Wiley-Interscience, New York, 1963, Vol. I, p. 593; (b) A. C. Cope, M. M. Martin, and M. A. 
McKervey, Quart, Rev. (London), 20, 119 (1966). 

128 (a) A. C. Cope, S. W. Fenton, and C. F. Spencer, J. Amer. Chem. Soc., 74, 5884 (1952); (b) A. C. 
Cope, A. H. Keough, P. E. Peterson, H. E. Simmons, Jr., and G. W. Wood, J. Amer. Chem. Soc, 79, 
3900 (1957). 

128 V. Prelog and K. Schenker, Helv. Chim. Acta, 35, 2044 (1952). 

130 A. C. Cope, G. A. Berchtold, P. E. Peterson, and S. H. Sharman, J. Amer. Chem. Soc, 82, 6366 

131 A. A. Roberts and C. B. Anderson, Tetrahedron Lett., 3883 (1969). 

316 Intramolecular Rearrangements 

Figure 6.19 The cyclodecyl cation. From J. D. Dunitz and V. Prelog, Angew. Chem., 72, 
896 (1960). Reproduced by permission of Verlag Chemie, GMBH. 

Then, in a subsequent fast step, a carbonium ion is formed that is attacked from 
the back side by solvent. 




In some transannular hydride shifts, hydride participation in the rate- 
determining step does, however, seem to occur. 132 

Higher-order shifts are facile in medium-sized rings. The geometry of the 
ring forces some of the transannular hydrogens to be within it, close to the lobe 
of the empty p orbital, which also protrudes into it. For example, the cyclodecyl 
cation has approximately the structure shown in Figure 6.19. 133 The 5-intra- 
annular hydrogen need hardly move to become bonded to the 1 -carbon. 


In the previous sections of this chapter we discussed migrations to electron- 
deficient carbon in which the electron deficiency was a result of departure of a 
leaving group with its pair of electrons. Although a carbonyl carbon is slightly 
electron-deficient because of the electron-withdrawing ability of the oxygen, 
migrations to it in uncharged ground-state compounds do not occur. However, 
if ( 1 ) the carbonyl compound is converted to its conjugate acid (Equation 6.49) 
so that a full positive charge resides on it or (2) the migration origin is made 

132 (a) N. L. Allinger and W. Szkrybalo, Tetrahedron, 24, 4699 (1968); (b) N. L. Allinger and S. 
Greenberg, J. Amer. Chem. Soc., 84, 2394 (1962). 

133 J. D. Dunitz and V. Prelog, Angew. Chem., 72, 896 (1960). 

134 For a general review, see: C. J. Collins and J. F. Eastham, in The Chemistry of the Carbonyl Group, 
S. Patai, Ed., Wiley-Interscience, New York, 1966, Vol. I, p. 761. 

Migrations to Carbony] Carbon 317 


R— C— C— R > R— C— C— R (6.49) 

I I + 

R R 

especially electron-rich, increasing the tendency of a group to migrate with its 
pair of electrons, rearrangements do occur. The aldehyde-ketone rearrangement 
(Problem 16) is an example of the first type, and the benzilic acid rearrangement 
is an example of the second type. 

Benzilic Acid Rearrangement 135 

Liebig observed the first intramolecular rearrangement in 1838 when he found 
that benzil in basic solution forms a new compound. 136 In 1870 Jena correctly 
established the product of the reaction as benzilic acid, but proposed an incorrect 
structure for the starting material to avoid postulating a skeletal rearrangement. 137 
In 1928 Ingold proposed the mechanism shown in Equation 6.50, which today 
is solidly supported by experimental evidence. 138 


II II II \ii 

II II step 1 , II I „.„„ o 

<j,—C— C— + "OH T ' ^-C-C-OH -^Ei* 

103 O- O HO O 

I II step 3 I II 

^-C-C-OH , ^— C— C— O- (6.50) 

* 4> 

The reaction is second -order overall, first-order each in benzil and in base. 139 
This is consistent with any of the three steps being rate-determining, since each 
depends on the concentrations of benzil and either of free base or of base that has 
already added to the benzil. Roberts and Urey carried out the rearrangement 
with 18 0-labeled base and found that the label was incorporated into unreacted 
benzil at a faster rate than that of the rearrangement. 140 Thus the first step must 
be rapid and reversible (although the first intermediate must exist long enough 
for the facile proton exchange, 

O O" O OH 

II I II I ± 

OH O" 

to take place) . That step 3 is not rate-determining was shown by Hine, who used 
~OD as base and found no deuterium isotope effect. 141 By elimination, that leaves 
the migration, step 2, as the rate-determining process. 

An interesting aspect of this rearrangement is that the phenyl group with 
the lower electron-donating ability usually migrates. For example, in 104 the 

135 For a review, see S. Selman and J. F. Eastham, Quart. Rev. (London), 14, 221 (1960). 

136 J Liebig, Justug Liebigs Ann. Chem., 25, 1 (1838). 

137 A.Jena, Justug Liebigs Ann. Chem., 155, 77 (1870). 

138 C. K. Ingold, Ann. Rept. Chem. Soc, 25, 124 (1928). 

139 F. H. Westheimer, J. Amer. Chem. Soc, 58, 2209 (1936). 

140 I. Roberts and H. C. Urey, J. Amer. Chem. Soc, 60, 880 (1938). 

141 J. Hine and H. W. Haworth, J. Amer. Chem. Soc, 80, 2274 (1958). 

318 Intramolecular Rearrangements 

substituted phenyl migrates 81 percent of the time if Z is m-chloro, but only 31 
percent of the time if Z is />-methoxy. 142 (Note that which group migrates can 
be determined only if one of the carbonyl carbons is labeled with 14 C.) Con- 
sideration of the mechanism in Equation 6.50 explains the anomaly. 

7 104 


If the second step is rate-determining, then the observed rate is given in Equation 

*<*» = A a [103] (6.51) 

where k 2 is the rate constant for step 2. The concentration of 103 is given by 
Equation 6.52 

[103] = ^[benzil] [OH"] (6.52) 

in which K 1 is the equilibrium constant for step 1. Substituting Equation 6.52 
into Equation 6.51, we obtain Equation 6.53: The observed rate is dependent 
on the equilibrium constant for the formation of 103 as well as on the rate of 
migration of the aryl group. 

*obs = *2*i[benzil] [OH"] (6.53) 

If the substituted phenyl is to migrate, then the intermediate 103a must 
be formed; migration of the phenyl requires 103b. Electron-withdrawing 
substituents will increase K 1 for the formation of 103a ; if K x is increased more 
than k 2 is decreased, more substituted phenyl will migrate than unsubstituted 

Z 103a Z 103 b 


Our consideration of rearrangements to electron-deficient heteroatoms must be 
brief. In discussing migrations to electron-deficient nitrogen, we first discuss three 
rearrangements that occur in carbonyl derivatives, the Beckmann, Hofmann, 
and Schmidt rearrangements, and then consider rearrangements of nitrenium 

142 M. T. Clark, E. C. Hendley, and O. K. Neville, J. Amer. Chem. Soc, 77, 3280 (1955). 

143 For a general review, see: (a) P. A. S. Smith, in Molecular Rearrangements, P. Mayo, Ed., Wiley- 
Interscience, New York, 1963, Vol. I, p. 457. For reviews of rearrangements to electron-deficient 
nitrogen, see: (b) D. V. Banthorpe, in The Chemistry of the Amino Group, S. Patai, Ed., Wiley-Inter- 
science, New York, 1968, p. 623. For a review of rearrangements to electron-deficient oxygen, see: 
(c)J. B.Lee and B.C. UfT, Quart. Rev. (London), 21, 429 (1967); (d) R. Curci and J. O. Edwards, in 
Organic Peroxides, D. Swern, Ed., Wiley-Interscience, New York, 1970, Vol. I, p. 199. 

Rearrangements to Electron-deficient Nitrogen and Oxygen 319 

Because of the high electronegativity of oxygen, an O — X bond will cleave 
heterolytically, producing a positive oxygen, only if X is an excellent leaving 
group. As a result, electron-deficient oxygen is formed most frequently in re- 
actions of peresters and aromatic peroxides, R — O — O — R' (R' = aryl or acyl). 
In these compounds, when "OR' departs, the negative charge on the leaving 
group is stabilized by resonance. Even here heterolytic cleavages are not uni- 
versal : The energy required for a heterolytic cleavage in the absence of anchi- 
meric assistance is ca. 50 kcal mole -1 , 144 whereas the energy for a homolytic 
cleavage to two alkoxy radicals is only ca. 30-40 kcal mole -1 . 145 Thus hetero- 
lytic cleavage usually takes place only with anchimeric assistance. 

The Beckmann Rearrangement 146 

The acid-catalyzed conversion of ketoximes and aldoximes to amides or amines 
(the amide is often hydrolyzed to the corresponding amine under the reaction 
conditions) is known as the Beckmann rearrangement after its discoverer. 147 
The reaction and its widely accepted mechanism are shown in Equation 6.54. 


R_C— R' „. > R— N=C— R' H2 °> R— N=C— R' , RNH-C-R' 


N \ ,„. (6.54) 

X)H 105 ^ ; 

The observation that picryl ethers of oximes (106) rearrange without a 
catalyst established that the role of the catalyst was to convert the hydroxyl 

into a better leaving group. 148 Some acids catalyze by simply protonating the 
oxime as in 107. Other acids may esterify the oximes. For example, Schofield 

R x 

R O- 



\ / 
H 3 C C=N 


CH, ( 

\ / 
H 3 C C=N 

H 8 C 

H 3 C 




144 E. Hedaya and S. Winstein, J. Amer. Chem. Soc, 89, 1661, 5314 (1967). 

146 S. W. Benson and R. Shaw, in Organic Peroxides, D. Swern, Ed., Wiley-Interscience, New York, 

1970, Vol. 1, p. 147. 

146 L. G. Donaruma and W. Z. Heldt, Org. Reactions, 11, 1 (1960). 

147 E. Beckmann, Ber. Deut. Chem. Ges., 20, 1507 (1887). 

148 A. W. Chapman and F. A. Fidler, J. Chem. Soc, 448 (1936). 

320 Intramolecular Rearrangements 

has suggested 149 that catalysis of 108 by sulfuric acid is due to the preliminary 
conversion of 108 to 109. 150 

The oxime of an aldehyde or ketone can often by separated into two geo- 
metrical isomers, the syn and anti forms. When the Beckmann rearrangement is 
carried out under nonisomerizing conditions, it is always the groups anti to the 
— OH that migrate. 151 For example, Curtin and co-workers carried out Beck- 
mann rearrangements on 110 and 111 in the solid phase by gently heating 
crystals of the compounds. The conditions do not allow interconversion of 110 
and 111; in 110 only the phenyl group migrates, whereas in 111 it is the p- 
bromophenyl group that shifts. 15 



HO 111 

When the catalyst is a Bronsted acid, migration is not stereospecific. Under 
these conditions, syn and anti forms are readily interconverted, presumably via 
the pathway shown in Equation 6.55. 

r' r; h r; oh r; oh 

\ H+ \ \ / \ / -H + \ / 

C=N . + C-4-N , C— N , C=N (6.55) 

R X X OH K /T X OH R /+ ^H ^ 

The stereochemistry of the reaction indicates that rearrangement is con- 
certed with departure of the leaving group, as is implied by Step 1 of Equation 
6.54. The question then remains whether this step or another is rate-determining. 
An answer can be found in the effect of the nature of the migrating group on the 
rate of reaction. If the migration step is rapid, it should not matter to the overall 
rate whether an electron-rich or an electron-poor group is migrating. On the 
other hand, if migration is the slow step, electron-donating substituents in the 
migrating group should increase the rate, and electron-withdrawing substituents 
should decrease it. Kinetic studies of the rearrangements of meta- and para- 
substituted acetophenone oximes (112) in concentrated H 2 S0 4 show that the 
rates do indeed vary with the electron-donating ability of the substituents and 
that a fairly good correlation exists between the rates of rearrangement and the 
Hammett o + constants for the substituents as shown in Figure 6.20. This 
observation indicates that some participation by phenyl occurs in the rate-deter- 
mining step and suggests 113 as the transition state. 153 Not all Beckmann re- 

149 B. J. Gregory, R. B. Moodie, and K. Schofield, J. Chem. Soc, B, 338 (1970). 

150 xhis intermediate has been observed in the firnr. See Y. Yukawa and T. Ando, J. Chem. Soc, D, 
1601 (1971). 

151 See note 143(a), (b), p. 318, and note 146, p. 319. 

152 J. D. McCullough, Jr., D. Y. Curtin, and I. C. Paul, J. Amer. Chem. Soc, 94, 874 (1972). 

153 See note 149. 

Rearrangements to Electron-deficient Nitrogen and Oxygen 321 


3.0 - 

6 + log * 





A m-Cl and m-Br 
A m-F 

-Me 3 N + A m-N0 2 A 

p_N0 2 A 




+ 0.3 

+ 0.6 

+ 0.9 

Figure 6.20 Plot of log k vs. ct + for the Beckmann rearrangement of acetophenone oximes 
in 98.2 percent sulfuric acid at 80°C. From B. J. Gregory, R. B. Moodie, and 
K. Schofield, J, Chem. Soc., 13, 338 (1970). Reprinted by permission of K. 
Schofield and The Chemical Society. 

arrangements need necessarily, however, have the same rate-determining step. 154 
Y Y 

CH 3 OH 


OS0 3 H 

That intermediate 105 in Equation 6.54 is formed in the Beckmann re- 
arrangement has been amply demonstrated both by diverting it to other pro- 
ducts 155 and by direct observation by nmr. 156 

If the mechanism in Equation 6.54 is correct, then oxygen transfer should 
be an intermolecular process. And in fact, when unlabeled acetophenone 

154 See note 143(a), p. 318. 

165 (a) A. Werner and A. Piguet, Ber. Deut. Chem. Ges., 37, 4295 (1904); (b) R. M. Palmere, R. T. 

Conley, and J. L. Rabinowitz, J. Org. Chem., 37, 4095 (1972). 

156 B.J. Gregory, R. B. Moodie, and K. Schofield, J. Chem. Soc, D, 645 (1969). 

322 Intramolecular Rearrangements 

oximes (112) are allowed to rearrange in ls O-enriched solvent, the product 
amide contains the same percentage of 18 as the solvent. 157 Alkyl or aryl 
migration, on the other hand, must be intramolecular, since a chiral migrating 
group retains its chirality during the migration. 158 

The Hofmann Rearrangement 159 

In 1882 Hofmann discovered that when amides are treated with bromine in 
basic solution, they are converted to amines with one carbon less than the 
starting amide. 160 He also isolated the N-bromo amine (114) and the isocyanate 
(115) as intermediates on the reaction path. The mechanism in Equation 6.56 
accounts for the products and the intermediates. This reaction (or the analogous 
rearrangement of the N-chloro amine) is now known as the Hofmann rearrange- 
ment or, because of its synthetic usefulness in eliminating a carbon atom, the 
Hofmann degradation. 

O O 

R— C— NH 2 



-C— NHBr 

+ 0=C=N— R 


-»■ R— C— NBr + H 2 


-> HO— C— NHR 

-*■ H 2 NR + C0 2 


In a most convincing demonstration of the intramolecularity of the migra- 
tion step, Wallis and Moyer carried out the Hofmann degradation on chiral 
116. This compound can be prepared in optically active form because the groups 
in the ortho position of the phenyl ring hinder the rotation that would convert 
116 to its mirror image 117. During rearrangement 116 would lose chirality if the 


116 117 

migrating bond simply stretched enough to allow rotation about itself. However, 
loss of chirality is not observed: 116 rearranges with retention of configuration. 161 
There is a question whether Equation 6.56 shows all the intermediates on 
the reaction path. If, instead of rearrangement being concerted with loss of 
halide ion as shown in Equation 6.56, the halide ion departed first, then a 
nitrene 162 would be formed as shown in Equation 6.57. To date no nitrene inter- 

157 See note 149, p. 320. 

158 (a) A. Campbell and J. Kenyon, J. Chem. Soc, 25 (1946); (b) J. Kenyon and D. P. Young, J. 
Chem. Soc, 263 (1941). 

159 E. S. Wallis and J. F. Lane, Org. Reactions, 3, 267 (1946). 

160 A. W. Hofmann, Ber. Deut. Chem. Ges., 15, 762 (1882). 

161 E. S. Wallis and W. W. Moyer, J. Amer. Chem. Soc, 55, 2598 (1933). 

162 A "nitrene" is a nitrogen-containing compound in which the nitrogen has only a sextet of elec- 
trons. Such a species is neutral but electron-deficient; cf. carbenes (Section 5.6). 

Rearrangements to Electron-deficient Nitrogen and Oxygen 323 

mediate in the Hofmann reaction has been proved, but the possibility remains 
that it is at least sometimes formed. 

O O 

II .. II .. „ 

R— C— N— Br ► R— C— N: + Br' (6.57) 

The Schmidt Rearrangements 163 

The group of rearrangements brought about by treatment of aldehydes, ketones, 
or carboxylic acids with hydrogen azide are known as Schmidt rearrangements. 
All are acid-catalyzed and all involve addition of HN 3 to the carbonyl group 
followed by dehydration. They are shown in Equations 6.58-6.60. 

O + OH OH H 

R _C--H -^U R— C-H -^U R__ C -N-N=N ^^ R-C=N-N=N ► 


HC=N— R + N 2 Ha °> H— C=N— R > H^C-NHR 


119a (6.58) 

R— C— R' —^- R— C— R' HN ' 3 > R— C— N— N=N " H2 °> R— C=N— N=N *• 

R' H R' 



r_C=N— R' + N 2 H '°> R— C— NRH 


119b (6.59) 


HN ) T. k XT V XT - H 2 

R_C— OH *-- R— C— N— N=N ^ R— C=N— N=N »- 

I I 

HOC=N— R +■ N 2 H '°> HO— C— NHR <• NH 2 R + C0 2 


119c (6.60) 

Although mechanisms can be formulated that do not involve dehydration 
and subsequent formation of the intermediates 119a-119c there is strong evi- 
dence that these steps take place. For example, tetrazoles, which are formed 
from 119 as shown in Equation 6.61, have been isolated as side products. Further 
evidence for the dehydration step was obtained by Hassner and co-workers, 

RC=N— R + HN— N=N »■ R— C— N— R ► R— C— N^R (6.61) 

/ \ // \ 

N N N N 

H /X N^ X N^ 


163 H. Wolff, Org. Reactions, 3, 307 (1946). 

324 Intramolecular Rearrangements 

who showed that acid-catalyzed rearrangement of vinyl azides gives the same 
products in the same ratio as the Schmidt rearrangement of the corresponding 
ketone under the same conditions. He postulated that the reaction paths of the 
two rearrangements converge at the common intermediate 118 as shown in 
Scheme 10. 164 
Scheme 10 

R \ / H 


/ \ R 

feN _ N R' X C _^_H 



R— C— R'^^- R— C— NH— NeeeN 

^ N=N— N R' 




In the Schmidt rearrangement of carboxylic acids the formation of the 
adduct is apparently usually not rate-determining. The evidence for this comes 
from studies of the comparative rate of nitrogen evolution from HN 3 in the 
presence and in the absence of carboxylic acids : When m- or />-nitrobenzoic 
acid is added to HN 3 in H 2 S0 4 , the rate of nitrogen evolution decreases. Thus 
HN 3 must be rapidly converted to an adduct from which loss of nitrogen is 
slower than from HN 3 itself. Moreover, the adduct, to be formed at all, must be 
formed more rapidly than N 2 is lost from HN 3 . 165 

The intramolecularity of the migration step in the Schmidt rearrange- 
ments has been convincingly demonstrated by showing the retention of chirality 
of the migrating group. 166 

In the Schmidt rearrangement of ketones the larger group, irrespective of 
its nature, tends to migrate. Apparently the intermediate 118 is formed so that the 
bulkier aryl or alkyl group is trans to the N 2 group. Then, as in the Beckmann 
rearrangement, the group trans to the leaving group prefers to migrate. The 
barriers to interconversion of the cis and trans forms are, however, lower in the 
Schmidt than in the Beckmann rearrangement. 167 

Nitrenium Ions 168 

The nitrenium ion (120) is isoelectronic with the carbocation. Until the middle 
1960s it was unknown, but at that time Gassman began an intensive investigation 

R— N— R 



164 A. Hassner, E. S. Ferdinandi, and R.J. Isbister, J. Amer. Chem. Soc, 92, 1672 (1970). 

165 L. H. Briggs and J. W. Lyttleton, J. Chem. Soc, 421 (1943). But see also V. A. Ostrovskii, A. S. 
Enin, and G. I. Koldobski, J. Org. Chem., U.S.S.R., 9, 827 (1973). 

166 See note 143(a), (b), p. 318. 

167 See note 164. 

168 P. G. Gassman, Accts. Chem. Res., 3, 26 (1970). 

Rearrangements to Electron-deficient Nitrogen and Oxygen 325 

to determine whether or not it exists. Since nitrogen is more electronegative than 
carbon, it was to be expected that the nitrenium ion would be less stable than its 
carbon analog. 

Gassman and Fox first synthesized and then solvolyzed N-chloroisoquinucli- 
dine (121). In refluxing methanolic silver nitrate, 121 is converted in 60 percent 
yield to the rearranged product, 122, as shown in Equation 6.62. 169 Since alkyl 
groups do not migrate to radical centers, this rearrangement clearly indicates 



AgNQ 3 ' 





that an electron-deficient nitrogen must have been formed. What it does not 
indicate is whether the reaction occurred via the nitrenium ion (123), as a 
discrete intermediate, or whether rearrangement is concerted with departure 
of the leaving group and 124 is the first-formed ion. 


123 124 

A nitrenium ion is unusual in that it has both a positive charge and a non- 
bonding pair. If the nitrenium ion (123) were formed, it must initially be pro- 
duced in the singlet state — that is, the lone pair must initially have its spins 
paired as shown in 123s. But if the lifetime of 123s were long enough, spin inver- 
sion to 123t might occur. (See Section 5.6, p. 258 and Section 13.2, p. 691). The 


singlet should be similar to a carbocation in character, but the triplet should 
behave like a nitrogen radical. 

Gassman and Cryberg solvolyzed 125 in a number of solvents containing 
methanol. 170 The predominant products were 126, 127, and 128. The first two, 
126 and 127, are solvolysis products derived from rearrangement to electron- 
deficient nitrogen. But 128 almost surely results from hydrogen abstraction 
from the solvent. The proposed mechanisms for their formation are shown in 
Scheme 1 1 . 

When the solvent is methanol-benzene, the products 126 and 127 pre- 
dominate. Their combined yield is 8.2 times greater than the yield of 128. 
However, when a bromine-containing solvent is mixed with the methanol, the 

169 P. G. Gassman and B. L. Fox, J. Amer. Chem. Soc, 89, 338 (1967). 

170 P. G. Gassman and R. L. Cryberg, J. Amer. Chem. Soc, 91 5176 (1969). 

326 Intramolecular Rearrangements 
Scheme 11 

H 3 C CH 3 
\ S< CH3 

125 C1 


H 3 C CH 3 

^CH 3 

H 3 C CH 3 



CH 3 

H 3 C CH 3 
CH 3 


+ / inversion / +/ [ +/ 


H 3 CCH 3 
CH 3 


H 3 C 

CH a 

N— H 

CH 3 

N— H 


H3C ^ H 3 

H 3 C 


H 3 C 
H 3 C 
CH 3 

\^CH 3 




relative yields change drastically. Table 6.2 gives the data. (Bromine, a "heavy 
atom," is known to catalyze singlet-triplet conversions — see Section 13.1, p. 687.) 
Thus in bromoform-methanol the ratio (126 + 127)/128 is only 0.02. This 
experiment indicates that a nitrenium ion must exist as a discrete intermediate — 
with a long enough lifetime to undergo spin inversion. 

Nitrenium ions can also be generated by solvolyzing esters of N,N-di- 
alkylhydroxylamines. 3,5-Dinitrobenzoates (129) were found to be the most 
useful hydroxylamine derivatives. 171 

Table 6.2 Products from Solvolysis of 125 

Percent yield 


126 + 127 




CH 3 OH— C 6 H 12 





CH 3 OH-/>Br 2 C e H 4 





CH 3 OH-CCl 4 





CH 3 OH-CHCl 3 





CH 3 OH-CHBr 3 





CH 3 OH-CH 3 OH 





Source: P. G. Gassman, Accts. Chem. Res., 3, 26 (1970). Reprinted by permission of the American 
Chemical Society. 

171 P. G. Gassman and G. D. Hartman J. Amer. Chem. Soc, 95, 449 (1973). 

Rearrangements to Electron-deficient Nitrogen and Oxygen 327 




N— O— C 



Heterolytic Peroxyester Decomposition: The Criegee Rearrangement 

In 1944 Criegee observed that toz/w-9-decalyl peroxyesters rearrange on standing 
to 1,6-epoxycyclodecyl esters. 172 Further study of the reaction showed that it 
has the characteristics of an ionic rather than a radical pathway: The rate is 


proportional to the anionic stability of "O — C — R and increases with the po- 
larity of the solvent. 173 Because no products were obtained that were the result 
of solvent intervention or of exchange with added salts, the reaction was postu- 
lated to have only intimate ion-pair intermediates as shown in Equation 6.64. 174 

O— O- 

-C— R 



-C— R 

O o— C— R 



Denney showed that if the carbonyl oxygen in /ra/w-9-decalyl peroxybenzoate is 
labeled with ie O, almost all the label is found in the carbonyl oxygen of the 
product. 175 This experiment dramatically demonstrates the closeness with which 

Table 6.3 Relative Rates of Rearrangement Reactions with 
Different Migrating Groups 

Ionic Decomposition of 

Acetolysis of 

Rearrangement of 

R CH 3 

II „ „ /„, 

CH 3 — C— C— CH 3 (CH 3 ) 2 CRCH 2 OTs R— C— N— O— C— \{J y 




Lossen Rearrangement of 

R— C— O— O— C— ( O 
CH 3 






CH 2 ^-p 

2.9 x 
2.3 x 
1.6 x 
1.1 x 

10 3 
10 5 
10 3 
10 s 









Source: A. E. Hedaya and S. Winstein, J. Amer. Chem. Soc, 89, 1661 (1967). Reprinted by permis- 
sion of the American Chemical Society. 

172 R. Criegee, Ber. Deut. Chem. Ges., 77, 722 (1944). 

173 R. Criegee and R. Kaspar, Justus Liebigs Ann. Chem., 560, 127 (1948). 

174 P. D. Bartlett and J. L. Kice, J. Amer. Chem. Soc, 75, 5591 (1953); (b) H. L. Goering and A. C. 
Olson, J. Amer. Chem. Soc., 75, 5853 (1953). 

176 D. B. Denney and D. G. Denney, J. Amer. Chem. Soc, 79, 4806 (1957). 

328 Intramolecular Rearrangements 

the carboxylate anion must be connected to the decalyl cation during the 

Winstein investigated the peroxybenzoate rearrangements further to see if 
there was neighboring-group participation in departure of the leaving group. 
He studied the products from rearrangement of 2-R-2-propyl-/>-nitroperoxy- 
benzoates and found that the more electron-donating R is, the greater is its 
migratory aptitude. Equation 6.65 shows the principal products formed if R is 
more electron-donating than methyl. 

R O O 

CH 3 — C— O— O— C^O/~ N ° 2 CH3 ° H) CH 3 — C— OR + O— C— /q\-N0 2 

CH 3 CH 3 

CH 3 — C=0 + ROH 

CH 3 + ROCH 3 

+ olefin from R + 

Winstein also found that the rate is highly dependent on the electron-donating 
ability of R — much more so than the rates of other intramolecular rearrange- 
ments (see Table 6.3). He therefore postulated that the migrating alkyl group 
provides anchimeric assistance to the departure of the nitrobenzoate anion and 
that the transition state for the rearrangement can be represented by a bridged 
structure such as 130. 


\. •'•> + '•■ 


/ : 

6- 6pnb 


Winstein estimated the rate acceleration due to anchimeric assistance in 
ionic perester decompositions as follows. By using Equation 6.66, in which the 
first term on the right-hand side is the difference in homolytic dissociation 

AA£„ = (AE^-AE^) + (/. — /,) (6.66) 

energies between peroxide and carbon-oxygen bonds and the second term is the 
ionization potential difference between oxygen and carbon, he estimated that the 
differences in energies of heterolysis of peroxide and carbon-oxygen bonds 
(AA£ H ) should be 22 kcal mole -1 (peroxide bond breaking being more costly). 
He then compared the observed enthalpies of activation (AH*) of aceto lysis of 
neopentyl tosylate (131) and £-butyl pertosylate (132) and assumed that they 
are a measure of the energies of heterolysis. He found that A//* for 131 was 10 
kcal higher than for 132. Thus methyl assistance is responsible for lowering the 
A//* for heterolysis of 132 by ca. 32 kcal mole -1 , which corresponds to a rate 
acceleration of 10 23 . 178 

176 See note 144, p. 319. 

Rearrangements to Electron-deficient Nitrogen and Oxygen 329 

CH 3 CH 3 

I I 

CH 3 — C— CH 2 — OTs CH 3 — C— O— O— Ts (6.67) 

CH 3 CH 3 

131 132 

Acid-catalyzed decompositions of hydroperoxides in which the leaving 
group is water also take place. An example is shown in Equation 6.68. That 
the pathway is actually one of migration concerted with departure of water as 
shown, and does not include intervention of the high-energy species RO + , 

CH 3 CH 3 

fli-O-O-H d^ X -T^U " " - -*° 

X-f \)-C-0-0-H ^=^ X ~(f V-C-O-O-H - 
CH 3 ^=^ CH 3 H 

O.H3 (-'H3 

CH 3 -A-0-^\-X -^* CH 3 -C-0^ r_ Vx 

CH 3 —C— O— ( 7 \- X > C=OH + HO— (( V-X (6.68) 

C— 6— ( \-X > C=OH + HO— f \-X 

O H 


has been demonstrated by the fact that the rates of rearrangement of Reaction 
6.68 correlate with the a + constants of the X substituent. 177 

The Baeyer-Villiger Oxidation 178 

In 1899 Baeyer and Villiger observed that peroxy acids convert ketones to 
esters. 179 The reaction is first-order each in ketone and in peroxy acid, and it is 
general acid catalyzed. Criegee first suggested the mechanism shown in Equation 
6.69. The role of the acid catalyst is to protonate the leaving group, thereby 
facilitating its departure. 180 

R OH + OH 

\ I II 

C=0 + HOOA ► R— C— O-pOA »■ R— C— OR + OA 

/ L^ ^ 

R R O 


133 »■ R— C— OR + HOA (6.69) 

The intermediate 133 has never been directly observed in a rearrangement 
reaction, but analogous structures are known for the addition of peroxyacetic 

177 A. W. de Ruyter van Steveninck and E. C. Kooyman, Rec. Trav. Chim. Pays-Bas, 79, 413 (1960). 

178 C. H. Hassall, Org. Reactions, 9, 73 (1957). 

179 A. Baeyer and V. Villiger, Ber. Deut. Chem. Ges., 32, 3625 (1899). 

180 M. F. Hawthorne and W. D. Emmons, J. Amer. Chem. Soc., 80, 6398 (1958). 

330 Intramolecular Rearrangements 

acid to aldehydes. 181 Doering and Dorfman provided strong support for the 
mechanism of Equation 6.69 when they showed that oxidation of benzophenone 
labeled with ie O gave phenyl benzoate in which all of the ls O was retained in 
the carboxyl group (Equation 6.70). 182 This ruled out symmetrical species such 
as 134 as intermediates on the reaction path. 

1BQ 18Q 

II , II 

<j>—C—<f, + HOOM, *" <f>—C—0<f> + HOA (6.70) 


The question remains: Is the formation of 133 or its destruction rate- 
determining? Experiment indicates that rearrangement is concerted and that 
in the oxidation of most ketones rearrangement is rate-determining. 

For example, Palmer and Fry oxidized para-substituted acetophenones-1- 
14 C as shown in Equation 6.71 and compared these rates of oxidation with the 


XhQJLh, + <HJ- -OH 


rates of oxidation of the unlabeled ketones. 183 As shown in Table 6.4, for all 
substituents except p-OCH 3 , there is a significant 14 C isotope effect. Thus for all 
the acetophenones other than the />-OCH a -substituted one, the rate-determining 
step is rearrangement. Rate-determining formation of 133 would not give an 
isotope effect, since this step does not involve significant bond alteration at the 
labeled position. 

Table 6.4 Isotope Effects for the Oxidation of Para-Substituted 

Acetophenones-1- 14 C with ot-Chlorobenzoic Acid in i,. ,'■'•,■?' (, 

Chloroform at 32 c C (Equation 6.71) 

X £i2/£i« 

CH 3 o 


CH 3 








Source: B. W. Palmer and A. Fry, J. Amer. Chem. Soc, 92, 2580 (1970). Reprinted by permission of 
the American Chemical Society. 

181 B. Phillips, F. C. Frostick, Jr., and P. S. Starcher, J. Amer. Chem. Soc, 79, 5982 (1957). 

182 W. v. E. Doering and E. Dorfman, J. Amer. Chem. Soc, 75, 5595 (1953). 
163 B. W. Palmer and A. Fry, J. Amer. Chem. Soc, 92, 2580 (1970). 

Rearrangements to Electron-deficient Nitrogen and Oxygen 331 

5 + log fc, 

Up-CH 3 




\ P = 






p-Cl j \ 






1 1 

\l m-N0 2 
p-N0 2 ^ 

r 2 Ti 







Figure 6.21 Plot of log k vs. a for the Baeyer-Villiger oxidation of substituted aceto- 
phenones by CF 3 COOOH in acetonitrile at 29.8°C. From M. F. Hawthorne 
and W. D. Emmons, J. Amer. Chem. Soc, 80, 6398 (1958). Reprinted by per- 
mission of the American Chemical Society. 

Further evidence for the mechanism of Equation 6.69 with the second step 
rate-determining is provided by substituent effects on the rate. For example, 
Figure 6.21 shows a plot of the logs of the rates of oxidation of substituted aceto- 
phenones by trifluoroperoxyacetic acid vs. the a values of the substituents. The p 
value is negative, indicating that electron-donating substituents in the migrating 
group increase the rate. 184 Furthermore, the rate of oxidation of cyclohexanone 
with peroxyacetic acid is only 1 /200th as fast as the rate with trifluoroperoxyace- 
tic acid. The greater basicity of the unfluorinated acid should make it a better 
nucleophile toward the carbonyl group, and if formation of 133 were rate-deter- 
mining, it should be the better oxidizing agent. On the other hand, the electron- 
withdrawing ability of the — CF 3 group should make trifluoroacetic acid the 
better leaving group, and thus if rearrangement concerted with O — O bond 
breaking is the rate-determining step, the trifluoroperoxyacetic acid should be 
the better oxidizing agent, as observed. 185 

Formation of the intermediate may become rate-determining if the migrat- 
ing group is especially reactive. For example when />-hydroxybenzaldehyde is 
oxidized by perbenzoic acid, the products are those shown in Equation 6.72. 
Over the pH range 2-7, the rate of this reaction, instead of showing acid catalysis, 

184 See note 180, p. 329. 

185 See note 180, p. 329. 

332 Intramolecular Rearrangements 

, , O O 

HO-f J- C— H + HOOC-/ ^> > (6.72) 

ii /~~\ ° /~~\ ° /~A 

O— O— C— ^ ^> J- H— C— O— ^ V-OH + HO-G-f ^> 

135 HO— <f V-OH + CO 

is faster at higher pH. Ogata and Sawaki suggest that their data are consistent with 
rate-determining formation of 135. This step would be accelerated in less acidic 
solution because the peroxybenzoic acid would be more dissociated. They also 
suggest that rate-determining formation of the intermediate adduct in Equation 
6.71 when X = OCH 3 is responsible for the unit 14 C isotope effect observed in 
that reaction. 186 

Theoretical calculations 187 and secondary deuterium isotope effects 188 
are also in agreement with the mechanism of Equation 6.69, as is the fact that the 
chirality of a migrating group is retained. 189 


'\J. Mustard gas (1) owes its deadliness to the fact that it immediately gives off 
HC1 when it mixes with atmospheric moisture. 1,5-Dichloropentane (2) hydrolyzes 
much more slowly. Explain. 

CHg — CH2 — S — CH2 — CH 2 CH2 — CH2 — C1T2 — CH2 — CH2 


1 2 

2. Acetolysis of 3 is a stereospecific reaction and gives only 4. Explain. 


,OMe /v^OMe 

A «* > [ I O 

HOAc I I || 

\^^Br ^ ~0— C— CH. 


( 3.) Explain the following observation : The trifluoroacetoxy group on trans-2- 
triflueroacetoxycyclohexyl tosylate (5) is 30 times more rate-retarding (relative to 
cyclohexyl tosylate) in strongly ionizing trifluoroacetic acid than in formic acid. 

186 Y. Ogata and Y. Sawaki, J. Amer. Chem. Soc, 94, 4189 (1972). 

187 V. A. Stoute, M. A. Winnik, and I. G. Csizmadia, J. Amer. Chem. Soc, 96, 6388 (1974). 

188 M. A. Winnik, V. Stoute, and P. Fitzgerald, J. Amer. Chem. Soc, 96, 1977 (1974). 

189 See note 143(a), (c), and (d), p. 318. 

Problems 333 


P— C— CF 3 



All five of the following reactions give pinacol and pinacolone. The products 
are formed in a similar ratio from each reaction. Write a mechanism for each reaction. 
What does the constant ratio of products tell you about any intermediate that may be 
formed ? 

H 3 C. 


CH a 

H 3 C o CH 3 

l + 

H 3 C CH 3 

H 3 C— C— C— CH 3 

I I 

H 3 C CH 3 

H 3 C— C— C— CH 3 

H 3 C CH 3 

H 3 C — C — C — CH 3 

HO NH 2 
H 3 C CH 3 

H 3 C — C — C — CH 3 

ho xm 2 



> (2) 






5. Explain why the migratory aptitude of the o-anisyl group is only 0.3 in the 
pinacol rearrangement. 

^yPredict the products expected from (a) S w l and (b) S w 2 substitutions of acetic 
acid on 'L-threo- and L-«ry^ro-3-phenyl-2-butyl tosylate and compare with the results 
actually obtained in Section 6.1, p. 275. 

7. The titrimetric first-order rate constant for the solvolysis of cyclopropylcarbinyl 
benzenesulfonate decreases with time. Explain. 

(SWExplain the following facts: (a) Acetolysis of 6 and 7 gives only 8. (b) The rate 
of acetolysis of 6 relative to 7 is ca. 44. (c) When 6a is solvolyzed, the product has the 
deuterium scrambled equally over carbons 1,3, and 5. 


A^ OT ' 




H . Mf MC 



334 Intramolecular Rearrangements 

9. The norbornonium ion is also formed as an intermediate in the solvolysis of a 
monocyclic arenesulfonate. This pathway is called the 7r-route to the norbornonium ion. 
What is the starting material for the 7r-route to this ion ? 

10. Predict the products, and whether each will be chiral or not, from the solvolysis 
of (a) optically active 9; (b) optically active 9a. How would you synthesize the sol- 
volysis intermediates by the 7r-route? (See Problem 9.) 



( 1 V. Write mechanisms for Reactions 6 and 7. 

J12< Treatment of ketone 10, labeled with 14 C in the 9-position, with acid gives the 
alco,hol 11 with the label equally scrambled between the positions shown. Write a 
mechanism for this reaction. 

CH 3 



,CH 3 

"*" HO' 



rite a mechanism for Reaction 8. 
O O 

<j,—C—C—<}> + ( (_) )— MgB 

CH 3 





14. The rearrangement of a-diazoketones to carboxylic acids or esters shown in 
Equation 9 is known as the Wolff rearrangement. 


R— C— C— N=N R '° H > 0=C— C—R' 




Taking into account the following facts, suggest a mechanism for the Wolff rearrange- 
ment, (a) The kinetics are clearly first-order in substrate and first-order overall, (b) In 


Problems 335 

aprotic media ketenes can sometimes be isolated, (c) The rate of rearrangement of 12 
is almost identical whether Z is — OCH 3 or — N0 2 . (d) The rate of rearrangement of 13 
is much faster if Z is — OCH 3 than if it is — N0 2 . 

O O 

Ar-C-cV0V Z zYO/-C-C-Ar 

N + N + 


N N 

12 13 

15. Write a mechanism for the reaction below. 


16. Propose a mechanism for the reaction in Equation 10, an example of the 
aldehyde-ketone rearrangement. 

H 3 C O H 3 C O 

I 1*11 H * I "II 

CH 3 — C— C— H -i-»- CH 3 — C— C— CH 3 (10) 

CH 3 H 

17. Propose a mechanism for the reaction in Equation 11, an example of the 
Lossen rearrangement. 

o o o 

II II -oh II 

CH 3 — C— NH— O— C— CH 2 CH 3 — ^^ CH 3 NH 2 + CO z + "O— C— CH 2 — CH 3 (11} 

18. Propose a mechanism for the reaction in Equation 12, an example of the 
Cur tins rearrangement. 


II - + 
CH 3 — C— N— N=N > CH 3 — N=C=0 + N 2 (12) 

19. Propose a mechanism for the following reaction. 


-N-C(CH 3 ) 3 -^g^ 

N — / OCH 3 

CH a O-/ \-N~C(CH 3 ) 3 + / \-N— C(CH 3 ) 3 

^ = ^ H 

336 Intramolecular Rearrangements 

20. Would you expect the cyclopropyl group to participate in the solvolysis of 15 ? 
Why or why not ? 

^ OTs 


1. P. D. Bartlett and C. G. Swain, J. Amer. Chem. Soc, 71, 1406 (1949). 

2. S. Winstein and R. B. Henderson, J. Amer. Chem. Soc, 65, 2196 (1943). 

3. D. D. Roberts and W. Hendrickson, J. Org. Chem., 34, 2415 (1969). 

4. Y. Pocker, Chem. & Ind. (London), 332 (1959). 

5. W. E. Bachmann and J. W. Ferguson, J. Amer. Chem. Soc, 56, 2081 (1934). 

7. C. G. Bergstrom and S. Siegel, J. Amer. Chem. Soc, 74, 145 (1952). 

8. S. Winstein and J. Sonnenberg, J. Amer. Chem. Soc, 83, 3235, 3244 (1961). 

9. R. G. Lawton, J. Amer. Chem. Soc, 83, 2399 (1961) ; P. D. Bartlett and S. Bank, J. 

Amer. Chem. Soc, 83, 2592 (1961). 

10. H. L. Goering and G. N. Fickes, J. Amer. Chem. Soc, 90, 2856 (1968). 

11. (a) R. C. Cookson and E. Crundell, Chem. Ind. (London), 703 (1959); (b) S. 

Winstein and R. L. Hansen, J. Amer. Chem. Soc, 82, 6206 (1960). 

12. R. Futaki, Tetrahedron Lett., 3059 (1964). 

13. J. F. Eastham, J. E. Huffaker, V. F. Raaen, and C.J. Collins, J. Amer. Chem. Soc, 

78,4323 (1956). 

14. A. Melzer and E. F. Jenny, Tetrahedron Lett., 4503 (1968). 

15. H. W. Moore, H. R. Shelden, D. W. Deters, and R. J. Wikholm, J. Amer. Chem. 

Soc, 92, 1675 (1970). 

16. M. Oka and A. Fry, J. Org. Chem., 35, 2801 (1970). 

17. H. L. Yale, Chem. Rev., 33, 209 (1943). 

18. A. A. Bothner-by and L. Friedman, J. Amer. Chem. Soc, 73, 5391 (1951). 

19. P. G. Gassman, G. A. Campbell, and R. C. Frederick, J. Amer. Chem. Soc, 94, 3884 


20. J. E. Baldwin and W. D. Foglesong, J. Amer. Chem. Soc, 90, 4303 (1968). 

Chapter 7 



In this chapter we shall discuss the destruction and formation of carbon-carbon 
multiple bonds by addition and elimination reactions, respectively. The mech- 
anism of aromatic substitution in which addition and elimination occur as 
separate steps will also be discussed. 


Carbon-carbon n bonds are relatively weak (~65 kcal/mole -1 ). They are also, 
unless substituted by strong electron- withdrawing groups, electron-rich. For 
these reasons addition to them by electrophilic reagents usually occurs readily. 
The exact mechani sm of addition depend s on the reagen t. 


The acid-catalyzed addition of water to a double bond is kinetically second- 
order, first-order each in olefin and in H 3 + . 2 This fact is equally consistent with 
the concerted addition of a proton and a water molecule from the same H 3 + 
and with initial attack of a proton to one side of the double bond followed by 

1 (a) P. B. D. de la Mare and R. Bolton, Electrophilic Additions to Unsaturated Systems, Elsevier, Amster- 
dam, 1966; (b) R. C. Fahey, in Topics in Stereochemistry, E. L. Eliel and N. L. Allinger, Eds., Wiley- 
Interscience, New York, 1968, Vol. 3, p. 237; (c) R. Bolton, in Comprehensive Chemical Kinetics, 
C. H. Bamford and C. F. H. Tipper, Eds., Elsevier, New York, 1973, Vol. 9, chap. 1. 

2 See note 1 (a) . 



338 Addition and Elimination Reactions 

addition of water. The latter mechanism, to which a formidable body of evidence 
points, is shown in Equation 7.1. 

N C=C / + H 3 0+ ^U ^C-C' + H 2 ^> -C-C- -^» -C-C- + H + 
/ \ /| + \ || || 

H H OH 2 H OH 

1 + (7.1) 

Fo r example, the ra te of hydration^ increases if the douhle bond bears 
electron-releasing snhstitnents. Sr. Hnbert, Lamm, and Keeffe have found that for 
a series of para-substituted styrenes (2), a linear correlation exists between 



log k of hydration and the a + constants of the substituent with slope p = —3.58. 
The linear correlation with a + rather than with a and the large negative value of 
p both indicate that a high positive charge density is located on the carbon alpha 
to the ring in the transition state. 3 

Fy-tJiprmnre the> accelerating ejfectjofjelectron-donating substituents_js 
cunruj^ive_imly_if_the_substituents are on the same side, of the jiooihle-boiid- (see 
Table 7.1). 4 Thus isobutylene is 10 3 -10 4 times more reactive than propylene, 
whereas the 2-butenes are of comparable reactivity to propylene. Thisis^con- 
sistent only wit h an asy jrjine&ieiraTrsrtion state in-which the. positive charge is, 
localized on on e carb ^n^£th_e_OTJgiriaLdQuble_bo^^_In ^accord with the sub- . 
stjtugntlell.ects of" Table 7.1, hydraikm^httays-g^s-zegiosperific?. Marfiwrnkaff.. 
additinn; that \ % the proto n adds tn the less snhsritoted-side of the double-bond. 
Also in agreement with a cationic intermediate but not with concerted addition is 
the fact that Wagner-Meerwein rearrangements sometimes occur during 
hydration. 6 

The question of which step of Equation 7. 1 is rate-determining remains. 
Schubert found that when styrene-/9,/9-</ 2 (3) is hydrated, the recovered, unre- 
acted 3 has not lost deuterons to the solvent. 7 If the protonated species (1) were 


3 (a) W. M. Schubert, B. Lamm, and J. R. Keeffe, J. Amer. Chem. Soc, 86, 4727 (1964) ; (b) W. M. 
Schubert and B. Lamm, J. Amer. Chem. Soc, 88, 120 (1966); (c) W. M. Schubert and J. R. Keeffe, 
J. Amer. Chem. Soc, 94, 559 (1972). 

4 Unpublished results of R. W. Taft, Jr., cited in P. D. Bartlett and G. D. Sargent, J. Amer. Chem. 
Soc, 87, 1297 (1965). 

6 Regiospecific is a term introduced by A. Hassner, J. Org. Chem., 33, 2684 (1968). If bonds can be 
made or broken in two or more different orientations but only one of the possible isomers is formed, 
the reaction is regiospecific. If there is a significant preponderance of one isomer formed, Hassner 
calls that reaction regioselective. Most workers use only the former term with qualifying adjectives 
such as "high" or "low." 

6 See note 1(a), p. 337. 

7 See note 3. 

Electrophilic Addition to Double and Triple Bonds 339 

Table 7.1 Effect of Methyl Substitution on the Rate 

of Hydration of Carbon-Carbon Double Bonds 

Olefins Relative Rate 

(CH 3 ) 2 C=CH 2 

10 3 -10 4 

H 3 C H 


/ Vu 0.71 

H CH; 


H H 

X c=c / 

/ \ 1.68 


CH 3 CH=CH, 

H 3 C .CH 3 

/ C=C \ 
H 3 C H 

H 3 C X 

C=CH a 
H 3 C 

H 3 C CH 3 

H 3 C X ~ X H 1° 3 -10 4 


Source: Unpublished results of R. W. Taft, Jr., cited in P. D. Bartlett and G. D. Sargent, J. Amer. 
Chem. Soc, 87, 1297 (1965). Reprinted by permission of the American Chemical Society. 

formed by a rapid equilibrium prior to the rate-determining process, then 
deuterons as well as protons should be lost from the intermediate carbocation in 
the reverse of step 1 in Equation 7. 1 . Furthermore when the substituted unlabeled 
styrenes are hydrated in deuterated solvents, the solvent deuterium isotope effects, 
^h 3 o + /^d 3 o + ) range in value from 2 to 4. Thu s the first step j sjate^deterrnining. 
This conclusion is extended to hydration of simple (nonaryl-substituted) alkenes 
by the fact that when 2-methylbutene-l is subjected to hydration conditions and 
recovered after 50 percent reaction, the starting material has not isomerized to 

H 3 C H 3 C 

\ h+ \ -H+ 

/ C=CH 2 > ^.C-^CHa -#-* 

/CHa /CHa 

H 3 C H 3 C 

H 3 C H 3 C 

C=CH 2 + ^C— CH 3 (7.2) 

CH 2 CH 

H 3 C H 3 C 

340 Addition and Elimination Reactions 

Table 7.2 Relative Rates of Hydration of Alkenes and Alkynes 


Alkyne Relative Rate 

<f> — CH=CH2 

<£CH=CHCH 3 
<£C=CCH 3 

nBuCH=CH 2 






Source: K. Yates, G. H. Schmid, T. W. Regulski, D. G. Garratt, Hei-Wun Leung, and R. Mc- 
Donald, J. Amer. Chem. Soc, 95, 160 (1973). Reprinted by permission of the American Chemical 

2-methylbutene-2 as would be expected if step 1 of Equation 7.1 were a rapid 
equilibrium (see Equation 7.2). 8 HydratiorL^ then, is_ aji_£xariiple of _a_ jeaction 
that proce eds via an Ad £ 2 (addition -electrophilic-secon d-order) mechanism. 

Taft originally suggested 9 that the mechanism for hydration involves an 
additional step, namely the rapid, reversible formation of a 77 complex from a 
proton and the olefin, and that this complex then rearranges, in the rate-deter- 
mining step, to the carbocation as shown in Equation 7.3. This is consistent with 
all the data discussed so far, but it has recently been shown to be incorrect. The 

H + H 

/ slow I I 

C > — C— C— (7.3) 

concentration of the n complex, like the equilibrium concentration of any acid, is 
determined solely by the pH. If its rearrangement is rate-determining, the 
rate should depend on the concentrations of alkene and of H 3 + . If proton 
abstraction is rate-determining, the rate should depend on the concentrations of 
alkene and of all the acid present — hydronium ion and undissociated acid. 
(Catalysis by H 3 + only is called specific acid catalysis; catalysis by H 3 + and 
undissociated acid is called general acid catalysis. These phenomena are discussed 
in greater detail in Chapter 8.) Kresge and co-workers studied the hydration of 
fra/u-cyclooctene and of 2,3-dimethyl-2-butene in phosphoric acid-bisulfate 
buffer solutions in which the amount of undissociated acid varied and found that 
the reactions exhibit general acid catalysis. 10 This behavior parallels that ob- 
served earlier in the hydration of styrene and substituted styrenes. 11 

8 J. B. Levy, R. W. Taft, Jr., and L. P. Hammett, J. Amer. Chem. Soc., 75, 1253 (1953). 

9 R. W. Taft, Jr., J. Amer. Chem. Soc, 74, 5372 (1952). 

10 A. J. Kresge, Y. Chiang, P. H. Fitzgerald, R. S. McDonald, and G. H. Schmid, J. Amer. Chem. 
Soc, 93,4907 (1971). 

11 See note 3(a), (c), p. 338. 

Electrophilic Addition to Double and Triple Bonds 341 

Alkynes generall y undergo acid-ca talyzfidJi ydration to form vinyl alc ohols, 
which :r apMLy_rparrangp_ tn ^ketones. These hydrations exhibit general acid 
catalysis, 12 and unreacted acetylenes recovered after partial reaction have not 
exchanged deuterium with the solvent. 13 Noyce and Schiavelli have found that 
the rate of hydration of ring-substituted phenylacetylenes is very dependent on 
the nature of the substituent, giving a linear correlation with a + (p = — 3.84). 14 
Thus all the evidence points to the transient slow formation of the unstable vinyl 
cation in a mechanism entirely analogous to that for hydration of alkenes as 
shown in Equation 7.4. As Table 7.2 shows, the rate of hydration of alkynes is also 

RC^CR + H 3 + -^- RC=G— R + H 2 > 



RC=C— R -5-U RC=C— R > R— C— CH 2 R (7.4) 


H z O H HO H 

comparable to that of alkenes. 15 This is most surprising in view of the much greater 
stability of a tricoordinated as opposed to a vinyl carbocation. 

Addition of Hydrohalides 

The addition of HX to double bonds in the dark and in the absence of free-radical 
initiators is closely related to hydration : The orientation of the elemen ts ofHXjn 
t he ad duct always mnrsp rmds to MarknwniknfT addition; 16 no deuterium 
exchange wish solvent is found in unreacted olefins recovered after partial reac- 
tion, nor is recovered starting material isomerized after partial reaction. 17 How- 
eygr J _the_ addition of HX apparently can proceed by_a_n umber of differen t 
mechanisms dependin gjpn the n^ure _ojJhe_siU2Str ate and Qn JLhjejeaction condi- 
tjons^ Thus when HC1 is added to i-butylethylene in acetic acid, the rate is first- 
order in each reactant and the products are those shown in Equation 7.5. 1B 
Since 4 and 6 were demonstrated to be stable to the reaction conditions, the 
rearranged product (5) can be formed only if a carbocationic intermediate is 
formed during reaction. However, the carbocation exists almost solely in an inti- 
mate ion pair, and the rate of collapse of the ion pair to products must be faster 
than, or comparable to, the rate of diffusion of CI ~ away from the carbocation. 
This must be so because the ratio of chloride to acetate products is unaffected by 

12 (a) W. Drenth and H. Hogeveen, Rec. Trav. Chim., 79, 1002 (1960); (b) E. J. Stamhuis and 
W. Drenth, Rec. Trav. Chim., 80, 797 (1961); (c) E.J. Stamhuis and W. Drenth, Rec. Trav. Chim., 82, 
394 (1963); (d) H. Hogeveen and W. Drenth, Rec. Trav. Chim., 82, 410 (1963); (e) D. S. Noyce and 
M. D. Schiavelli, J. Amer. Chem. Soc, 90, 1020 (1968). 

13 See note 12(d). 

14 See note 12(e). 

15 (a) Note 12(a); (b) D. S. Noyce, M. A. Matesich, M. D. Schiavelli, and P. E. Peterson, J. Amer. 
Chem. Soc, 87, 2295 (1965) ; (c) K. Yates, G. H. Schmid, T. W. Regulski, D. G. Garratt, H.-W. Leung, 
and R. McDonald, J. Amer. Chem. Soc, 95, 160 (1973). 

16 See note 1(a), p. 337. 

17 Y. Pocker, K. D. Stevens, and J. J. Champoux, J. Amer. Chem. Soc, 91, 4199 (1969). 

18 (a) R. C. Fahey and C. A. McPherson, J. Amer. Chem. Soc, 91, 3865 (1969); (b) Rearranged 
acetate corresponding to 5 is not stable to the reaction conditions but reacts with CI ~ to form 5. 

342 Addition and Elimination Reactions 

H 3 C H 

H 3 C H 

1 1 
CH3 — G — C=Cri2 


HC1 - 


1 1 
-+ CH 3 — C— C— CH 3 + 

CH 3 

H 3 C CI 

Relative amounts: 

H 3 C H 

CH 3 — C— C— CH 3 + CI 

CI CH 3 

Relative amounts: 

2 : 

H 3 C H 

I I 
[ 3 — C— C— CH 3 (7.5) 

H 3 C OAc 


the concentration of HC1 or by added chloride ion in the form of tetramethyl- 
ammonium chloride. If the nature of the products depended on the environment 
outside the ion pair, the ratio of chloride to acetate would increase with increasing 
chloride ion concentration in the solution. Such rapid collapse of the carbocation 
implies that the addition of the proton to the olefin is rate-determining. This con- 
clusion is supported by the fact that an isotope effect of £ H /A: D = 1 . 1 5 is found 
when the rate of addition of HC1 in acetic acid is compared with the rate of 
addition of DC1 in DOAc. Thus thejnechanism can be clas sified as A d B 2 and is 
shown in Scheme l. 19 

Scheme 1 

CH 3 

CH 3 Cl- 

H 3 C CH 3 

CH 3 — C— CH=CH a + HC1 



CH 3 — C — CH — CH 3 

1 ,2-shift 

1 1 

CH 3 — C — C — CH 3 

+ 1 

CH 3 

/ CH 3 







H 3 C CI / 
1 1 * 

H 3 C H 

H 3 C CH 3 

\ \ 
CH 3 — C — O — CH 3 

1 1 
Crl 3 — C — C — C rl 3 

1 1 
CH3 — C — C — CH 3 

H 3 C H 

H 3 C OAc 

1 1 



When HC1 is added to cyclohexene under the same conditions as were em- 
ployed in the addition to J-butylethylene, the nature of the products is similar 
(Equation 7.6), but some of the other characteristics of the reaction are quite 

+ HC1 2°^> / \ + / \ (7 . 6) 


different. In this case the ratio of cyclohexyl chloride to cyclohexyl acetate is low 
(0.3) at low HC1 concentrations and in the absence of added chloride ion, but it 
increases sharply to approximately 2 if the reaction mixture is made 0.226 M in 

19 See note 18 (a). 

Electrophilic Addition to Double and Triple Bonds 343 

tetramethylammonium chloride (TMAC) . Furthermore, if the stereochemistry 
of the reaction is studied by using cyclohexene-l,3,3-d 3 as substrate, the five pro- 
ducts shown in Equation 7.7 are always found but their relative amounts depend 

H D 



D H H 

7 8 

D D 



H H 

9 10 X = CI 

11 X = OAc 

strongly on the chloride ion concentration. Thus the ratio of cyclohexyl^Moride 
derived from syn a ddition (7), relative to _th at formed by anti addition (8) , 
jkcreaggs^markedly wjth_chloride jonjconcentration whereas the rado^£thejyn- 
fbjmed^hloride_ad duct (7) to t he ant.i-formed a cetate adduct (9) remains un- 
c hange d. (Note that 10 and 11 tell us nothing about the stereochemistry of addi- 
tion but, since the amount of 10 formed by syn addition relative to that formed by 
anti addition should be equal to the ratio of 7 : 8, we can focus our discussion on 
7, 8, and 9 alone.) No acetat e formed b y syn addition is found. 20 

Analysis of the rate and product data show that the rate equation is com- 
posed of three terms (Equation 7.8) ; each includes the concentrations of olefin and 
of acid, but one also includes the concentration of chloride ion and another the 
concentration of acetic acid. 21 

rate = k± [HC1] [olefin] + A 2 [HC1] [olefin] [CI"] + A 3 [HC1] [olefin] [HO Ac] (7.8) 

Fahey has suggested that all the facts are consistent with the products being 
formed by three competing reactions. The first, responsible for the second-order 
rate term, is an ion-pair mechanism like that found in the hydrochlorination of 
/-butylethylene. Such a pathway, which invo lves collapse of the ionpair_(see_ 
a bove), accoimts.ibj. the q/7?.H T!l aHHiir t_ajicLso me of the ant i-YlG\ ad duct. Th e 

tprnnfj_ar|d third j^artinrayrespnnsihlp fpr i;\\e $ecnr\An™\jh\r^terrn<i in the rate 

20 R. C. Fahey, M. W. Monahan, and C. A. McPherson, J. Amer. Chem. Soc, 92, 2810 (1970); 
R. C. Fahey and M. W. Monahan, J. Amer. Chem. Soc, 92, 2816 (1970). 

21 This is actually a simplified form of the rate equation for Reaction 7.6. Fahey found that it is not 
the concentration of HC1, but its activity as represented by Satchell's acidity function, A [D. P. N. 
Satchell, J. Chem. Soc, 1916 (1958)], that should be included in each term of the rate equation. See 
note 20. 

344 Addition and Elimination Reactions 

e quatio n_a nd fa din g to anti HC1 a nd_fl wft-HOAc ad ducts, re_srjectiyely, are 
termolecu lar processes jyithjrjnf 1 ^ 1 "" "rat^ 19.axuL.13..... 

V> + :/ 





Such mechanis ms are called Ad3 (addition-t ermolecular) . Ad3 transition states 
analogous t o 12and 13 but l e ading to syn ad ductsTare, precluded by the steric 
requirements of th e addend s. 22 Thus increased chloride ion concentration in- 
creases the contribution of the second term of the rate equation relative to the 
other two, and anti-HCl adduct is formed more rapidly than syn-HGl or -HO Ac 

Why does hydrochlorination of <-butylethylene not also proceed in part by a 
termolecular mechanism? The apparent reason is shown in Table 7.3: The 
carbocation formed from i-butylethylene is more stable than the cyclohexyl 
cation, and therefore k± of Equation 7.8 is larger for i-butylethylene. Furthermore, 
<-butylethylene has a small k 2 because of steric interference of the bulky t-butyl 
group in a termolecular transition state. Table 7.3 gives the estimated rate con- 
stants, k lt k 2 , and k 3 of Equation 7.8 for four olefins. The rate constant, k 1} de- 
creases with the ability of the substrate to stabilize a positive charge. The larger 
value of k 2 for 1,2-dimethylcyclohexene than for cyclohexene means that the j8 
carbon in the transition state of the Ad3 mechanism has some cationic character 

Table 7.3 Estimated Rate Constants for Addition to Olefins 
in HCl/HOAc Solutions at 25°C 


lO 8 *! 

M" l s 


10 8 /t 3 
M -2 sec -1 






<10" 5 


1.0 x 10- 3 


Source: R. C. Fahey and C. A. McPherson, J. Amer. Chem. Soc., 93, 2445 (1971). Reprinted by per- 
mission of the American Chemical Society. 

22 See note 20, p. 343. 

Electrophilic Addition to Double and Triple Bonds 345 

as shown in 12. 23 This conclusion is consistent with the universality of Markowni- 
koff addition in hydrochlorinations. 

With a variety of different mechanisms available, it is not surprising that the 
characteristics of hydrochlorination depend on the reaction conditions. Thus, in 
nitromethane, a medium that gives extensive Wagner-Meerwein shifts during 
hydrochlorination, olefins react according to the third-order rate law, 

k = [olefin] [HC1] 2 

The fact that rearrangements occur implicates a carbocation intermediate. When 
the reaction is carried out with DC1, olefin recovered after several half-lives con- 
tains no deuterium. Thus, formationof the intermediate must be rate-determining. 
Apparently, the role of the second HC1 molecule is to assist the first in ionizing, 
and the HC1 2 ~ anion is produced as shown in Equation 7.9. Predominant anti 
addition is observed — presumably because a third HC1 attacks from the back 
side in a second fast step. 24 

)«=/ + 2HC1 

,-■._. H H 

H— C1--C1---H "* 

\ I HCI v 1/ 


The characteristics of the addition of HBr to double bonds are similar to 
those of the addition of HC1. However, in acetic acid 1 ,2-dimethylcyclohexene 
gives more anti addition if HBr is the addend. 25 Also, as Figure 7.1 shows, 
when HX is added to a double bond in acetic acid, the ratio of alkyl halide 
to alkyl acetate increases sharply as the concentration of HBr is increased 
but is almost independent of the concentration of HC1. Fahey suggests that 
the much larger acid dissociation constant of HBr (AA" d = 10 3 — 10*) is respon- 
sible for both of these facts. Hydrobromic acid acts as a better halide source, 
and Ad3 addition is favored. 26 

Electrophilic addition of HC1 to triple bonds can apparently also go by bi- 
or termolecular mechanisms. Thus in acetic acid 3-hexyne (14) gives predom- 
inantly anti addition through an Ad3 pathway, but 1-phenylpropyne (15), which 
can form the resonance-stabilized vinyl cation (16), gives predominantly syn 
addition through an ion pair Ad £ 2 mechanism. 27 

/ — — \ <f>— C=C— CH 3 <j>— C=CHCH 3 

14 15 16 

Addition of Halogens 

Brom ination of double bonds is stro ngly accel erated_by_electron-relea sing sub - 
stitutes and retai^e33y.-elecitoIi^vith_drawing_ones__ (see Tables 7.4 and 7.7) 
and is~thereiored early_an_glecti pphilic a ddition. T_he_rate_ ofx^ction_is_alw.ays 

23 R. C. Fahey and C. A. McPherson, J. Amer. Chem. Soc, 93, 2445 (1971). 
" Y. Pocker and K. D. Stevens, J. Amer. Chem. Soc, 91, 4205 (1969). 

26 R. C. Fahey and R. A. Smith, J. Amer. Chem. Soc, 86, 5035 (1964). 

28 R. C. Fahey, C. A. McPherson, and R. A. Smith, J. Amer. Chem. Soc, 96, 4534 (1974); see also 
D.J. Pasto, G. R. Meyer, and B. Lepeska, J. Amer. Chem. Soc, 96, 1858 (1974). 

27 R. C. Fahey and D.-J. Lee, J. Amer. Chem. Soc, 88, 5555 (1966) ; 89, 2780 (1967) ; 90, 2124 (1968). 

346 Addition and Elimination Reactions 



+ HBr 


+ HC1 





Figure 7.1 Variation in the alkyl halide to alkyl acetate product ratio with HX con- 
centration for reaction in HOAc at 25°C. From R. C. Fahey, C. A. 
McPherson, and R. A. Smith, J. Amer. Chem. Soc, 96, 4534 (1973). Reprinted by 
permission of the American Chemical Society. 

first-orderjn_ olefin. but for olefins of widely different reactivity it can be either 
'first- or^semnd-o rder in mo lecular bromine depending on i the reaction conditions. 
At )nw mnrpntr^tinrn nf hmminp a nd in water and alcoholic, solvents, the rate 
expre ssion is second-order overall and first-order in bromine. U nder these condu . 
tjons, then, additi on OCCUrS by an Ad c 9 mechanism. However, in less polar sol- 
vents (e.g., acetic acid) or when the bromine concentration is high, a second 

Table 7.4 Relative Rates of Second-Order 
Reactions with Bromine in 
Water at 25°C 

R in RCH=CH, 

Relative Rate 

CH 3 

CH 2 OH 


CH 2 CN 



1.1 x 10" 3 
3 x 10- 7 

Source: Data of J. R. Atkinson and R. P. Bell, J. Chem. Soc, 3260 (1963). Table reproduced from 
P. B. D. de la Mare and R. Bolton, Electrophilic Additions to Unsaturated Systems, Elsevier, Amsterdam, 
1966, p. 115. Reprinted by permission of The Chemical Society, Elsevier, R. P. Bell, and P. B. D. 
de la Mare. 

Electrophilic Addition to Double and Triple Bonds 347 

molecule of bromine helps to polarize the first in the transition state as in 17. 28 

Br... Br— Br ^ * 

: 6- 


\ ••■'•. / 

C— C 

/ ;v \ 


In the presence of added nucleophiles or in hydroxylic solvents, a mixture of 
products is often obtained, as shown in Equation 7.10. 

Br 2 + C=C. 

/ y- 



Br Br 


Br OS 

Br Br 

Bromine normally adds anti to a nonc onjugated a l kene. F or example, cis-2- 
butene gives exclusively the D,L-2,3-dibromobutanes (Equation 7.11), whereas 
trans-2-butene gives only the corresponding meso compound (Equation 7.12). 29 
Similarly, 4-i-butylcyclohexene gives only the trans dibromides (18 and 19) . 30 

CH 3 

H- -CH 3 

/ C=C \ 
CH3 CH 3 



CH 3 


2B (a) See note 1 (a), p. 337. (b) Olah has obtained competitive rate data for the addition of bromine 
to a series of alkenes in 1,1,2-trichloro-trifluoroethane solution at — 35 Q C. The rate of bromination 
of 2,3-dimethyl-2-fc>utene relative to that of ethene was 5680, whereas the relative rates of these 
compounds in methanol are 1.8 x 10 6 (Table 7.7). Olah concluded that in nonpolar medium the 
olefinic carbons bear only a small positive charge in the transition state and suggested that his data 
could be explained by initial formation of a n complex that then cleaves to the bromonium ion as in 
the following equation : 

a ~— Br 



\ / 

C=C + Br 2 


\ / \ / 

/ C — C \ 

+ Br, 


The transition state would resemble the ir complex. [G. A. Olah and T. R. Hockswender, Jr., J. 

Amer. Chetn. Soc, 96, 3574 (1974) and references therein.] 

a9 (a) W. G. Young, R. T. Dillon, and H.J. Lucas, J. Amer. Chem. Soc, 51, 2528 (1929); (b) R. T. 

Dillon, W. G. Young, and H.J. Lucas, J. Amer. Chem. Soc, 52, 1953 (1930); (c) J. H. Rolston and 

Y. Yates, J. Amer. Chem. Soc, 91, 1469 (1969). 

30 E. L. Eliel and R. G. Haber, J. Org. Chem., 24, 143 (1959). 

348 Addition and Elimination Reactions 

/ \ 

H CH a 



CH 3 H 

>=C X J*- l/l (7.12) 


In 1 937 Rob e rts and Kimball pointed out that the observed stereochemistry is 
incompatible with the tbrmation of an lntermediate-Tcwbeeatierr ^20) (Equation 
7. 14- J and suggested that arTInlelThedlate'^fomonium iorr" f21) is formed in 
wMcTT~tne~entering bromine, using one of its unshared electron pairs, bonds to 
bothjcar^on|_oXJl^.double bqndJ(Equation 7.15). Rotation about the C a — C^ 
bond is impossible in 21, and Br ~ must attack back side from the Br + to give 
anti addition. 31 

\ / k ♦ 

Br 2 + C=C > — CAC— + Br" (7.14) 


Br 2 + 

N C=c' — Y*\ + Br" (7-15) 

/ \ 


The bromonium ion concept does rationalize the stereochemistry of bromine 
additions to double bonds very satisfactorily if it is recognized that olefins that 
can form highly stabilized carbocations need not form such a structure. As al- 
ready noted, nonco njugated olefins give predomin antly anti addit ion. Conju- 
gated olehns 2 _jn_ which thejntermediate carbocation wouIdTBe stabilized by 
r esonance, j io weverj give a mixture of syn and anti addu ctsT 

For example, both cis- and <rarc.r-phenylpropene give a mixture of threo- and 
erythro- 1,2-dibromo-l-phenylpropane with bromine in acetic acid in the ratios 
indicated in Equation 7.16. 32 Note that in both these compounds anti addition 
still predominates, and that an equilibrium mixture of syn and anti adduct is not 
obtained. The results cited in Table 7.5 show.thaLi f the /3 c arhnn i<^ rparlpj^vpn 
mor e able to stabilize ajpositiy e charge, the amou nt nf an ti addi tion decreases 

The s^l vnt also affi^s the stereoche rriistry..B romin a tio nj3f r£fr^and-foa»--2- 
butgnes_givca 100 percent nnti-addition-eveftia- solvents of- very Mgh ionizing 

31 I. Roberts and G. E. Kimball, J. Amer. Chem. Soc, 59, 947 (1937). 

32 See note 29(c), p. 347. 

Electrophilic Addition to Double and Triple Bonds 349 

\ /CH 3 

Br 2 + /C=C N 



CH 3 

K /H 
Br 2+ = 

H CH„ 

from cis: 27% 
from trans: 73% 


CH 3 - 




CH 3 Br 

+ 1/ 



CH 3 -/ ^~ 

+ ^ 











power bu t,_aS-T-a ble 7 . 6 shows, the -amount-of anti addition to aj-pheriyTprdp?ne 
goes down as the diele ctnc_constant of the medium increases. 33 

Yates suggests that weak bridging between the bromine and the /3 carbon 
may occur in the intermediate even when the /8 carbon bears a benzene ring as 
shown in 22. But as the /J carbon becomes less electron-deficient or as the solvating 
power of the solvent increases, this bridging becomes less important and the 
stereoselectivity decreases. 34 

CH a 



Although the stereochemistry of bromination of alkenes could result from a 
freely rotating carbocation and a cyclic bromonium ion competing with each 

Table 7.5 Stereochemistry of Dibromoadducts from Olefin and 
Bromine in Acetic Acid at 25°C 

Percent Anti 

Percent Anti 





H 3 </ 


X CH 3 


H CH 3 


H 3 </ 

/CH 3 



H 3 C ,H 
3 \ / 
,/ \ 
4> CH 3 



CH 3 


H 3 C . CH 3 


Source: J. H. Rolston and K. Yates, J. Amer. Chem. Soc, 91, 1469 (1969). Reprinted by permission 
of the American Chemical Society. 

3 J- H. Rolston and K. Yates, J. Amer. Chem. Soc, 91, 1477, 1483 (1969). 
1 See note 29, p. 347, and note 33. 

350 Addition and Elimination Reactions 

Table 7.6 Stereochemistry of Dibromoadduct of 
cw-Phenylpropene in Various Solvents 


Percent Anti 




Acetic acid 



Tetrachloroe thane 



Methylene chloride 



Acetic anhydride 






Source: J. H. Rolston and K. Yates, J. Amer. Chem. Soc, 91, 1477 (1969). Reprinted by permission 
of the American Chemical Society. 

Table 7.7 Relative Rates of Bromination of Alkyl-Substituted Olefins with 
Molecular Bromine in Methanolic Sodium Bromide at 25°C 


Relative Rate 


Relative Rate 



(CH 3 ) 2 C^CH2 


CH2 = Gri — GH 3 


(CH 3 ) 2 C=CHCH 3 


H CH 3 

/ C = C \ 
H 3 C H 


(CH 3 ) 2 C=C(CH 3 ) a 


H H 



H 3 C CH 3 

Source: Data from J.-E. Dubois and G. Mouvier, Bull. Soc. Chim. France, 1426 (1968). Reprinted by 
permission of the Societe Chemique de France. 

other as intermediates, stereochemistry alone is not conclusive evidence for a bro- 
monium ion. For example, the stereochemistry could also be a result of competi- 
tion between Ad3 and Ad E 2 mechanisms. Olefins that cannot form stable carbo- 
cations might react via an Ad3 pathway to give anti addition, whereas conju- 
gated olefins might form carbocations via the Ad £ 2 mechanism to give 
nonstereoselective addition. 

There is, however, other evidence that speaks for the bromonium ion concept 
and against competition between Ad £ 2 and Ad3 pathways. 35 We have already 
noted that, in polar solvents, addition of bromine to multiple bonds is first-order 
in bromine when bromine is present in low concentration. Moreover, as Table 
7.7 shows, increasing the number of substituents on the double bond cumulatively 
increases the rate of bromination of nonconjugated olefins in polar solvents 
irrespective of whether each new substituent is on the same or on the other 
olefinic carbon as the last. 36 Dubois has found that the bimolecular rate constants 
for addition of bromine to alkyl substituted ethylenes are correlated by 

log* a = -2.99 2 o* + 7.61 

35 For a summary, see R. C. Fahey and H.-J. Schneider, J. Amer. Chem. Soc, 90, 4429 (1968). 

36 J.-E. Dubois and G. Mouvier, Bull. Soc. Chim. France, 1426 (1968). 

Electrophilic Addition to Double and Triple Bonds 351 

where 2 a * represents the sum of the Taft a* values for the four substituents 
on the double bond. 37 Thus, in the transition state the positive charge is distrib- 
uted over both carbons of the double bond — a very different situation from 
that obtaining in hydration or hydrochlorination of double bonds (see, for 
example, Table 7.1). 

From the stereochemical evidence we might expect that the effect of sub- 
stituents on the rate of bromination of substituted styrenes in polar solvents would 
not be cumulative. 38 And, indeed, 23, 24, and 25, when brominated under the 
conditions of Table 7.7, have the relative rates shown. Furthermore, the logs of 
the rates of bromination of ring-substituted styrenes show a linear correlation 

<£CH=CH 2 <£CH 3 C=CH 2 <£CH=CHCH 3 

23 24 25 

Relative rates: 1 87 25 

with the <r + constants of the substituents with slope p x -4.5. 39 

Another piece of evidence for the bromonium ion is that addition is less 
regiospecific when bromine is the electrophile then when H 3 + attacks. With 
molecular bromine we cannot, of course, observe the site at which the original 
electrophilic bromine attacks, but with unsymmetrical reactants such as HOBr or 
BrCl we can. Thus, for example, the addition of BrCl to propene in aqueous HC1 
gives only 54 percent of the Markownikoff addition product (26) and 46 percent 
of the anti-Markownikoff product (27). 40 The chloride ion apparently has the 

GH3 — GH — CH2 CH3 — CH — CH2 

CI Br Br CI 

26 27 

choice of attacking either of two carbons, both of which carry approximately equal 
positive charges — a situation that would exist in the bromonium ion. 

Recently Olah has observed the unsubstituted bromonium ion and several 
alkylated bromonium ions by nmr spectroscopy after dissolving a-bromohalides 
in SbF 5 -S0 2 solution at low temperatures. 41 All four hydrogens of the unsub- 
stituted ion were equivalent. 

The bromonium ion (28) has actually been isolated as the tribromide salt. 



This ion is stable because it cannot be attacked from the back side. 42 

37 J.-E. Dubois and E. Goetz, J. Chim. Phys., 63, 780 (1966). 

3B J--E. Dubois, J. Toullec, and G. Barbier, Tetrahedron Lett., 4485 (1970). 

39 J. A. Pincock and K. Yates, Can. J. Chetn., 48, 2944 (1970). 

40 P. B. D. de la Mare and S. Galandauer, J. Chem. Soc, 36 (1958). 

41 G. A. Olah, J. M. Bollinger, and J. Brinich, J. Amer. Chem. Soc, 90, 2587 (1968); G. A. Olah and 
J. M. Bollinger, J. Amer. Chem. Soc, 89, 4744 (1967); 90, 947 (1968). 

"J. Strating, J. H. Wieringa, and H. Wynberg, J. Chem. Soc, D, 907 (1969). 

352 Addition and Elimination Reactions 

Molecular fluorine, because of its very low bond dissociation energy, 
usually reacts uncontrollably with organic compounds. 43 Merritt, however, has 
observed electrophilic addition of F 2 to cis- and taz/w-l-phenylpropenes at low 
temperatures. The mode of addition is predominantly syn. j\_fluon3mumion, in 
which the fl uorine is positively charged, would be very unstable and ^PP_grgntIy~ 
does not form . 44 Attempts to form a three-membered ring fluoronium ion in 
superacid medium have also failed. 45 

Electrophilic addition of CI., arH T 3 tr > alkpne s is simil ar in mechanism to the 
e lectrophilic addition of Br 9 . 4 6 The rate of chlorination in acetic acid is second- 
order, first-order each in olefin and in chlorine. 47 Predominantly anti addition to 
alkyl-substituted double bonds occurs, indicating that a chloronium ion is 
formed. 48 Further evidence for the chloronium ion is that addition of hypo- 
chlorous acid to double bonds is not entirely regiospecific. For example, addition 
to propene gives 91 percent of the Markownikoff product 29, and 9 percent of 
the anti-Markownikoff product, 30. Phenyl-substituted alkenes give a mixture of 
syn and anti adducts with Cl 2 as they do with Br 2 . 49 

CH3CH — Cr±2 CH3CH — CH2 


29 30 

Iodination is usually second- 50 or third- 51 order in I 2 . The role of the addi- 
tional I 2 molecules, apparently, is to assist in breaking one I — I bond in the rate- 
determining step. Because iodine is less electronegative than bromine, the 
iodonium ion can compete with carbocation formation even when the bro- 
monium ion cannot. 52 Thus IN 3 with «s-/3-deuterostyrene gives anti addition 
only, whereas BrN 3 with the same olefin gives a 1 : 1 mixture of syn and anti 
adducts. 53 Chloronium and iodonium ions have been observed in superacid 

Electrophilic additions of the halogens to alkynes have not been much 
studied. In acetic acid a given olefin reacts with bromine 10 3 to 10 5 times more 
rapidly than the corresponding acetylene. However, the relative rates are 
enormously solvent-dependent and decrease with solvent polarity. Thus bromina- 
tion of styrene is 2590 times faster than bromination of phenylacetylene in acetic 
acid, but only 0.67 times as fast in H 2 0. Solvation of the transition state must be 

43 See note 1(a), p. 337. 

44 R. F. Merritt, J. Amer. Chem. Soc, 89, 609 (1967). 
46 See note 41, p. 351. 

46 See note 1, p. 337. Chlorination of olefins in nonpolar media in the absence of radical inhibitors 
may proceed by a radical pathway. [M. L. Poutsma, J. Amer. Chem. Soc., 87, 2161, 2172 (1965).] 

47 I. R. C. McDonald, R. M. Milburn, and P. W. Robertson, J. Chem. Soc., 2836 (1950) and earlier 
papers in this series (by Robertson and co-workers). 

46 (a) See note 35, p. 350; (b) R. C. Fahey and C. Schubert, J. Amer. Chem. Soc, 87, 5172 (1965); 
(c) R. C. Fahey, J. Amer. Chem. Soc, 88, 4681 (1966); (d) M. L. Poutsma and J. L. Kartch, J. Amer. 
Chem. Soc, 89, 6595 (1967). 
49 See note 35, p. 350, and note 48(b), (c). 

60 N. J. Bythell and P. W. Robertson, J. Chem. Soc, 179 (1938). 

61 (a) J. Groh and J. Szelestey, Z. Anorg. Allgem. Chem., 162, 333 (1927); (b) J. Groh, Z. Anorg. 
Allgem. Chem., 162, 287 (1927); (c) J. Groh and E. Takacs, Z. Physik. Chem. Leibzig, 149A, 195 (1930). 

52 See note 1(a), p. 337. 

53 A. Hassner, F. P. Boerwinkle, and A. B. Levy, J. Amer. Chem. Soc, 92, 4879 (1970). 

Electrophilic Addition to Double and Triple Bonds 353 

very important. The rate trends in chlorination parallel those for bromination. 54 
The limited facts available indicate that the mechanism is similar to that of 
addition to olefins. Pincock and Yates have studied the addition of bromine to a 
number of alkyl- and arylacetylenes in acetic acid. At low bromine concentra- 
tions the reaction is second-order, first-order each in Br 2 and in acetylene. 
Alkylacetylenes give only anti addition, indicating that a bromonium ion lies 
on the reaction path. Ring-substituted phenylacetylenes, however, give both syn 
and anti addition; and the logs of the rates correlate linearly with the a + con- 
stants of the substituents, giving a very large negative p value ( — 5.17). In these 
compounds, open vinyl cations are apparently formed as intermediates. 55 

Hydroboration 56 

The jiddition of a boron hydride across a double or triple bond (E quation .LIZ) is 
called hydroboration. 

\ \ / II 

B— H + C=C > — C— C— (7.17) 

/ / \ 

H B 
H /X H 

We include it here despite uncertainty about whether attack is initiated by 
electrophilic boron or nucleophilic hydrogen or both simultaneously. 57 

In additions of diborane, the major product is formed by the attachment of 
boron to the less substituted carbon. For example, addition of diborane to 
1-hexene (31) gives a product that has 94 percent of the boron attached to the 
terminal carbon. Similarly, diborane added to 2-methylbutene-2 (32) gives 98 
percent of boron incorporation at C 3 . 58 

CH 3 

CHaCHoCrioCHoCH^CHo CH 3 — G=GH — Grl 3 

4% 96% 2% 98% 

31 32 

If, instead of diborane, a boron hydride substituted with bulky alkyl groups 
is added to a double bond, the regiospecificity increases. Thus £u(3-methyl-2- 
butyl)borane reacts with 1-hexene to give 99 percent terminal boron incorpora- 
tion (Equation 7.18). 59 

Electronic effects as well as steric effects are important in determining the 
orientation of addition as is shown, for example, by the data in Table 7.8. The 
regiospecificity is increased as 2-butene is substituted in the 1 position by increas- 

54 See note 15(c), p. 341. 

66 (a) J. A. Pincock and K. Yates, Can. J. Chem., 48, 3332 (1970) ; (b) J. A. Pincock and K. Yates, 

J. Amer. Chem. Soc, 90, 5643 (1968). 

66 H. C. Brown, Hydroboration, W. A. Benjamin, Menlo Park, Calif., 1962. 

67 See note 1(a), p. 337. 

68 H. C. Brown and G. Zweifel, J. Amer. Chem. Soc, 82, 4708 (1960). 
59 H. C. Brown and G. Zweifel, J. Amer. Chem. Soc, 82, 3222 (I960). 

354 Addition and Elimination Reactions 

Table 7.8 Orientation of Addition of Diborane to Substituted 2-Butenes 

Percent of Boron in 
Position 3 of Product 







Source: H. C. Brown and R. M. Gallivan, Jr., J. Amur. Chem. Soc, 90, 2906 (1968). Reprinted by 
permission of the American Chemical Society. 

ingly strong electron-withdrawing groups. 60 Boron must then bear a partial 
positive charge in the transition state. 

H 3 C CH 3 \ 

H— C— C 1 — BH + CH 3 CH 2 CH2CH 2 CH=CH 2 > 

H 3 C H / 2 


Percent of Boron in 


Position 2 of Product 









OCH 2 <£ 






CH 3 CH 2 CH 2 CH 2 CH— CH 2 + CH 3 CH 2 CH 2 CH 2 CH— CH 2 (7.18) 


H B— C B H n H 5 C n — B H 

CsHn CsHu 

99% 1% 

Hydroboration always givps sy n addi tion of {he eler"P"te-a£-bfn*>n-- a^rl 
h ydrogen to a double bon d. For example, hydroboration of 1-methylcyclopentene 
gives only the product shown in Equation 7.19. 61 


60 H. C. Brown and R. M. Gallivan, Jr., J. Amer. Chem. Soc, 90, 2906 (1968). 

61 H. C. Brown and G. Zweifel, J. Amer. Chem. Soc, 81, 247 (1959). This constant stereospecificity 
suggests a four-center transition state, 

\ / 

c— C 

/: :\ 
• •/ 



[A. Strietweiser, Jr., L. Verbit, and R. Bittman, J. Org. Chem., 32, 1530 (1967); D. J. Pasto, B. 
Lepeska, and T. C. Cheng, J. Amer. Chem. Soc, 94, 6083 (1972).] Direct concerted 2 + 2 cyclo- 
addition of B — H to a carbon-carbon double bond involving only the orbitals of the B — H a bond 
and the 17 orbital of the double bond is not allowed by orbital symmetry considerations. However, 

Pasto has suggested that the great exothermicity of hydroboration (e.g., BH 3 + 3CH 2 =CH 2 > 

B(CH 2 CH 3 ) 3 , AH = —99 kcal mole -1 ) means that the transition state would be very early on the 
reaction pathway and that orbital symmetry is either not developed sufficiently to control the course 
of the reaction or does not apply. 

1 ,2-Elimination Reactions 355 

The work of H. C. Brown has made hydroboration an enormously useful 
synthetic reaction. Oxidation of the adduct with alkaline hydrogen peroxide re- 
moves the boron smoothly without rearrangement and replaces it by a hydroxy 
group. The oxidation proceeds entirely with retention of configuration. For 
example, the product of Reaction 7.19 is converted by oxidation to trans-2- 
methylcyclopentanol in high yields (Equation 7.20). 

^ Ov" OH (720) 

'H \ / H 

Thus hydroboration of a double bond followed by peroxide oxidation is a con- 
venient procedure for converting the olefin into the alcohol corresponding to 
anti-Markownikqff addition of water. 

Alkynesalso react with boron hydrides be aring bulky ojganic groups to give 
attacnment of boron to the less substituted position;! 2 .syn_ addition I^ again the 
rule^-The adducts can__bgjimoothly converted^ the ctr-olefins byjreatment with 
aceii£_acid--at-0°G {Equation 7.21 ). fe3 

\ \ / HOAc \„ / 

R-feC-R + B-H > /C=C -^ / C=C X ( 7 - 21 ) 

H B H H 


The opposite of an addition to a double bond is a 1,2-elimination reaction. In 
solution, where the reaction is promoted by solvent or by base, the most common 
eliminations (and those to which we shall limit our discussion) are those that 
involve loss of HX, although loss of X 2 from 1,2-dihalides and similar reactions 
are also well known. The mechanisms of eliminations of HX are of three main 
types: (1) The Ej^ (elimination, first-order), shown in Equation 7.22, which is the 
reverse of the Ad E 2 reaction and which has the same first, and rate-determining, 

II II B - \ / 
— C— C— > — C— C— + X- ► C=C + BH (7.22) 

| | slow + I / \ 

X H H 

step as the S N ] reaction; (2) the E x cB (elimination, first-order, conjugate base) 
reaction of Equation 7.23, which involves initial abstraction of a proton followed 

II II \ / 

— C— C— + B" > — C— C— + BH > C=C + X" (7.23 

II I - / x 

X H X 

82 G. Zweifel, G. M. Clark, and N. L. Polston, J. Amer. Chem. Soc, 93, 3395 (1971).. 
63 H. C. Brown and G. Zweifel, J. Amer. Chem. Soc, 81, 1512 (1959). 

61 For reviews, see: (a) W. H. Saunders, in The Chemistry ofAlkenes, S. Patai, Ed., Wiley-Interscience, 
New York, 1964, p. 149; (b) D. V. Banthorpe, Elimination Reactions, Elsevier, Amsterdam, 1963; 
(c) J. F. Bunnett, Survey Prog. Chem., 5, 53 (1969); (d) W. H. Saunders, Jr., and A. F. Cockerill, 
Mechanisms of Elimination Reactions, Wiley-Interscience, New York, 1973; (e) A. F. Cockerill, in 
Comprehensive Chemical Kinetics, C. H. Banford and C. F. H. Tippett, Eds., Elsevier, New York, 1963, 
Vol. 9, chap. 3. 

356 Addition and Elimination Reactions 

by loss of X~; and (3), the E 2 (elimination, second-order) reaction shown in 
Equation 7.24, in which the base attacks the fi proton at the same time as the 
C — X bond cleaves. 65 


I I 
-C— C- 

+ B" 


I i 
— C— C— 

i I 
L X*- 

\ / 

-+ ,C=C. + HB + X- (7.24) 



We shall discuss each of these mechanisms and also, very briefly, 1,2-elimin- 
ations that require assistance of neither solvent nor base. 

The Ej Reaction 

As already noted in Section 5.1, solvolysis of alkyl derivatives often leads to a 
mixture of substitution and elimination products (see Scheme 1 of Chapter 5). It 
was also mentioned there that although the rate of solvolysis changes with the 
leaving group, when t he solvent is of high dielectric constant the rat 1r » nf ^lbstitn- , 
tinn to fliminnfin n prndnr fs is inHqvnHpnt nf thp Ipovipg crrnnp For example, in 
80 percent aqueous ethanol, <-butyl iodide solvolyzes over 100 times as rapidly as 
£-butyl chloride, but the ratio of elimination to substitution products is the same 
for the chloride and iodide. 66 It was evidence of this sort that made early investi- 
gators postulate that first-order elimination (EJ and first-order substitution 
(S^l) share a preliminary, rate-determining step. Then, they suggested, in a 
second step, the fully solvated carbocation either adds solvent (S w l reaction) or 
gives up a proton to the solvent (E x reaction). 

Further investigation, however, showed that in solvents of low ionizin g 
p ower the ratio of substitution to eliminatio n dep ends on the natu re of the leav- 
ing grou p. For example, as Table 5. 1 (p. 2 1 6) shows, in glacial acetic acid, when 
the leaving group is CI", elimination accounts for 73 percent of the product; 
but when it is CH 3 — S — CH 3 , only 12 percent alkene is formed. Thggej acts a re^ 
consistent wu ^formationijf-ifit imat c io n~ p ai r s in thf» Ips e Hieg^r iatin g solv ents in 
whic h the leav ing gro up is the^basejthayrejna ves the pr oton, f rom the ff carbon 
(see Section 5.1). 

Whether a /3 proton is lost from the same or the opposite side of the molecule 
as the leaving group, that is, whether syn or anti elimination obtains in a Ej 
mechanism depends on the reaction conditions. If a solvated, planar carbocation 

65 Sneen has suggested that most elimination reactions proceed by initial ionization of the leaving 
group to form an ion pair and that this first step (either fast or rate-determining) is followed by 
attack of base. Thus the S N 2, S N 1, E 2 , and Ej reactions all proceed by one "merged" mechanism. 
For a discussion of this view, see Section 5.4, p. 244 and R. A. Sneen, Accts. Chem. Res., 6, 46 (1973). 
For further examples of cases where second-order eliminations apparently do proceed by slow base 
attack on an intimate ion pair, see K. Humski, V. Sendijarevic, and V. J. Shiner, Jr., J. Amer. 
Chem. Soc, 96, 6186 (1974), and references therein; and W. T. Ford and R.J. Hauri, J. Amer. Chem. 
Soc, 95, 7381 (1973). Bordwell, on the other hand, suggests that most eliminations proceed either by 
initial isomerization of the leaving group or by initial abstraction of the proton and that very few 
eliminations are concerted. See F. G. Bordwell, Accts. Chem. Res., 3, 281 (1970) and F. G. Bordwell, 
Accts. Chem. Res., 5, 374 (1972). For the purposes of the discussion in this chapter, we shall use the 
classification scheme just outlined, which is accepted by most workers in the field. 

66 K. A. Cooper, E. D. Hughes, and C. K. Ingold, J. Chem. Soc, 1280 (1937). 

1,2-Elimination Reactions 357 

is formed, then the /3 proton lost to solvent in the second step should come with 
equal probability from either the same or the opposite side of the plane as the 
original leaving group. This prediction is in accord with experimental results. 67 
If, however, an intimate ion pair is formed and the leaving group rather than the 
solvent acts as t he base, t hen_s yn elimination should res ult. This p rediction has 
also been borne out by experiment. 68 For example, Skell and Hall studied the 
elimination of ery/Aro-3-d 1 -2-butyl tosylate. 69 As shown in Scheme 2, syn elimina- 
tion would give nondeuterated or-2-butene and deuterated trans-2-butene, but 
anti elimination would yield deuterated cis- and nondeuterated /ranj-2-butene. 
In poorly ionizing nitromethane the product is almost entirely that of syn 
elimination ; thus the tosylate pulls off the proton or deuteron from the same side 
of the molecule from which it departed. In aqueous ethanol, however, a mixture 
of syn and anti elimination products is obtained. 70 

Scheme 2 

H CH, 

H CH, 

H 3 C .CH 3 H 3 C H 

H D H CH 3 

H 3 C X X CH 3 H 3 C x / D 

/C =c x + C=C 

H H H CH 3 

In elimination reactions in which a /3 hydrogen may be lost from one of two 
carbons, the question of which way the double bond will be oriented arises. 
Sayt zeff's ru le st ates that in E 3 reactions the double hnnH will he oriented towa rd 
th e more highly substitut ed ca rbon. (Thus elimination that gives the more h ighly 
substituted of two p ossible pro duc ts is called San tzeff elimination. E limination that 
giv es the less substi t uted prQiiucl_is_called Hofmannjlimingtion.) .It is easy to see 
why E 1 react ion usually leads to S^ytg efjf elimination The transition state for the 
prOctuct-determinTng step has some double-bond character, and thus the lowest- 
energy transition state will be that leading to the most stable double bond. It is 
well substantiated that alkyl groups lower the energy of the double bond through 
hyperconjugation. Saytzeff's rule is, however, not necessarily obeyed when the 
carbocation remains part of an intimate ion pair. For example, elimination of 
HX from 

CH 3 




67 See note 64, p. 355. 

68 (a) T. Cohen and A. R. Daniewski, J. Amer. Chem. Soc, 91, 533 (1969) ; (b) P. S. Skell and W. L. 
Hall, J. Amer. Chem. Soc, 85, 2851 (1963). 

69 See note 68(b). 

70 For a similar example, see Humski, et al., J. Amer. Chem. Soc, 96, 6186 (1974). 

358 Addition and Elimination Reactions 

Table 7.9 

| H 3 C CH 3 H 3 C H 

CH 3 — C— CH 2 CH 3 AcOH > C=C + /C= c v + CH 2 =C— CH 2 CH 3 

I V X H V X CH 3 I 


trans terminal 


Percent cis 

Percent trans 

Percent terminal 






Source: D.J. Cram and M. R. V. Sahyun, J. Amer. Chem. Soc, 85, 1257 (1963). Reprinted by per 

mission of the American Chemical Society 

in glacial acetic acid gives the products shown in Table 7.9. As_t he leaving groy ip 
becomes more basic, Saytzeff el imination becomes less arj d less imp ortant 
and Hofmann_ product begins t o prcrlnmip ate_ The change in product compo- 
sition can be explained by a consideration of Hammond's postulate. The more 
basic the counter-ion that pulls off the proton, the more the transition state 
for the product-determining step will look like carbocation and the less double- 
bond character it will have. Then the orientation of the double bond in the pro- 
duct depends more on the relative acidity of the two kinds of protons than on the 
relative stabilities of the possible double bonds. In solution the y-methyl group 
renders the /3-methylene hydrogens less acidic than the /3-methyl hydrogens ; thus 
the more basic the counter-ion the more terminal olefin results. 

Carbanion Mechanisms 71 

If, instead of a good leaving group as is required for the E 1 reaction, a com- 
pound has a poor leaving group but a highly acidic proton, elimination may take 
place through the consecutive reactions shown in Equations 7.25 and 7.26. These 
are usually called E^B reactions but, depending on the relative magnitudes of 

_ J— X - 
I I 

I I 
-c— C— X 

I I 

the rate constants and on the degree of separation between BH and the anion, 
Equations 7.25 and 7.26 actually describe four different mechanisms. Table 7.10 
shows Bordwell's summary of the characteristics of these mechanisms. 

If k x is much greater than both k^ x and k 2 of Equations 7.25 and 7.26 — 
that is, if the /3 hydrogen is very acidic but the leaving group is poor — then if 
sufficient base is present, formation of the anion will be almost complete before 

D.J. McLennan, Quart. Rev., 21, 490 (1967). 

, BH + C— C— X 

*-. | 1 



* a / " \ 

1 ,2-Elimination Reactions 359 

Table 7.10 Carbanion Elimination Mechanisms 



Descriptive Title 





First-order anion 


(El) anion 



Preequilibrium anion 


(E lC B) R 



("reversible" anion) 

Preequilibrium ion pair 


(EicB) ip 



Second-order anion 


(E lC B)x 



Source: F. G. Bordwell, Accts. Chem. Res., 5, 374 (1972). Reprinted by permission of the American 
Chemical Society. 

" The element effect is denned as k x \k y , where k x and k y are the rates of elimination of HX and HY 
(X and Y are different elements), respectively, from a single substrate. 

loss of X begins. An example of a reaction that goes by this [the (Ej)^^ 
mechanism is shown in Equations 7.27 and 7.28. 72 This reaction proceeds at the 
same rate with triethyl- or with tri-n-butylamine. Furthermore, if more than an 


1 1 



Ar— C— C— H + R 3 N: 
1 1 

— ^-> Ar— C— C(CN) 2 + R 3 NH 

fast | _ + 



Ar— C— C(CN) 2 

Ar CN 

slow > V.— r/ + p.n- 
CN / X CN 




equimolar amount of base is present, the rate is independent of the base concen- 
tration and is equal to A 2 [SH], where HS is the substrate. 73 Both these facts 
indicate that abstraction of the proton, which is rendered highly acidic by two 
electron-withdrawing groups, is not involved in the rate-determining step. The 
(Ei) anion mechanism is rare because of the high acidity required of the /3 hydro- 
gen. 74 

In the other three variations of the carbanion mechanism, an equilibrium 
concentration of carbanion is formed, which then either returns to starting 
material or decomposes to products. 

If the /3 proton is slightly less acidic than required for the (E^,,^,, mech- 
anism and k _ 1 is comparable to k y but k 2 is still small, the anion forms from the 
starting material in a rapid equilibrium and the leaving group departs in a 
subsequent slow step. This is called the (E^B^ ("R" for "reversible") mech- 
anism. Because k 2 is much smaller than k 1 and k_ lt we can assume that k 2 does 
not affect the equilibrium concentration of the anion of the substrate, S ~ ; then 

72 Z. Rappoport and E. Shohamy, J. Chem. Soc, B, 2060 (1971). 

73 Actually, in this case one does not need an equimolar quantity of base, because HCN is such a 

->- R 3 N + HCN. 

weak acid that free base is continually reformed by R 3 NH + CN~ 

74 See also, however: (a) F. G. Bordwell, K. C. Yee, and A. C. Knipe, J. Amer. Chem. Soc, 92, 5945 

(1970); (b) F. G. Bordwell, M. M. Vestling, and K. C. Yee, J. Amer. Chem. Soc, 92, 5950 (1970). 

360 Addition and Elimination Reactions 

the concentration of S~ can be found according to Equation 7.29 and the rate of 
elimination will be that of Equation 7.30. 75 

= * l[H S][B] 
A_ 1 [BH + ] 


rate = (7. .30) 

*-i[BH + ] 

Examination of Equation 7.30 shows that the rate of an (E 1 cB) R reaction 
should be independent of the base concentration if the buffer ratio, B/BH + is 
kept constant — that is, the reaction should exhibit specific base catalysis (see 
Section 7.1, p. 340 and Chapter 8, p. 405). An example of such a reaction is 
elimination of methanol from 33. Not only is specific base catalysis observed, but 

O OCH 3 


also, in agreement with rapid and reversible formation of carbanion, in deuter- 
ated solvent the rate of incorporation of deuterium into the substrate is 226 
times faster than the rate of elimination. 76 

The (E^B)^ mechanism is a close cousin of the (E 1 cB) R mechanism. The 
difference is that in the former the free anion is not formed but exists as an ion 
pair with the protonated base as counter-ion. An example of a reaction that goes 
by this mechanism is the formation of bromoacetylene from cis-l,2-dibro- 
moethylene and triethylamine (Equation 7.31). 77 If the rate of elimination from 
deuterated 1 ,2-dibromoethylene is compared to the rate from nondeuterated 
material, k H lk D ~ 1. Therefore proton abstraction is not involved in the rate- 
determining step. Because added Et 3 ND X" does not affect the rate and be- 

H H k .. _ „ 

X C=C , ' ' ^C=Cv — ^-> HC=CBr + HNEt 3 Br" (7.31) 

Br Br 

cause deuterium exchange with solvent does not take place, the (E^B^ mech- 
anism cannot be involved. Apparently the intimate ion pair either goes back to 
starting material or loses Br~ in a slow step; free carbanion is not formed. 

Finally, there is the (E^B): ("I" for "irreversible") mechanism, in which 
the leaving group is so good that proton abstraction becomes rate-determining. 

75 Note that in this and the following EjcB mechanisms the rates are not really independent of the 
base concentration and therefore the "1" part of the classification may be misleading, but it is 
analogous to the S E 1 reaction of Equations 5.24 and 5.25. 

76 L. R. Fedor, J. Amer. Chem. Soc, 91, 908 (1969). For other examples of the (EjcB),, mechanism, 
see J. Crosby and C. J. M. Stirling, J. Chem. Soc, B, 671, 679 (1970). 

77 W. K. Kwok, W. G. Lee, and S. I. Miller, J. Amer. Chem. Soc, 91, 468 (1969). 


HNEt 3 ] 







Br J 

1,2-Elimination Reactions 361 

For this case (k 2 » k x , k_ 1 ) the rate equation reduces to Equation 7.32. Reac- 

rate = A 1 [B][HS] (7.32) 

tions of this sort, then, should be dependent on the base concentration — that is, 
they should be general-base catalyzed. Elimination of benzoic acid from 34 

CH 3 — C— CH 2 — CH 2 — O— C- 




exhibits general base catalysis. It therefore does not go by an (E 1 cB) B 
mechanism. Although the E 2 mechanism is also general-base catalyzed, it is 
excluded, because the rate is independent of the nature of the substituents on the 
phenyl ring. The rates of authentic E 2 reactions, in which carbon-leaving-group 
bond breaking is involved in the rate-determining step, do depend on the nature 
of the leaving group. 78 An (E 1 cB) I mechanism thus seems indicated. 79 Note that 
34 differs from 33 only in that benzoate is a much better leaving group than 
methoxide. This is only one example of several in the literature that show how 
sensitive the various carbanion elimination mechanisms are to changes in the 
structure of the reactants and to the reaction conditions. 80 

Carbanion mechanisms may give either syn or anti elimination. For example, 
Hunter and Shearing studied the butoxide-catalyzed elimination of methanol 
from 35 and 36. Since deuterium exchange with solvent is in close competition 
with elimination, the mechanism is probably (E 1 cB) B . The ratio ofsyn/anti 

OCD 3 H'7 \-OCD 

elimination varies by a factor of approximately 75, depending on the cation of 
the butoxide salt, and decreases in the order, Li + > K + > Cs + > (CH 3 ) 4 N + . 
Hunter and Shearing attribute the changing stereochemistry to the tendency of 
the cation to coordinate with the methoxy group of the substrate. Li + , which 
has the strongest coordinating ability, gives mostly syn elimination; (CH 3 ) 4 N + , 
which has the weakest, gives predominantly anti. 81 

In the carbanionic mechanisms for elimination, if the substrate has two 
proton-bearing /3 carbons, the more acidic protons will be removed. Thus in 
alkylated substrates the double bond will be oriented toward the less substituted 
carbon and Hofmann elimination is obtained. 

7B A. K. Colter and D. R. McKelvey, Can. J. Chem., 43, 1282 (1965). 

79 R. C. Cavestri and L. R. Fedor, J. Amer. Chem. Soc, 92,. 610 (1970). 

80 See also L. R. Fedor and W. R. Glave, J. Amer. Chem. Soc, 93, 985 (1971) and note 74(b), p. 359. 

81 D. H. Hunter and D.J. Shearing, J. Amer. Chem. Soc, 93, 2348 (1971); D. H. Hunter and D.J. 
Shearing, J. Amer. Chem. Soc, 95, 8333 (1973). 

362 Addition and Elimination Reactions 
Table 7.11 Hammett p Constants for Reaction 7.33 



+ 2.07 







S(CH 3 ) 2 




N(CH 3 ) 3 


Source: W. H. Saunders, The Chemistry of Alkenes, S. Patai, Ed., Wiley-Interscience, New York, 
1964, p. 155, Table 1. Reprinted by permission of Wiley-Interscience. 

E 2 Eliminations 82 

The rates of a large number of eliminations are (1) second-order, first-order 
each in base and in substrate ; (2) decreased if j8-deuterium is substituted for /3- 
hydrogen; and (3) strongly dependent on the nature of the leaving group. The 
mechanism of these reactions (shown - in Equation 7.24), in which C — H and 
C — X bond breaking are concerted, is E 2 . 

Substituent and isotope effects show that Equation 7.24 must actually 
describe a spectrum of transition states in which the relative extents of C — H and 
C — X bond breaking vary according to the specific substrate and to the reaction 
conditions. For example, a comparison of the rates of ethoxide-catalyzed elimina- 
tion of HX from 37 and 38 in ethanol at 30°C shows that A; H /A D varies from 3.0 
when X = + N(CH 3 ) 3 to 7.1 when X = Br. 83 Similarly, if X is kept constant, 

(O/ - CD 2 CH 2 X /q\— CH 2 CH 2 X 

37 38 

the logs of the rates of Reaction 7.33 correlate linearly with the o- values of the 
substituents, but the slopes of the correlation lines depend on X and are given in 
Table 7.11. The extent of bond breaking in the transition state must, then, 
depend on X. 

Y— /q\— CH 2 CH 2 X + C 2 H 5 0" > Y-/ Q/ CH = CH 2 ( 7 - 33 > 

The EiCB-Ei elimination spectrum Several investigators suggested 
tha\ the spectrum of E 2 transition states ranges from one similar to that of E x cB 
elimination, in which C — H bond breaking has proceeded considerably further 

82 See note 64, p. 355, and D. V. Banthorpe, in Studies on Chemical Structure and Reactivity,]. H. Ridd, 
Ed., Methuen, London, 1966, p. 33; N. A. LeBel, in Advances in Alicyclic Chem., 3, H. Hart and G. J. 
Karabatsos, Eds., Academic Press, New York, 1971, p. 196. 
63 W. H. Saunders, Jr., and D. H. Edison, J. Amer. Chem. Soc, 82, 138 (1960). 

1 ,2-Elimination Reactions 363 

c— c 



C — C 

Figure 7.2 Projection in the horizontal plane of the E 2 reaction path. A poorer leaving 
group will facilitate motions R 2 and J_ x , causing shift of the transition state to* 
and change of the reaction path from the solid curve to the dashed curve. 





C— C 






C— C 



C— C 








C— C 



than C — X bond breaking (39) to one similar to that of the E 1 reaction, 41. 8 * 
Intermediate would be the fully concerted transition state 40. 







\: y 

\: / 



C— c 




/ :'\ 

/ :\ 


: \ 







1 See note 64, p. 355. 

364 Addition and Elimination Reactions 

The reacting bond rule, discussed in Section 2.5 (p. 103) and in Section 5.4 
(p. 246^ can be used to predict the effect on the E 2 reaction of changing the 
leaving group. 85 As in Chapter 2, the concerted reaction is broken down into the 
two stepwise mechanisms of which it is a composite. The E 2 reaction described 
here is a composite of the Ej and E x cB mechanisms. In Figure 7.2 the starting 
material is placed at the top left and the product at the bottom right of a two- 
dimensional projection of the energy surface for an E 2 elimination. At each of the 
two remaining corners is placed one of the two intermediates that would obtain 
if the reaction were stepwise. The two reaction pathways along the edges from 
starting material to product describe the stepwise reactions. A diagonal pathway 
describes the concerted reaction. Reacting bond rule 1 (equivalent to Hammond's 
postulate) tells us that a poorer leaving group, which makes motion over the 
transition state more difficult, will cause the transition state to come later on the 
reaction path — that is, will shift it in the direction indicated by arrow R x . But 
leaving group motion is also involved in the vibration designated by J_ ± and 
J_ 2 ; reacting bond rule 2 states that a change in structure that tends to shift the 
equilibrium point of a vibration will do so. The poorer the leaving group, the 
more the equilibrium point of the vibration of the reaction path will be shifted 
along J_ x (toward the E 2 cB mechanism) . The composite result of the poorer 
leaving group on the transition state, then, will be to move it to point *'. The 
extent of C — X bond breaking is not much affected, but the C — H bond is more 
broken and the carbanion character of the transition state increased. 

The predictions of the reacting bond rules are borne out by the p values of 
Table 7.11. More negative charge is localized on C^ when the leaving group is 
the less reactive + N(CH 3 ) 3 than when it is the more reactive I". The isotope 
effects mentioned above fit this explanation if it is assumed that when Br ~ is the 
leaving group the proton is approximately half transferred at the transition state. 
The smaller value of £ H /A: D when + N(CH 3 ) 3 departs is a result of an unsym- 
metrical transition state in which the proton is more than half transferred. 

The Winstein-Parker elimination spectrum More recently, Winstein 
and Parker have proposed that the spectrum of E 2 transition states is actually 
wider than had been previously supposed. 86 They observed that not only 
strong proton bases (i.e., hard bases) such as hydroxide and alkoxide, 
which have traditionally been used as catalysts for the E 2 reaction, but 
also bases weak toward hydrogen but strong toward carbon (soft bases) are 
very effective in catalyzing E 2 reactions. For example, f-butyl bromide, which had 
been thought to undergo only E x elimination, actually eliminates by a bimole- 
cular mechanism in which CI ~ is a more effective catalyst than />-nitrophenoxide 
although the latter is 10 10 times stronger as a hydrogen base. 87 The Winstein- 
Parker spectrum extends from the EjcB-like transition state (39) — called by 
them E 2 H — to one in which the base is pushing out the leaving group rather 
than attacking the proton (43). The latter is designated E 2 C. In the center of the 

85 See R. A. More O'Ferrall, J. Chem. Soc, B, 274 (1970) for a slightly different treatment. 

86 P. Beltrame, G. Biale, D. J. Lloyd, A.J. Parker, M. Ruane, and S. Winstein, J. Atner. Chem. Soc, 94, 
2240 (1972) and references therein. 

87 A. J. Parker, M. Ruane, D. A. Palmer, and S. Winstein, J. Amer. Chem. Soc, 94, 2228 (1972). 

1,2-Elimination Reactions 365 

Winstein-Parker spectrum is the E 2 transition state (42), in which the base pulls 
off the proton and pushes off the leaving group simultaneously. 88 



H--B H B 

\: / \: : \: :/ 

x i 

E 2 H E z E 2 C 

39 42 43 

When a hard base is used as catalyst, the reaction will be more E 2 H-like, 
whereas a soft base will cause it to be E 2 C-like. Weakly acidic substrates and 
good leaving groups also shift the reaction path to a more E 2 C-like mechanism. 

When hard bases are the catalysts, the rate of elimination of a compound 
depends on the proton basicity of the catalyst as shown in Equation 7.34 (where 
k E is the rate constant for bimolecular elimination) : 89 

log k E = log pK A + constant (7.34) 

Conversely, when soft bases are used, elimination rates, as would be expected 
from transition state 43, show no such correlation. Instead there is a relationship 
between the rate of elimination and the rate of S N 2 substitution by the base as 
shown in Equation 7.35 (where k s is the rate constant for bimolecular substitution 
and X is a constant) : 

log k E = X log k s + constant (7.35) 

For example, Figure 7.3 shows a plot of \og k E vs. log k s for cyclohexyl tosylate 
with a number of soft bases. 90 

Abstraction of the /3 proton in E 2 C reactions has a low isotope effect. For 
example, Reaction 7.36 has a A H /A D of only 2.3 91 This is consistent with the iso- 

88 Bunnett has contended that weak base-catalyzed eliminations do not involve bonding between the 
base and C„ but considers them to be part of the E 2 spectrum of which 39 and 41 are extremes. 
Bunnett suggests that weak hydrogen bases are good catalysts only when the leaving group is so 
good as to make possible a transition state in which the C„ — H bond breaking is very small. As 
evidence for his point of view he cites, for example, the facts that : ( 1 ) the rate of theophenoxide- 
catalyzed elimination of HBr from 1 is approximately five times faster than from 2; (2) in contrast, 
S„2 substitution is predominant with 2 but undetectable with 1 [J. F. Bunnett and D. L. Eck, J. 

H CH 3 H 

I I I 

H 3 C — C — C — CH3 H 3 C — C — CH 3 

Br CH 3 Br 

1 2 

Amer. Chem. Soc, 95, 1897, 1900 (1975)]. Bunnett maintains that if the E 2 C transition state involves 
partial bonding of the base to C;,, steric effects on the E 2 C transition state should be similar to those 
on the S N 2 transition state. It is difficult to assess this argument because in the looser E 2 C transition 
state (see p. 366) the nucleophile would be farther away from the (-butyl group. For a further dis- 
cussion of this controversy, see W. T. Ford, Accts. Chem. Res., 6, 410 (1973). 
89 This is the Brensted relationship. 

80 A.J. Parker, M. Ruane, G. Biale, and S. Winstein, Tetrahedron Lett., 2113 (1968). 
91 G. Biale, A. J. Parker, I. D. R. Stevens, J. Takahashi, and S. Winstein, J. Amer. Chem. Soc, 94, 
2235 (1972). 

366 Addition and Elimination Reactions 


O acetone, 75°C 
A ethanol, 35°C 
V methanol, 75°C 

i* ~OAc 

cr o/ 

y74-N02C6H 4 S _ 

k E 


Slope = 1.19 

Br~Q/o4-N02C6H 4 S" 
A> 4-N0 2 C6H 4 Cr 


1 / 

y^c 6 H 5 s- 

^ 4-N0 2 C 6 H 4 S _ 

1 1 1 

log k": 

Figure 7.3 Relationship between elimination and substitution rates of cyclohexyl tosylates 
with soft bases. From A. J. Parker, M. Ruane, G. Biale, and S. Winstein, 
Tetrahedron Lett., 2113 (1968). Reprinted by permission of Pergamon Press. 

tope effect expected from a nonlinear configuration of carbon, hydrogen, and 
base in the transition state. 92 

(D)H H 
I I 
CH 3 — C— C— CH 3 + Cl- 


From the effect of changing solvents on rates, it is apparent that an E 2 C 
transition state is loose — that is, both base and leaving group are solvated ions. 
For example, elimination of toluenesulfonic acid from cyclohexyl tosylate by 
CI ~~ proceeds only approximately 50 times faster in acetone than in methanol. 
Compare this with the rate enhancement of about 10 6 when the S#2 reaction of 
CH 3 OTs is transferred from protic to aprotic solvent. 93 (See also Section 4.3.) 
This indicates that the double bond must be highly developed in the transition 

Orientation of double bonds If the double bond can be oriented to- 
ward either of two carbons in an E 2 reaction, the product depends on where the 
transition state of the particular reaction lies in the spectrum. Since all E 2 transi- 
tion states have some double-bond character, the relative stability of the possible 
double bonds will always be of some importance to product determination. In an 
E 2 C reaction the double bond is apparently so highly developed at the transition 
state that the relative olefin stability is the controlling factor in deciding the pro- 
duct. In an E 2 H reaction, however, the relative acidity of the two kinds of 

92 See Section 2.7 and R. A. More O'Ferrall, J. Chem. Soc, B, 785 (1970). 

93 See note 86, p. 364. 

1 ,2-Elimination Reactions 367 
Table 7.12 Orientation of the Double Bond in the Products of Reaction 7.37 












N(Bu) 4 Br 



N(Bu) 4 Cl 









Source: R. A. Bartsch and J. F. Bunnett, J. Amer. Chem. Soc, 90, 408 (1968). Reprinted by permission 
of the American Chemical Society. 

Table 7.13 Products of Reaction 7.38 with Various Bases 

Percent Percent 

Base Solvent (CH 3 ) 2 C=CHCH 3 (CH 3 ) 2 CHCH=CH 2 


Source: G. Biale, D. Cook, D.J. Lloyd, A.J. Parker, I. D. R. Stevens, J. Takahashi, and S. Win- 
stein, J. Amer. Chem. Soc, 93, 4735 (1971). Reprinted by permission of the American Chemical 

hydrogens is of overriding importance to product determination. Since the 
acidity of the proton, the reactivity of the leaving group, and the strength of the 
base all help determine where the transition state lies in the spectrum, all of these 
affect the ratio of Hofmann to Saytzeff product. 

The strong electron-withdrawing ability of fluorine, which renders the j8 
protons acidic, the low reactivity of this halogen as a leaving group, and the 
strength of the base toward hydrogen assures that Reaction 7.37, when X = F, 
lies well toward the E 2 H end of the spectrum. The data in Table 7.12 show that, 

CH 3 (CH 2 ) 3 CH— CH 3 ~° CI S CH 3 (CH 2 ) 2 CH=CHCH 3 + 

^ CH 3 (CH 2 ) 3 CH=CH 2 (7.37) 

as expected, the more acidic primary protons are lost preferentially to the less 
acidic secondary ones, giving predominantly Hofmann-type product. In the 
series of increasing atomic weight, the halogens become simultaneously less 
electron-withdrawing and better as leaving groups; therefore as the fluorine is 
substituted in turn by CI, Br, and I, Reaction 7.37 moves more toward the E 2 C 
end of the spectrum and Saytzeff products become more important. 94 

The importance of the base in determining the nature of the transition state 
and thereby the product can be seen from Table 7.13. When Reaction 7.38 is 
carried out with KCMBu in f-butanol (E 2 H conditions), 76.9 percent Hofmann 
olefin is obtained. However, when the same reaction is carried out with 
+ N(Bu) 4 Br" (E 2 C conditions), 97.3 percent Saytzeff product is obtained. The 

' R. A. Bartsch and J. F. Bunnett, J. Amer. Chem. Soc, 90, 408 (1968). 

368 Addition and Elimination Reactions 

proportion of Saytzeff olefin in the ammonium bromide-catalyzed elimination is 
even higher than when the same substrate undergoes E^^ elimination. 95 

CH 3 

H 3 C H 

-C— CCH 3 
I I 
H OTs 



H 3 C H 

y v 


CH a 

CH 3 
+ CH 3 — C— CH=CH 2 



H. C. Brown has suggested that steric factors are of primary and almost sole 
importance in determining the position of the double bond. According to Brown, 
Hofmann product predominates when a large leaving group makes it even more 
difficult for the base to abstract the more hindered protons. 96 He has asserted that 
data similar to those of Table 7. 12, which seem at first glance to be contrary to his 
theory, support it further : He says that fluorine takes up more space in the transi- 
tion state than iodine because fluorine is more solvated. 97 However, the entropies 
of activation for Reaction 7.37 with X = F, CI, Br, or I are all very similar; 
therefore increased solvation of fluorine seems not to be the proper explanation 
for the preponderance of Hofmann product when X = F. 9B 

More recently, Bartsch and co-workers have shown that in E 2 H eliminations 
of HI from 2-iodobutane, the positional orientation of the double bond is con- 
trolled almost entirely by the strength of the base (if the attacking atom is kept 
constant) unless really outsized bases are used. 99 In Table 7.14 are listed some of 

Table 7.14 Relative Olefinic Proportions from Reactions of 2-Iodobutane 




pK a of Conjugate 
Acid in DMSO 

Percent 1- 
Butene in 
Total Butenes 

Butene: cis- 


Potassium /i-nitrobenzoate 


5.8 ± 0.1 



Potassium benzoate 


7.2 ± 0.2 



Potassium /j-nitrophenoxide 


7.5 ± 0.1 



Potassium o-nitrophenoxide 


7.5 ± 0.2 



Potassium acetate 


7.4 ± 0.1 



Potassium /i-aminobenzoate 


8.0 ± 0.2 



Potassium 2,6-di-tert-butyl- 


19.2 ± 0.4 



Potassium phenoxide 


11.4 ± 0.2 



Sodium 2,2,2-trifluoroethoxide 


14.3 ± 0.2 



Sodium methoxide 


17.0 ± 0.5 



Sodium ethoxide 


17.1 ± 0.4 



Sodium re-propoxide 


18.5 ± 0.3 



Potassium teri-butoxide 


20.7 + 0.4 


Source: R. A. Bartsch, G. M. Pruss, B. A. Bushaw, and K. E. Wiegers, J. Amer. Chem. Soc, 95, 3405 
(1973). Reprinted by permission of the American Chemical Society. 

95 G. Biale, D. Cook, D. J. Lloyd, A. J. Parker, I. D. R. Stevens, J. Takahashi, and S. Winstein, 
J. Amer. Chem. Soc, 93, 4735 (1971). 

96 See note 82, p. 362. 

97 H. C. Brown and R. L. Klimisch, J. Amer. Chem. Soc, 88, 1425 (1966). 

98 See note 94, p. 367. 

99 (a) R. A. Bartsch, G. M. Pruss, B. A. Bushaw, and K. E. Wiegers, J. Amer. Chem. Soc, 95, 3405 
(1973); (b) R. A. Bartsch, K. E. Wiegers, and D. R. Guritz, J. Amer. Chem. Soc, 96, 430 (1974). 

1 ,2-Elimination Reactions 369 

AAG*(kcal mole" 1 ) 


13 / 



>O l2 



8 / 

X 9 




4 r\ 

/ 2 



1 1 







Figure 7.4 Plot of the free-energy difference for formation of 1-butene and /ran.f-2-butene 
vs. the pK a of the conjugate acid of the base. System numbers refer to Table 7.14. 
From R. A. Bartsch, G. M. Pruss, B. A. Bushaw, and K. E. Wiegers, J. Amer. 
Chem. Soc, 95, 3405 (1973). Reprinted by permission of the American Chemical 

the oxyanion bases studied, the p^ a 's of their conjugate acids, and the products 
obtained. The ratio of to m-2-butene remains approximately con- 
stant, but the percentage of 1-butene changes by almost fourfold over the range 
of bases studied. From the product composition, Bartsch determined, for each 
reaction system, the difference in the free energies of activation for the formation 
of 1-butene and fra/tf-2-butene. In Figure 7.4 these values are plotted against the 
pAa's of the conjugate acids of the bases. A good straight line is obtained for all 
the bases studied except 2,6-di-<-butylphenoxide, for which the difference in 
energies of activation is smaller than would be expected from the pK a of 2,6-di-<- 

Stereochemistry 100 Since all E 2 transition states have some double- 
bond character, E 2 eliminations, if they are to go at all well, require that H and X 
be either syn- or anti-periplanar in the transition state. The two geometries for 
transition states of the E 2 H reaction are shown in Figure 7.5a and 7.5b. All 
other things being equal, anti elimination is expected to be of lower energy than 
syn elimination, since the transition state leading to the former (Figure 7.5b) is 
entirely staggered whereas the transition state leading to the latter (Figure 7.5a) 
is partially eclipsed. 101 For the E 2 C reaction, only anti elimination via a transi- 

100 For reviews, see: (a) J. Sicher, Angew. Chem. Int. Ed., 11, 200 (1972); (b) S. Wolfe, Accts. Chem. 
Res., 5, 102 (1972). 

101 J. Hine, J. Amer. Chem. Soc, 88, 5525 (1966). 

370 Addition and Elimination Reactions 




Figure 7.5 (a) Transition state for E 2 H-syn elimination, (b) Transition state for £ 2 H-anti 
elimination, (c) Transition state for E 2 C elimination. 

tion state similar to that shown in Figure 7.5c is expected, since base attacks the 
molecule backside to the leaving group but frontside to the /3 hydrogen. 

Let us now turn to the experimental results to see if these predictions are 
borne out in fact. It has long been known that E 2 H reactions normally give 
preferentially anti elimination. For example, reaction of Tn&ro-stilbene dibromide 
with potassium ethoxide gives m-bromostilbene (Reaction 7.39), whereas 
reaction of the D,L-dibromide gives the trans product (Reaction 7.40). 102 A 
multitude of other examples exist — see, for example, note 64 (p. 355) and note 82 
(p. 362). 


4> Br 

1 H <f> 


Br H 




Br d> 
\ / I 

I $ H 







E 2 H reactions do, however, give syn elimination when: (1) an H — X di- 
hedral angle of 0° is achievable but one of 180° is not or, put another way, H and 
X can become syn-periplanar but not trans-periplanar ; (2) a syn hydrogen is much 
more reactive than the anti ones; (3) syn elimination is favored for steric reasons; 
and (4) an anionic base that remains coordinated with its cation, that, in turn, is 
coordinated with the leaving group, is used as catalyst. The very great importance 
of category 4 has only begun to be fully realized in the early 1970s. 

P. Pfeiffer, Z. Physik. Chem. Leibzig, 48, 40 (1904). 

1 ,2-Elimination Reactions 371 

An example of category 1 is found in the observation by Brown and Liu that 
eliminations from the rigid ring system 44, induced by the sodium salt of 2- 
cyclohexylcyclohexanol in triglyme, produces norborene (98 percent) but no 
2-deuteronorbornene. 103 The dihedral angle between D and tosylate is 0°, but 

Crown ether present: 









that between H and tosylate is 120°. However, when the crown ether (45), which is 
an excellent complexing agent for sodium ion, is added to the reaction the 
amount of syn elimination drops to 70 percent (the sodium ion fits into the center 
of the crown ether molecule) . Apparently, coordination of the sodium ion to 
both the leaving group and the base in the transition state, as in 46, is responsible 
for some of the syn elimination from 44 in the absence of crown ether (category 4 
above). 104 







H OTs 






Category 2 is exemplified by E 2 elimination from 47, in which the tosylate 
group can become periplanar with either H x or H 2 . However, H x is activated and 

103 H. C. Brown and K.-J. Liu, J. Amer. Chem. Soc, 92, 200 (1970). 

104 R. A. Bartsch and R. H. Kayser, J. Amer. Chem. Soc, 96, 4346 (1974). When the leaving group is 
positively charged, reduced ion pairing reduces the amount of syn elimination : J. K. Borchardt and 
W. H. Saunders, J. Amer. Chem. Soc, 96, 3912 (1974). 

372 Addition and Elimination Reactions 

H 2 is not ; when treated with potassium /-butoxide in f-butanol at 50 C C, elimina- 
tion of Hj is greatly preferred. 105 However, when the crown ether, 48, is added, 
the amount of syn elimination is reduced. The results shown below are obtained. 


Again coordination of the cation must be partially responsible for the syn elimi- 
nation. 106 

Product of Elimination from 47 

[48], M \^~* ^ 

0.00 89.2 10.8 

0.031 46.5 53.5 

0.10 30.1 69.9 

0.22 30.8 69.2 

Source: From R. A. Bartsch, E. A. Mintz, and R. M. Parlman, J. Amer. Chem. Soc., 96, 4249 (1974). 
Reprinted by permission of the American Chemical Society. 

The role of steric factors in determining the syn/anti ratio has been investi- 
gated by Saunders and co-workers. From experiments with deuterated substrates 
they calculated that formation of 3-hexene from f-pentoxide-catalyzed decom- 
position of 3-n-hexyltrimethylammonium iodide (49) proceeds 83 percent by syn 
and 17 percent by anti elimination. They also found that syn elimination gives 
almost entirely trans olefin, but anti elimination gives cis product, a phenomenon 
noted previously and called the syn-anti dichotomy. Saunders proposed that the 
reason for the small amount of anti elimination is that the bulky trimethyl- 
ammonium group forces the terminal methyl groups on the n-hexyl moiety as far 
away from it as possible, and thus hinders approach to an anti hydrogen. (The 
two staggered rotamers of 49 in which one hydrogen is anti are shown in 49a and 
49b.) The anti hydrogen is less hindered in 49b, so that the anti elimination that 
does take place gives cis olefin. The major pathway, syn elimination, could occur 
from rotamers 49a, 49b, or 49c, but syn elimination from 49b or loss of H x from 

106 C. H. DePuy, R. D. Thurn, and G. F. Morris, J. Amer. Chem. Soc, 84, 1314 (1962). 
106 R. A. Bartsch, E. A. Mintz, and R. M. Parlman, J. Amer. Chem. Soc., 96, 4249 (1974). 

] ,2-Elimination Reactions 373 

49c would cause the two alkyl groups to be eclipsed in the transition state. These 
are the two pathways for syn elimination leading to cis olefin. Syn elimination 
from 49a and loss of H 2 from 49c allows the two alkyl groups to be anti in 

N(CH 3 ) 3 
H„ __ CH 

YTY \ 

CH 3 

N(CH 3 ) 3 
H 2 C^^H 


N(CH 3 ) 3 

H 2 C'^J^^H H 2 C'^7'^H H 2 C^^-^^H 


CH 3 







CH 2 
CH 3 

the transition state. Therefore syn elimination gives trans olefin. 107 In accord with 
Saunders' theory, other bulky ammonium salts also show the syn-anti dichotomy, 
whereas unhindered ones appear to eliminate entirely anti. 108 

E 2 C reactions give entirely anti elimination. This fact seems to be universal, 
and the need for anti elimination is even more important than formation of the 
most stable product. 109, 110 Thus, for example, 50 with N(Bu) 4 Cl gives >99.9 
percent 51, whereas the other diastereomer, 52, gives >99.9 percent 53. 111 
Of course, 51 is the more stable olefin. 

CH 3 

CH a O' 

CH 3 Q 

CH 3 

CH 3 

N(Bu) 4 Cl 


CH a O 


CH 3 


Because of the greater acidity of a vinylic than an alkyl proton, vinyl 
halides, RHC=CRX, are more likely than alkyl halides to undergo E 3 cB 
elimination. However, when the proton is not rendered even more acidic by a 
vicinal electron-withdrawing group, and when the basic catalyst is not too 
strong, E 2 reaction obtains. Then anti elimination is much the preferred pathway. 

107 D. S. Bailey and W. H. Saunders, Jr., J. Amer. Chem. Soc, 92, 6904 (1970). 

108 D. S. Bailey, F. C. Montgomery, G. W. Chodak, and W. H. Saunders, Jr., J. Amer. Chem. Soc. 
92,6911 (1970). 

109 See (a) note 86, p. 364; (b) note 95, p. 368. 

110 G. Biale, A. J. Parker, S. G. Smith, I. D. R. Stevens, and S. Winstein, J. Amer. Chem. Soc. 92, 1 15 

111 See note 95, p. 368. 

374 Addition and Elimination Reactions 

Thus, for example, 54 gives entirely 55 when treated with NaOMe in methanol, 
but under the same conditions 56 gives only the allene 57. 112 

CH 3 (CH 2 ) 2 Br 

; \ / NaOMe 

/C=C -^^ CH 3 (CH 2 ) 2 CeeeeC(CH 2 ) 2 CH 3 

H (CH 2 ) 2 CH 3 ' (7.44) 

54 55 

CH 3 (CH 2 ) 2 CH 2 CH 2 CH 3 

/C=C ^^> CH 3 (CH 2 ) 2 C=C=CHCH 2 CH 3 

H Br ' V H (7.45) 

56 57 

The substrate /3-Alkyl substituents affect the rate of E 2 eliminations 
differently depending on the leaving group. In ammonium and sulfonium salts 
they have little effect (but generally decrease the rate slightly), whereas in halides 
and tosylates they usually increase the rates. 113 These facts can be readily 
accommodated by the Winstein-Parker spectrum of transition states. The leaving 
group in an 'onium salt is relatively poor and strongly electron-withdrawing. 
Therefore eliminations from such compounds lie toward the E 2 H end of the 
spectrum and /3-alkyl groups, which decrease the acidity of the /3 hydrogen, 
decrease the rate of elimination. Eliminations from halides and tosylates lie 
farther toward the E 2 C end of the spectrum, in which the double bond is more 
well developed. Since alkyl groups increase the stability of a double bond, /? sub- 
stituents increase the rate of these reactions. 

a- Alkyl substituents have little effect on E 2 H-type reactions. However, they 
increase the rate of E 2 C-type reactions — again presumably because of the 
stabilizing effect of the alkyl group on the incipient double bond in the transition 
state. 114 In terms of hard and soft acid-base theory, it might also be said that 
alkyl substituents on the carbon make that carbon a softer acid and thereby 
render it more susceptible to attack by a soft base. Thus 58 reacts approximately 
250 times faster than 59 with N(Bu) 4 Cl. 115 


CH 3 CH 3 

CH 3 — C— CH 3 CH 3 — C— H 
Br Br 

58 59 

The leaving group The relative reactivity of a leaving group in an E 2 
elimination depends on where, in the spectrum of transition states, the transition 
state of the particular reaction lies. If the reaction is very E 2 C-like, the reactivities 

112 S. W. Staley and R. F. Doherty, J. Chem. Soc, D, 288 (1969). 

113 See note 82, p. 362. 

114 See note 86, p. 364, and note 95, p. 368. 
116 See note 95, p. 368. 

1 ,2-Elimination Reactions 375 


log* 5 

Figure 7.6 Response of rates of elimination of HX (log k E ) and substitution (log k s ) of 
cyclohexyl X, induced by NBu 4 Cl in acetone containing lutidine at 75°C, 
to change of leaving group X. From P. Beltrame, G. Biale, D. J. Lloyd, A. J. 
Parker, M. Ruane, and S. Winstein, J. Amer. Chem. Soc, 94, 2228 (1972). 
Reprinted by permission of the American Chemical Society. 

of the leaving groups correlate very well with their corresponding reactivities in 
the S w 2 reaction. For example, Figure 7.6 shows such a correlation between the 
rate of elimination of HX from cyclohexyl X by CI _ and the rate of bimolecular 
substitution of X in cyclohexyl X by CI ~. As might be expected, if elimination is 
more E 2 H-like, no such correlation exists. Then the electron-withdrawing ability 
of X becomes of primary importance in determining reactivity. 

Substitution vs. elimination Since in both S N 2 and E 2 reactions a 
Lewis base attacks the substrate and causes another Lewis base to depart from 
the substrate, these reactions naturally compete with one another. If it is k eptin 
mind, as s taJej_abovg 1 J:hat a and /3 substituents increase the rate_ofE Ji CLreac.tiQns, 
have li ttle ^ffec^on E 2 H reactions, but retard S^xeactions! the_predominant 
product can usu a lly~^ e!pxQ3iclMZ(IglITJ^ e 7.15). Thus, <-alkyl halides give 
principally elimination products with all bases. Secondary substrates are bor- 
derline and favor either elimination or substitution depending on the exact re- 
action conditions. For example, if the attacking reagent is a hard base, elimination 
competes well with substitution. If a soft base is used, unhindered secondary 
substrates give predominantly substitution, but hindered substrates give predom- 
inantly elimination. 

Eliminadmi£frorn_primary halides us ing soft jjasesdq^notj ake place at all, 
but eliminations _using. hard bases . do. 1 16 

116 See note 95, p. 368. 

376 Addition and Elimination Reactions 

Table 7.15 The Effect of Substrate and Base on the 

Competition Between Substitution and Elimination 






CH 3 


-C— Br 


CH 3 

CH 3 


CH 3 - 

-C— Br 


CH 3 

CH 3 - 

-CH— CH 3 



NBu 4 Cl Acetone 




NBu 4 Cl Acetone 







CH 3 — C — CH — CH 3 


NBu 4 Cl 



1 1 
H 3 C Br 

CH 3 


CH 3 — CH — C — CH 3 


NBu 4 Cl 



Br CH 3 

CH3CH2CH2 — Br 


NBu 4 CI 


CH3CH2CH2 — Br 





Source: G. Biale, D. Cook, D.J. Lloyd, A.J. Parker, I. D. R. Stevens, J. Takahashi, and S. Win- 
stein, J. Amer. Chem. Soc, 93, 4735 (1971), Table 1. Reprinted by permission of the American 
Chemical Society. 

Pyrolysis of Esters 117 

Pyrolyses of esters (60) and xanthate esters (61), either in the gas phase or in 

solution, give 1,2-elimination (Equations 7.46 and 7.47). These reactions are 

H R O „ „ O 

I I II A \ / N 

R_C— C— O— C— R' > C=Q + HO-C-R' 

I I 

R R 


H R S 


R— C— C— O— C— S— CH 3 
I I 
R R 







C=C + COS + CH 3 SH 
R R 


117 For a general review of olefin-forming eliminations in the gas phase, see: A. Maccoll, in The 
Chemistry of Alkenes, S. Patai, Ed., Wiley-Interscience, New York, 1964, p. 203; see also note 64(d) 
and 64(e), p. 355. 

Nucleophilic Addition to Multiple Bonds 377 

synthetically useful because, unlike E 1 and E 2 eliminations, there are no accom- 
panying side reactions such as substitution or rearrangement. Both types of 
pyrolyses give predominantly Hofmann elimination. Xanthates decompose at 
considerably lower temperatures than the corresponding esters, and therefore 
often give a higher yield of olefin and a lower yield of tar. They are conveniently 
prepared in situ by the reactions shown in Equation 7.48. 

H R 

I I 
R-C-C-OH + CS 2 + NaOH 
I I 
R R 

H R S 


->• R— C— C— O— C— S"Na H 

-* 61 (7.48) 

R R 

Isotope effects and the large negative entropies of activation for the pyrolyses 
make it appear probable that the transition states for Reactions 7.46 and 7.47 are 
62 and 63, respectively. Substituent effects, however, indicate that the transition 
states do have some polar character. 

O H. R 

R, -< x 

R R 




CH 3 — S— C 



.-H, /R 

-A v 

R R 



When the electron density of a carbon-carbon bond is reduced by strongly 
electron-withdrawing substituents, nucleophilic attack at one of the vinylic or 
acetylenic carbons may occur. Electron withdrawal may be either by induction 
or by resonance. Examples of nucleophilic addition are shown in Equations 

CF,=CFo + RSH 

ArCH=C(CN) 2 

*CH a N(CH3)30H 

o o o 


CH 2 =CH— C— CH 3 + CH 3 C— CH— C— OEt 

(1) KCN 


> CF 2 — CF 2 


> ArCH— CH(CN) 2 


(1) addition 
(2) protonation 

O CH 2 — CH 2 

CH 3 C— C— H 

>- I 




(7.49) 119 

(7.50) 120 

-C— CH 3 

(7.51) 121 

118 (a) S. Patai and Z. Rappoport, in The Chemistry of Alkenes, S. Patai, Ed., Wiley-Interscience, New 
York, 1964, p. 464; (b) E. Winterfeldt, Angew. Chem. Int. Ed., 6, 423 (1967). 

119 W. K. R. Musgrave, Quart. Rev. (London), 8, 331 (1954). 

120 See note 118(a). 

121 J. A. Markisz and J. D. Gettler, Can. J. Chem., 47, 1965 (1969). 

378 Addition and Elimination Reactions 

O o 9 CH 2 CH 2 -C^N 

(1) addition ^ CH 3 C- 

II 'I (l) addition pu r* r* XJ 

CH 2 =CH— C=N + CH 3 C— CH— C— OEt — > u,n 3 c— y— ±i , ? 52)1 

(2) protonation I \ "/ 



CF 3 H 

CH 3 C S CCF 3 + -OCH 3 " )add "' 011 > \=c( (7.53)i 

(2) protonation / \-ir- 

CH 3 


In general, the mechanisms of nucleophilic additions to double bonds have 
not been as much studied or systemized as those of electrophilic addition. 
Reactions 7.51 and 7.52 are examples of the very useful Michael condensation, 
in which a carbanion adds to an a,)3-unsaturated carbonyl or nitrile compound. 
The usefulness of these reactions arises from the fact that the number of ways of 
building longer carbon chains from smaller ones is limited. 

The mechanism of the Michael condensation is not actually a 1,2-addition 
as implied in Equations 7.51 and 7.52, but rather a 1,4-addition as shown in 
Equation 7.54. Protonation occurs first on the oxygen atom because 64b contri- 
butes more to the overall structure of the anion than 64a. The stereochemistry of 
1,2-addition in the Michael condensation is therefore irrevelant to the mechanism 
of the condensation. 124 Other nucleophilic additions to alkenes 125 and alkynes 128 
go either syn or anti depending on the particular reaction. 


II - II I H * 

R'~ + R 2 C=CR— C— R > R 2 C— C— C— R « »- R 2 C— C=C— R -2— > 

R' R R' R 

64a 64b 


I I il 

R 2 C— C=C— R > R 2 C— C— C— R (7.54) 


R' R R' R 

The rate-determining step in nucleophilic additions is usually nucleophilic 
attack on the multiple bond. 127 For example, the entropy of activation of a 
Michael condensation is always a large, negative quantity. This arises from the 
fact that in the transition state the five atoms, 0=C — C — C=0 of the anion 
and the four atoms, C=G — C=0 (or C=C — C=N) of the a,)3-unsaturated 
carbonyl (or nitrile) system are all restricted to one plane to allow maximum 

122 See note 121. 

123 E. K. Raunio and T. G. Frey, J. Org. Chem., 36, 345 (1971). 

124 R. A. Abramovitch, M. M. Rogic, S. S. Singer, and N. Venkateswaran, J. Org. Chem., 37, 3577 
(1972), and references therein. 

126 See note 118, p. 377. 

126 For example, see (a) E. Winterfeldt and H. Preuss, Chem. Ber., 99, 450 (1966) ; (b) K. Bowden and 
M. J. Price, J. Chem. Soc, B, 1466 (1970). 

127 See note 118, p. 377. 

Electrophilic Aromatic Substitution 379 

7r-overlap. 128 Nucleophilic additions in which the second step, protonation of the 
intermediate carbanion, is rate-determining are also known. 129 


The substitution of an electrophile for another group on an aromatic ring is 
electrophilic aromatic substitution (Equation 7.55) . Although the leaving group 
is most often H + , it may also be another Lewis acid. Perrin has found that the 
order of leaving group abilities is H + » I + > Br + > N0 2 + > Cl + , which is 

+ E 2 + > k^^Ji + Ei+ (7.55) 


also the order of the ability of the group to bear a positive charge. When E 1 in 
Equation 7.55 is not H — that is, when an electrophile attacks a substituted aro- 
matic ring, not ortho, meta, or para to the substituent but directly at the position 
bearing the substituent — then attack is at the ipso position. 131 

After a brief discussion of the nature of the attacking species in some of the 
most important types of electrophilic aromatic substitution, we shall examine the 
mechanism and the effect of substituents on rates and products. 

Substitution by halogen may be carried out in three ways: (1) by molecular 
halogenation, in which polarized X 2 itself acts as the electrophile (Equation 
7.56) ; (2) by molecular halogenation with a catalyst, in which the role of the 
catalyst is to polarize the halogen molecule; and (3) by positive halogenation in 
which the halogen is the cation of a salt. 132 

-X-X«++ I II >\ || + H + X- (7.56) 

Iodination by molecular iodine is slow and operates only when the aromatic 
substrate is particularly reactive. Iodination can, however, be effected by using 
O O 

IC1, CH 3 COI or CF 3 COI as reagents. Addition of zinc chloride to an iodination 
reaction in which I CI is the reagent increases the rate by assisting in breaking the 
I — CI bond. 133 Usually positive I + is the attacking reagent in these reactions. 
Bromination with molecular bromine takes place readily. The reaction is 

126 See note 121, p. 377. 

129 L. A. Kaplan and H. B. Pickard, J. Amer. Chem. Soc, 93, 3447 (1971). 

130 p or rev ; ewS) see: ( a ) L. Stock, Aromatic Substitution Reactions, Prentice-Hall, Englewood Cliffs, 
New Jersey, 1968; (b) R. O. C. Norman and R. Taylor, Electrophilic Substitution in Ben zenoid Com- 
pounds, Elsevier, Amsterdam, 1965; (c) E. Berliner, Prog. Phys. Org. Chem., 2, 253 (1964); (d) L. M. 
Stock and H. C. Brown, Adv. Phys. Org. Chem., 1, 35 (1963). For deviations from the "normal" 
mechanism, see P. B. D. de la Mare, Accts. Chem. Res., 7, 361 (1974). 

131 (a) C. L. Perrin, J. Org. Chem., 36, 420 (1971); (b) C. L. Perrin and G. A. Skinner, J. Amer. 
Chem. Soc, 93, 3389 (1971). 

132 R. M. Reefer and L. J. Andrews, J. Amer. Chem. Soc, 78, 5623 (1956). 

133 J. R. Barnett, L. J. Andrews, and R. M. Keefer, J. Amer. Chem. Soc, 94, 6129 (1972). 

380 Addition and Elimination Reactions 

normally carried out in acetic acid. Under these conditions the kinetics are 
second-order in bromine ; the second molecule of Br 2 polarizes the first, and the 
overall reaction is that of Equation 7.57. 

ArH + 2Br 2 > ArBr + H + + Br 3 - (7.57) 

The addition of I 2 to the reaction mixture increases the rate, because I 2 Br~ is 

O O 

formed more readily than Br 3 ~ . HOBr, CH 3 COBr and CF 3 COBr can also all be 
used as sources of electrophilic bromine, the last being particularly reactive. 134 
The attacking species is usually the entire molecule, but Br + may be formed at 
times. 135 Lewis acids such as A1C1 3 catalyze bromination by forming Br + as in 
Equation 7.58. 

A1C1 3 + Br 2 > AlCLjBr + Br + (7.58) 

Chlorination with molecular chlorine also occurs readily and is usually 
first-order in Cl 2 . Apparently chlorine is electronegative enough so that an addi- 
tional Cl 2 is not required to polarize the CI — CI bond at the transition state. 
Stronger Lewis acids such as FeCl 3 do, however, catalyze the reaction by assist- 
ing in bond polarization. HOC1 and CH 3 COCl also act as chlorinating agents, 

but free Cl + is never formed. The reactive species from HOC1 are C1 2 (formed 

by dehydration of two molecules of acid) and H 2 OCl, both of which deliver Cl + 

to the aromatic n system. 136 

Direct fluorination of aromatic rings is so exothermic that a tarry mixture of 
products is obtained. Reaction of benzene with the xenon fluorides, XeF 2 or 
XeF 4 , does give fluorobenzene, but the mechanism is probably free radical rather 
than polar. 137 

Nitration of an aromatic ring 138 to give ArN0 2 is most often carried out 
with nitric acid in sulfuric acid; however, concentrated nitric acid, aqueous 
nitric acid, and nitric acid in polar organic solvents are also commonly used, as is 
preliminary nitrosation followed by oxidation of the aromatic nitroso compound 
(ArNO). Alkyl nitrates (RON0 2 ) are also nitrating agents in the presence of 
some Bronsted and Lewis acids. 139 

When the reagent used is nitric acid, the attacking species is usually the 
nitronium ion, N0 2 + . That this ion exists has been abundantly proven. For 
example, cryoscopic measurements show that each molecule of nitric acid dis- 
solved in sulfuric acid gives rise to four ions. This result is best explained by the 
equilibria shown in Equations 7. 59-7.6 1. 140 Raman spectra also show that in 

134 See note 133. 

136 See, however, H. M. Gilow and J. H. Ridd, J. Chem. Soc, Perkin Trans. II, 1321 (1973). 

136 C. G. Swain and D. R. Crist, J. Amer. Chem. Soc, 94, 3195 (1972). 

137 (a) M. J. Shaw, H. H. Hyman, and R. Filler, J. Amer. Chem. Soc, 91, 1563 (1969); (b) T. C. 
Shieh, E. D. Feit, C. L. Chernick, and N. C. Yang, J. Org. Chem., 35, 4020 (1970). 

138 For a review, see: J. G. Hoggett, R. B. Moodie, J. R. Penton, and K. Schofield, Nitration and 
Aromatic Reactivity, Cambridge University Press, London, 1971. 

139 G. A. Olah and H. C. Lin, J. Amer. Chem. Soc, 96, 2892 (1974) and references therein. 

140 R. J. Gillespie, J. Graham, E. D. Hughes, C. K. Ingold, and E. R. A. Peeling, Nature, 158, 480 

Electrophilic Aromatic Substitution 381 

highly acidic media nitric acid is completely converted to NO a + . 141 In fact, 
nitronium salts such as N0 2 + BF 4 ~ have actually been isolated and can also be 
used for aromatic nitrations. 142 

HN0 3 + H 2 S0 4 __ 


HS0 4 + H 2 0— N0 2 


H 2 — N0 2 

1 H 2 + N0 2 ' 


H 2 + H 2 S0 4 , H 3 + + HS0 4 " (7.61) 

That the nitronium ion not only exists but also can be the reactive species 
has been shown. For example, the rate of nitration of toluene (and of other aro- 
matics) in solutions of nitric acid in nitromethane were independent of the 
concentration of toluene. 143 Thus the slow step must be the formation of the reac- 
tive species prior to attack on the toluene ring. This rules out HN0 3 as the nitrating 
agent. That protonated nitric acid, formed as shown in Equation 7.62, is not the 
reactive species follows from the fact that the rate does not become first-order in 

2HN0 3 z " H 2 6— N0 2 + NO3- (7.62) 

toluene when N0 3 ~ is added to the reaction. A rate first-order in toluene would 

be expected if H 2 — N0 2 were the nitrating agent, because the equilibrium in 

Equation 7.62 would be driven to the left and toluene would have to compete 

with N0 3 - for H 2 — N0 2 (see the discussion of the partition effect, p. 385). 144 

Protonated nitric acid has also been ruled out as the reactive species in aqueous 

sulfuric acid. At various acid strengths the rate of nitration correlates with the 

acidity function H R , which is defined by equilibria of the type shown in Equation 

7.63, rather than with the acidity function H , defined by equilibria of the type 

AOH + SH+ 7 " A+ + H 2 + S (7.63) 

shown in Equation 7.64 (see Section 3.3). 145 The fact that nitronium salts are 

AOH + SH+ > A— OH + S (7.64) 


excellent nitrating agents is direct proof of the ability of N0 2 + to substitute an 
aromatic ring. 146 

Nitronium ion is not, however, invariably the reactive species. For example, 
nitric acid in acetic anhydride shows a greater than usual selectivity between 
toluene and benzene (see p. 394) , indicating that another, less reactive, nitrating 
agent is formed. 147 

Sulfonation of an aromatic substrate to produce ArSO a H is usually brought 
about by reaction of the aromatic with concentrated sulfuric acid or with sulfur 

141 C. K. Ingold and D.J. Millen, J. Chem. Soc, 2612 (1950) and references therein. 

142 G. A. Olah, S. Kuhn, and A. Mlinko, J. Chem. Soc, 4257 (1956). 

143 G. Benford and C. K. Ingold, J. Chem. Soc, 929 (1938). 

144 E. D. Hughes, C. K. Ingold, and R. I. Reed, J. Chem. Soc, 2400 (1950). 

145 F. H. Westheimer and M. S. Kharasch, J. Amer. Chem. Soc, 68, 1871 (1946). 

146 See note 142. 

147 S. R. Hartshorn, R. B. Moodie, and K. Schofield, J. Chem. Soc, B, 1256 (1971). 

382 Addition and Elimination Reactions 

trioxide in organic solvents. 148 When S0 3 is used in fairly dilute solution, the 
attacking species is S0 3 itself. In concentrated sulfuric acid, however, the 
mechanism is more complex. Fuming sulfuric acid (in which the mole fraction of 
S0 3 > 0.5) is actually a mixture of S0 3 and ionized and nonionized monomers, 
dimers, trimers, and tetramers of H 2 S0 4 (the three latter formed by dehydration) . 
As more water is added, the tetramer and trimer disappear, and the amount of 
dimer decreases. The reactive species in sulfuric acid thus depends on the amount 
of water in the acid and on the reactivity of the substrate. The reactive species in 
aqueous sulfuric acid are H 2 S0 4 + and H 2 S 2 7 , the latter being more important 
at higher acid concentrations. In fuming sulfuric acid H 3 S 2 7 + and H 2 S 4 13 
are also involved. 149 

Aromatic compounds are usually readily alkylated or acylated by a Friedel- 
Crafts reaction. 150 The combination of reagents used most commonly for aro- 
matic alkylation is an alkyl halide with a strong Lewis acid (Equation 7.65). 
However, alkenes, alcohols, mercaptans, and a number of other types of organic 

R— X + A + ArH ► Ar— R + AX + H+ (7.65) 

compounds also alkylate aromatic rings when a Friedel-Crafts catalyst is present. 
The order of reactivity of Lewis acids as catalysts varies from reaction to reaction 
but is most commonly A1C1 3 > SbCl 5 > FeCl 3 > TiCl 2 > SnCl 4 > TiCl 4 > 
TeCl 4 > BiCl 3 > ZnCl 2 . The attacking species is sometimes the carbocation 

<J + 6- 

itself and sometimes an alkyl halide-Lewis acid complex (e.g., R — X-A1C1 3 ). 
For example, benzene reacts with n-propyl chloride at low temperatures to yield 
predominantly n-propylbenzene, but at higher temperatures cumene is the major 
product (Equation 7.66). 151 Isomerization most probably occurs via a free 

^/\^^CH 2 CH 2 CH 3 
+ CH 3 CH 2 CH 2 C1 -^v [Oj + 

-6°C 60% 

+ 35°C 40% 



148 For a review, see H. Cerfontain, Mechanistic Aspects in Aromatic Sulfonation and Desulfonation, 
Wiley-Interscience, New York, 1968. 

149 A. Koeberg-Telder and H. Cerfontain, Rec. Trav. Chim., 90, 193 (1971). 

150 For a comprehensive review of all aspects of the Friedel-Crafts reaction, see G. A. Olah, Ed., 
Friedel-Crafts and Related Reactions, Vols. 1-4, Wiley-Interscience, New York, 1963-1965. 

151 V. N. Ipatieff, H. Pines, and L. Schmerling, J. Org. Chem., 5, 253 (1940). 

Electrophilic Aromatic Substitution 383 

Acylations are most often carried out with BF 3 or A1C1 3 and an acyl halide, 
anhydride, ester, or a carboxylic acid (Equation 7.67). 


° - R-C 

BF 3 or 
A1C1 ; 

R - c - Y + O 5r O + HY ^ 


Y = halide, OCR, OR, or OH 

Apparently the attacking species is most often an acyl cation, R — C=0 < > 

R— C=6. 152 

The action of nitrous acid on aromatic amines produces aromatic diazonium 
ions (Equation 7.68), which are weak electrophiles. Correlation of the rate of 

ArNH 2 + HNO a — — ► ArN=N OH" + H z O (7.68) 

diazonium coupling, as Reaction 7.69 is called, with pH shows that the reactive 
species must be the free diazonium ion rather than ArN 2 OH. 153 

ArN 2 + OH- + Ar'H > ArN=NAr' + H 2 (7.69) 

Some metals, such as mercury and thallium, that form covalent carbon- 
metal bonds react in electrophilic aromatic substitutions. Both ionic [e.g., 
Hg(C10 4 ) 2 ] and covalent [e.g., Hg(OAc) 2 ] mercuric compounds react; the 
attacking species, depending on the reagent and on the reaction conditions, may 
be Hg 2 + , HgX + , or HgX 2 . 154 The only reagent that has been found to give high 


yields of arylthallium compounds is Tl(OCCF 3 ) 3 . 155 The nature of the attacking 

O O 

II + II 

species has not been studied, but presumably it is Tl(OCCF 3 ) 3 or Tl(OCCF 3 ) 2 . 


The products, ArTl(OCCF 3 ) 2 , are useful in organic synthesis because the thallium 
group can be introduced into a substituted aromatic ring highly regiospecifically 
and can then be replaced by another group such as I or CN. An example is 
shown in Scheme 3. Regiospecific introduction of aromatic substituents by direct 
means is often difficult to carry out (see p. 39 1 ) . 

152 F. R. Jensen and G. Goldman, in Friedel-Crafts and Related Reactions, G. A. Olah, Ed., Vol. 3, 
p. 1003. 

153 R. Wistar and P. D. Bartlett, J. Amer. Chem. Soc, 63, 413 (1941). 

154 (a) A.J. Kresge, M. Dubeck, and H. C. Brown, J. Org. Chem., 32, 745 (1967) ; (b) C. Perrin and 
F. H. Westheimer, J. Amer. Chem. Soc, 85, 2773 (1963). 

155 (a) E. C. Taylor and A. McKillop, Accts. Chem. Res., 3, 338 (1970) ; (b) A. McKillop, J. D. Hunt, 
M.J. Zelesko, J. S. Fowler, E. C. Taylor, G. McGillivray, and F. Kienzle, J. Amer. Chem. Soc, 93, 
4841 (1971); (c) E. C. Taylor, F. Kienzle, R. L. Robey, A. McKillop, and J. D. Hunt, J. Amer. Chem. 
Soc, 93, 4845 (1971). 

384 Addition and Elimination Reactions 

Scheme 3 


2*-'n2 v - ,n 3 


a ^n 2 un 3 


73° C 

2 V-Jii2 v - ,J ^ 1 3 

oi ° 

^TI(OCCF 3 ) 2 

+ Til 



+ Til 

(Note that the replacement of Tl by I is an oxidation-reduction reaction.) 

A priori, the two most likely mechanisms for electrophilic aromatic substi- 
tution on benzene, in the absence of strong base, 156 are (1) direct displacement, 
the transition state for which is shown in 65, and (2) a two-step reaction in which 


156 At least two other special mechanisms exist that are not considered in this chapter. The first is 
electrophilic aromatic substitution via a carbanion. This pathway is sometimes followed if a strong 
base is present or if the substrate is a metal-substituted aromatic. For example, Mach and Bunnett 
have found that the presence of i-BuOK, i-BuOBr brominates 1,3,5-tribromobenzene by the 
mechanism shown below: 


H H H 

[M. H. Mach and J. F. Bunnett, J. Amer. Chem. Soc, 96, 936 (1974). For other examples see this paper 
and J. F. Bunnett, Accts. Chem. Res., 5, 139 (1972).] 

The second special mechanism that we shall not consider is actually not a separate mechanism 
but is an electrophilic addition to one of the aromatic double bonds followed by an elimination 
reaction. An example is shown below: 


+ Cl 2 


- HOAc 

This reaction generally requires both a reactive electrophile and a reactive aromatic. For a discussion 
of it and the pitfalls of not recognizing that it occurs see ref. 1 d. 

Electrophilic Aromatic Substitution 385 

the electrophile first forms some sort of intermediate complex with the aromatic 
ring and subsequently a proton is lost (Equation 7.70). 

E + + I U I ^^ IUI E+ -f-> I U I +BH (7.70) 




In experiments of major importance, first published in 1950, Melander 
found that in the nitration and bromination of a number of benzene derivatives 
the tritium isotope effect [k s jk T ) is not 10-20 as is to be expected if carbon- 
hydrogen bond breaking occurs in the rate-determining step, but rather is less 
than 1.3. The direct displacement mechanism was thus ruled out, and the two- 
step mechanism of Equation 7.70 with the first step rate-determining was 
implicated. 157 

Examination of the rate equation for the mechanism of Equation 7.70 
reveals the probable origin of the small isotope effects observed by Melander. 
Using the steady-state approximation for the concentration of the intermediate 
complex (66), the observed rate is calculated to be 

rate = [Ar][E + ] 2L J ' — (7.71) 

1 + (k 2 B/k^) 

When the second step is very fast compared to the reverse of the first step — that 
is, when ^[BJ/A.i » 1 — Equation 7.71 can be simplified to 

rate = ^[ArjrE + J (7.72) 

In this case a primary isotope effect of 1.0 would be expected, since only the rate 
constant for the first step, in which no bond breaking occurs, is involved in the 
rate equation. When the reverse of the first step is very fast compared to the 
second step — that is, k 2 [B]lk_ 1 « 1 — then the observed rate is linear with k 2 as 
shown in Equation 7.73. 

kik 2 TBI 
rate = [Ar][E + ] ' J (7.73) 

In this case a large isotope effect would be expected. If, however, k 2 [B] X k_ u 
then Equation 7.71 cannot be simplified, and the magnitude of k 2 will affect the 
overall rate albeit in a less than linear way. Then, even if k 2 > k lt some isotope 
effect should be observed. The small isotope effect of Melander's experiments 
make it appear that the first step is slower than the second, but that k^ 1 competes 
favorably with k 2 . When the second step becomes kinetically important in spite 
of the first step being the slow step, we have an example of the partitioning effect — 
so-called because the kinetic significance of the second step arises from the way 
in which the intermediate partitions itself. Since 1950 a very large number of 
electrophilic substitutions have been examined for isotope effects ; in the absence 
of special circumstances (see below), the isotope effects found are usually very 
small. 158 

157 L. Melander, Ark. Kemi, 2, 211 (1950). 

158 For reviews, see note 130(c) and H. Zollinger, Adv. Phys. Org. Ctiem., 2, 163 (1964). 

386 Addition and Elimination Reactions 

Studies of the effect of base concentration on rate also provide strong sup- 
port for the two-step mechanism. The simple displacement mechanism with 
transition state 65 should be first-order in base, as can be seen from the rate 
equation for this mechanism, 

rate = £ 3 [Ar][E + ][B] (7.74) 

In the two-step mechanism, if k 2 [B]/k_ 1 » 1, no base catalysis whatsoever 
should be observed; if k 2 {B]/k_ 1 « 1, a linear dependence on base is expected; 
and if A: 2 [B]/A;_ 1 X 1, nonlinear dependence on base should result. 

Zollinger observed that Reaction 7.75 is not catalyzed by pyridine and does 
not show an isotope effect. 159 In this case the two-step mechanism must be 
operative, and k 2 is so large that k 2 \B\jk_ 1 is always much larger than 1 even at 




CI + 


S0 3 - SO-s- 

low base concentrations. For Reaction 7.76, however, there is a nonlinear 
correlation between rate and the concentration of pyridine. A deuterium isotope 



r \ 

C1 + 

so 3 - 



effect (k H lk D ) of 6.55 was found for this reaction in pure water, but at pyridine 
concentrations of 0.0232 M and 0.905 M it decreased to 6.01 and 3.62, respec- 
tively. 160 The fact that the rate is not first-order in base rules out both a simple 
displacement mechanism and a two-step mechanism with proton loss rate- 
determining (see Equation 7.73). We shall return shortly to a consideration of 
why this reaction is catalyzed by base and has an isotope effect after we have 
ascertained the nature of the intermediate (66) in electrophilic aromatic substi- 

Two possibilities for the intermediate complex (66) exist. The first is a w 
complex (68) in which the electrophile is coordinated with the entire n system or 

159 R. Ernst, O. A. Stamm, and H. Zollinger, Helv. Chim. Acta. 41, 2274 (1958). 

160 H. Zollinger, Helv. Chim. Acta, 38, 1597, 1623 (1955). 

Electrophilic Aromatic Substitution 387 

with a single it bond as shown in 68 and 69. 161 The second possibility for 66 is 70, 
a a complex in which the electrophile has formed a a bond with one carbon of the 
aromatic ring. 162 


it complex 7r complex a complex 

68 69 70 

There is an abundance of evidence that both n complexes and a complexes 
exist as stable species. For example, nmr studies have shown that the GH 2 protons 
of the ethyl fluoride-boron trifluoride complex absorb at slightly lower fields in 
the presence of toluene. Thus a new complex, which includes toluene and in which 
the CH 2 group bears more positive charge than it does in the absence of toluene, is 
formed. However, the aromatic protons of toluene absorb at almost the same 
frequency in the presence of BF 3 -FCH 2 CH 3 as in its absence; 183 thus, the new 
complex is probably that shown in 71. 



Another example is the complex that benzene forms with iodine. The infrared 
spectrum in a frozen nitrogen matrix shows that in the complex, the benzene 
symmetry in the ring plane is not altered. The n complex 72, with the iodine 
axial, has been proposed as the structure. 164 



Sigma complexes have also been observed in the nmr. For example, when 
m-xylene is dissolved in HF + SbF 5 at - 35°C, the proton magnetic resonance 
spectrum shown in Figure 7.7 is obtained. The peak at 4.7 ppp downfield from 
TMS is due to two parafinnic protons. The structure that best fits the spectrum 

181 (a) G. A. Olah, S. Kobayashi, and M. Tashiro, J. Amer. Chem. Soc, 94, 7448 (1972); (b) D. V. 
Banthorpe, Chem. Rev., 70, 295 (1970). 

162 G. A. Olah and Y. K. Mo, J. Amer. Chem. Soc, 94, 9241 (1972). 

163 T. Oyama and R. Nakane, J. Org. Chem., 34, 949 (1969). 

164 L. Fredin and B. Melander, J. Amer. Chem. Soc, 96, 1672 (1974). 

388 Addition and Elimination Reactions 

Figure 7.7 Proton magnetic resonance spectrum at 60 Mc/sec of the 4H + -m-xylenonium 
ion in HF + SbF 5 at -35°C. From D. M. Brouwer, E. L. Mackor, and C. 
MacLean, in Carbonium Ions, G. A. Olah and P. v. R. Schleyer, Eds., Wiley- 
Interscience, New York, 1970, Vol. 2, chap. 20. Reprinted by permission of 

is 73. At higher temperatures the spectra of aromatic o- complexes usually change; 
the lines broaden and eventually coalesce due to intramolecular hydrogen shifts. 165 
A few stable a complexes such as 74 and 75 have been prepared and isolated in 
the form of salts. 166 

CH 3 



73 74 75 

The fact that n and a complexes do form is not proof that either or both are 
intermediates in electrophilic aromatic substitution. However, Table 7.16 gives 
strong evidence that a complexes are the usual intermediate. Electron-donating 
groups greatly stabilize a complexes of benzene derivatives but only slightly 

165 For reviews, see: (a) G. A. Olah, Angew. Chem., Int. Ed., 12, 173 (1973); (b) D. M. Brouwer, 
E. L. Mackor, and C. MacLean, in Carbonium Ions, G. A. Olah and P. v. R. Schleyer, Eds., Wiley- 
Interscience, New York, 1970, Vol. 2, chap. 20. 

166 G. A. Olah and S. J. Kuhn, J. Amer. Chem. Soc, 80, 6535, 6541 (1958). 

Electrophilic Aromatic Substitution 389 

Table 7.16 Relative Rates of Aromatic Substitutions and Relative a and 77 
Complex Stabilities of Methylbenzenes 



Relative Rate 

Relative Rate 

a Complex 

■n Complex 

of Bromination, 

of Chlorina- 




Br 2 in 85% 

tion, Cl 2 in 


(ArH4-HF— BF 3 )° 

with HC1° 


















1,3- Dimethyl 
















































Source: G. A. Olah, Accts. Chem. Res., 4, 240 (1971). Reprinted by permission of the American 

Chemical Society. 

From equilibrium constant measurements. 

stabilize it complexes. Thus 1,2,3,5-tetramethylbenzene forms a complexes that 
are 2 billion times more stable than those of toluene, but its v complexes are only 
more stable than those of toluene by a factor of 3. The rate of bromination of 
benzene derivatives also increases drastically with methyl substitution; and the 
relative rates are very similar to the relative stabilities of the a complexes. 
Apparently the transition state resembles the a complex. As Table 7.16 shows, 
there is also a close correlation between rates of chlorination in acetic acid and a 
complex stability. 

Now that we have determined that the intermediate in electrophilic aro- 
matic substitution is usually a a complex (see, however, p. 394), let us return to a 
consideration of Reaction 7.76. Two factors probably combine to cause the 
observed isotope effect and base catalysis. First, the strong electron-donating 
groups stabilize the intermediate 76 (Equation 7.77) and make departure of the 
proton more difficult than proton loss in many other electrophilic substitutions. 
[Remember, however, that k 1 < k 2 (see p. 386).] Second, steric interactions 
between the large diazonium group and the nearby substituents increase the rate 




390 Addition and Elimination Reactions 

of decomposition (k^) of 76 back to starting material. Both factors, then, work 
together to cause A 2 [B]/A;_ 1 in water to be small, and a large isotope effect is 
observed. As [B] is increased, the ratio necessarily becomes larger and the isotope 
effect decreases. 167 The effect of steric factors on the size of the isotope effect is 
neatly demonstrated by the fact that the isotope effect for bromination of 77, 78, 
79, and 80 increases in the order 77 < 78 < 79 < 80. 168 

© )°i y°i. isx 

77 78 79 80 

A few examples are known in which the second step of an electrophilic aromatic 
substitution is rate-determining. For example, 67 is brominated by Br 2 and BrOH 
at approximately the same rate, even though the latter is usually much the more 
reactive reagent. Moreover, the rate of reaction is first-order in base. These facts 
point to the two-step mechanism pf Equation 7.70 with the second step rate- 
determining. 189 

As has already been mentioned, in a two-step mechanism in which the first 
step is rate-determining, electron-donating groups on the aromatic ring increase 
the rate of electrophilic aromatic substitution. Likewise, electron-withdrawing 
groups decrease it. The overall rate enhancement (or dimunition) arises from a 
sum of the group's inductive (/) and resonance (R) effects. Table 7.17 gives the 
relative rates of mononitration of a number of benzene derivatives. 

Aromatic substituents that increase the rate relative to hydrogen direct the 
electrophile predominantly to the ortho and para positions. Substituents that 

Table 7.17 Relative Rates of Nitration of Benzene Derivatives" 
R in C 6 H 5 R Relative Rate 



CH 3 ' 




CH 2 C1 

CH 2 CN 





C0 2 CH 2 CH 3 

CH 2 N(CH 3 ) 3 
N0 2 

2.6 x 10- 5 
6 x 10" 8 

■N(CH 3 ) 3 

1.2 x 10-8 

Source: C. K. Ingold, Structure and Mechanism in Organic Chemistry, 2nd ed., Cornell University Press, 
Ithaca, N.Y., 1969, p. 290. Reprinted by permission of Cornell University Press. 
° The reaction conditions were not the same for all the nitrations listed, and therefore the relative 
rates are only approximate. However, apparently none of the nitrations were carried out using 
conditions under which formation of + N0 2 is rate-determining or using the very reactive, unselec- 
tive + N0 2 X" salts. 

167 See note 160, p. 386. 

168 E. Baciocchi, G. I. Illuminati, G. Sleiter, and F. Stegel, J. Amer. Chem. Soc, 89, 125 (1967). 

169 M. Christen and H. Zollinger, Helv. Chim. Acta, 45, 2057, 2066 (1962). 

Electrophilic Aromatic Substitution 391 

decrease the rate (except for the halogens, see Problem 7.11) direct the electro- 
phile predominantly to the meta position. To understand why this is so, we must 
consider the nature of the transition state, but since the transition state is often 
similar to the a complex we shall use the a complex as a model for the transition 

If the electrophile attacks the benzene ring at a position ortho or para to a + / 
substituent (i.e., to one electron-donating by inductive effect), the activated com- 
plex will be similar to 81 or 82, respectively. Resonance structures 81c and 82c 
are of particularly low energy because in these the positive charge is localized on 
the carbon that bears the + / group. Attack at the meta position does not allow 
such a resonance structure to be drawn. 

If attack is ortho or para to a group that is electron-donating by resonance 
( — O — R, — NR 2 are, for example, + R groups) an additional resonance struc- 
ture for the transition state can be drawn (81d or 82d, respectively). There is no 
such stabilization for meta substitution. 

->■ etc. 

81c 81d 

Now we can also understand why meta attack is preferred in a deactivated 
ring. Only if attack is at that position do none of the resonance structures of the 
transition state have a positive charge on that carbon that bears the electron- 
withdrawing group. 

392 Addition and Elimination Reactions 
Z Z 

Because the rate of substitution varies with position, in a benzene derivative 
it is more informative and frequently more useful to talk about partial rate factors 
than about relative rates. A partial rate factor is denned as the rate at one particular 
position in the benzene derivative relative to the rate of substitution at one position 
in benzene. Let us, for example, calculate the para and meta partial rate factors 
{p ; and m f , respectively) for bromination of toluene with bromine in aqueous 
acetic acid. Toluene brominates 605 times faster than benzene under these 
conditions. The product is 66.8 percent p-, 0.3 percent m-, and 32.9 percent o- 
bromotoluene. Attack at the para position of toluene occurs 0.668 x 605 times 
as fast as attack at all six positions of benzene but (0.668 x 605 x 6 = 2420) 
times as fast as at one position of benzene. Therefore p f CH: > for bromination of 
toluene under these conditions is 2420. There are only three times as many total 
carbons in benzene as meta carbons in toluene. Therefore m f CH 3 = 0.003 x 
605 x 3 = 5.5. The definitions of the partial rate factors for monosubstituted 
benzenes {<f> — R) are given in Equations 7.78-7.80. 


7o para 




% meta 




% ortho 






The rates of electrophilic substitutions at the para and meta positions of 
benzene derivatives can be correlated by the linear free-energy relationships 
shown in Equations 7.81 and 7.82. 170 

log/,/ = <j p + p (7.81) 

\ogm f *=<j m +p (7.82) 

The substituents in a benzene derivative may affect the rate of electrophilic attack 
at the ortho position by steric interaction and secondary bonding (e.g., hydrogen 
bonding or charge-transfer complexing) as well as by electrical influence. There- 
fore a + is not necessarily constant but depends on the size and nature of the 
electrophile, and a correlation of rates of ortho substitution is less satisfactory. 
(See Section 2.2, p. 61 and Figure 2.2.) 

In general, the less reactive a reagent is, the more selective it is in attacking 
an activated rather than a deactivated site. In 1953 H. C. Brown observed that 

S f = log 


CH 3 

m f c *3 


170 See note 130(d), p. 379. 

Electrophilic Aromatic Substitution 393 

Figure 7.8 The relationship between S f and \ogp f CH s for a number of electrophiles. 
From L. M. Stock'and H. C. Brown, Advan. Phys. Org. Chem., 1, 35 (1963). 
Reprinted by permission of Academic Press (London). 

the selectivity of an electrophile in choosing between the para and meta positions 
of toluene is linearly related to its selectivity in choosing between toluene and 
benzene. If the selectivity factor, S f , is defined by Equation 7.83, then the inter- 
and intramolecular selectivities are correlated by Equations 7.84 and 7.85 in 
which b and b' are empirical constants. These empirical equations can also be 

log/.^H 3 = bSj (7 . 84) 

log m, CH 3 = b'S, (7.85) 

derived from the linear free-energy relationships of Equations 7.81 and 7.82. 171 
If, for example, 7.82 is subtracted from 7.81 and 7.81 is divided by the result, one 
obtains, after rearrangement 

a p(CH 3 ) — " m(CH 3 ) 

Thus b of Equation 7.84 is 

° P(CH3) (7.87) 

<* P(CH 3 ) — o m(CH 3 ) 

Figure 7.8 shows the straight line obtained when S f , for a wide variety of 
nucleophiles, is plotted against the p f cn * factor for these reagents. One point 
deviates sharply from the line. That point corresponds to nitration with 
N0 2 + BF 4 ~. (Similar deviations are also found for other highly reactive electro- 
philes not shown on this plot. 172 ) This reagent is very unselective in choosing 

171 See note 130(d). 

172 (a) G. A. Olah, Accts. Chem. Res., 4, 240 (1971) ; (b) G. A. Olah and S. Kobayashi, J. Amer. Chem. 
Soc., 93,6964 (1971). 

394 Addition and Elimination Reactions 

Table 7.18 Relative Rates of Aromatic Nitration of Benzene 
Derivatives with N0 2 + BF 4 _ and with CH 3 ON0 2 -BF 3 

Benzene Derivative N0 2 + BF 4 - in Sulfolane" in Nitromethane 

H 1.0 1.0 

Methyl 1.6 25.5 

1,2-Dimethyl 1.7 192.3 

1,3-Dimethyl 1.6 285.5 

1,4- Dimethyl 1.9 295.5 

1,2,3-Trimethyl 914.6 

1,2,4-Trimethyl 1076.2 

1,3,5-Trimethyl 2.7 956.8 

1,2,3,4-Tetramethyl 2154.5 

1,2,3,5-Tetramethyl 1861.2 

1,2,4,5-Tetramethyl 2188.3 

Pentamethyl 2545.3 

" G. A. Olah, S.J. Kuhn, and S. H. Flood, J. Amer. Chem. Soc. 83, 4571 (1961). 
6 G. A. Olah and H. C. Lin, J. Amer. Chem., Sac., 96, 2892 (1974). 
Reprinted by permission of the American Chemical Society. 

between toluene and benzene, but if it does choose toluene it is very selective in 
substituting at the ortho and para positions rather than the meta. Further study 
of this reagent reveals that it is only three times more reactive to 1,3,5-trimethyl- 
benzene than it is to benzene. (Compare this to a factor of 2 x 10 6 when the 
electrophile is Br 2 in acetic acid, Table 7.16.) Relative rates of nitration of a 
number of methylated benzenes by N0 2 + BF 4 " are shown in Table 7.18. Olah 
has attributed the low intermolecular selectivity to the transition state structure. 
He has suggested that when the electrophile is very reactive, the transition state 
resembles the starting material and is similar to a 77 complex. Since methylation 
does not much increase the stability of a 77 complex (Table 7.16), it would thus 
not much increase the rate of nitration. 

According to Olah, the high intramolecular sensitivity arises from the 
orbital symmetry requirements of this transition state. The electrophile can only 
interact with two p orbitals that have the same sign in the highest occupied 
molecular orbital (83). Thus transition states 84 and 85 are possible, but 86 is not. 

CH, tj CH 3 


83 84 85 86 

The activated complex 84 can open only to the ortho a complex; 85 opens to the 

para and (less often) to the meta a complex. 173 

Olah's original experiments, in which the intermolecular selectivities were 

determined by direct competition for the electrophile by toluene and benzene, 

have given rise to controversy and criticism. 174 Schofield and Moodie suggested 

173 See note 161(a), p. 387. 

174 For a summary, see J. H. Ridd, Accts. Chem. Res., 4, 248 (1971) and also C. D. Johnson and K. 
Schofield, J. Amer. Chem. Soc, 95, 270 (1973). 

Nucleophilic Aromatic Substitution 395 

that the reactions in question do have transition states similar to the u complexes 
but are so fast that they are essentially over before the reactants are mixed ; the 
ratio of products then depends on the local concentrations of the two aromatic 
substrates. To settle the controversy, Olah attempted to determine the rates of 
nitration of benzene and of toluene by N0 2 + BF 4 ~ separately, but they were too 
fast for measurement. More recently, Olah and Lin carried out competitive 
nitrations using methyl nitrate (CH 3 ON0 2 ) as a nitrating agent. 175 In the ab- 
sence of catalysts this compound is inert to aromatic compounds, but in the 
presence of BF 3 it is highly reactive (see p. 380) . Thus the aromatic compounds 
and the nitrating agent could be well mixed before the reaction was started. As 
Table 7.18 shows, the intramolecular selectivity of this nitrating agent is much 
greater than that of N0 2 + BF 4 ~ and is apparently similar to that of more classical 
nitrating agents (see Table 7.17). For the purposes of settling the controversy, 
then, the results are inconclusive. Olah suggests that CH 3 ON0 2 -BFg is more 
selective than N0 2 + BF 4 ~ because the nitrating agent is not free N0 2 + but a 
polarized complex, 87. Thus to reach the transition state the N — O bond must be 

CH3— 9---N0 2 
S-BF 3 


further weakened. It is possible, however, that poor mixing is responsible for the 
results with NO a + BF 4 - . 176 


Because H~ is not a good leaving group, nucleophilic displacements on unsub- 
stituted aromatics rarely occur. However, if there is a suitable leaving group on 
the ring, nucleophilic aromatic substitution may take place by one of three 

If the ring bears strongly electron- withdrawing substituents as well as a good 
leaving group, nucleophilic displacements (called S N Ar or activated aromatic 
nucleophilic substitutions) take place under mild conditions. The kinetics are 
second-order, first-order each in aromatic substrate and in nucleophile. An 
example is shown in Equation 7.88. 178 A body of evidence has been accumulated 

-CH 3 


H 3 COOCr \x""-N0 2 \/ H.,COOC 


175 See note 139, p. 380. 

176 For theoretical calculations having to do with this point see W. J. Hehre and P. C. Hiberty, 
J. Amer. Chem. Soc, 96, 7165 (1974). 

177 (a) J. Miller, Nucleophilic Aromatic Substitution, Elsevier, Amsterdam, 1968; (b) J. F. Bunnett, 
Quart. Rev. (London), 12, 1 (195a). 

178 P. Carniti, P. Beltrame, and Z. Cabiddu, J. Chem. Soc, Perkin II, 1430 (1973). 

396 Addition and Elimination Reactions 

that points to an addition elimination mechanism (Equation 7.89) for these 
reactions that is analogous to the mechanism for electrophilic aromatic substi- 

X + Y- 

- (oy^ 



Meisenheimer first showed that a complexes (88) can exist by isolating 89 in 
the form of a salt. 179 Since then a host of other Meisenheimer complexes have been 
isolated or identified by spectroscopy or other physical methods. 180 But the 
existence of Meisenheimer complexes does not prove that they lie on the reaction 

.CH 3 

H 3 Cs 



path of S A -Ar reactions. That they do is corroborated by the relative reactivities 
of the halides as leaving groups. In a one-step displacement, the leaving group 
order should be the same as in aliphatic S N 2 reactions, that is, I > Br > CI > F. 
However, fluorinated aromatics are often much the most reactive compounds. 
For example, Reaction 7.90 is 3300 times faster when X = F then when X = I. 


H— N 

N0 2 

+ HX 




On the other hand, leaving groups that are similar in electronegativity but 
different in other chemical properties are similar in reactivity. As X in Reaction 
7.90 is changed, the rate decreases in the order Br > CI > — S0 2 C 6 H 5 > 
— OC 6 H 4 N0 2 -/> > I, but there is only a fivefold difference in reactivity between 
Br and I. 181 The greater reactivity of fluorinated aromatics and the absence of an 
"element effect" point to a two-step mechanism in which expulsion of the leaving 
group is not involved in the rate-determining step. 

The second step does become rate-determining when the nucleophile is 
more reactive or when the leaving group is poor. For example, E A for Reaction 
7.91, in which polarizable sulfur is the attacking atom, is 0.4 kcal mole -1 greater 

179 J. Meisenheimer, Ann., 323, 205 (1902). 

180 (a) M. R. Crampton, Adv. Phys. Org. Cham., 7, 211 (1969); (b) M.J. Strauss, Accts. Chem. Res., 7, 

181 (1974). 

181 J. F. Bunnett, E. W. Garbisch, Jr., and K. M. Pruitt, J. Amer. Chem. Soc, 79, 385 (1957). 

Nucleophilic Aromatic Substitution 397 

when X = F than when X = I. 182 Bunnett has demonstrated the effect of the 
mobility of the leaving group on the mechanism in a study of the effect of added 
base on the rate of Reaction 7.92. Expulsion of ArO - is much easier from the 


+ -s^ 


+ x 


N0 2 N0 2 

intermediate 92 than from 91. Thus if loss of ArO - is rate-limiting, Reaction 
7.92 should be base-catalyzed. When 90a is used as substrate, strong acceleration 
by base is observed; but when 90b is the substrate, added base has almost no 
effect on rate. 183 



H— N 


+ HOAr (7.92) 



N0 2 




_ jr 



2 N 




ArO N- 

N0 2 


182 K. C. Ho, J. Miller, and K. W. Wong, J. Chem. Soc, B, 310 (1966). 

183 J. F. Bunnett and C. F. Bernasconi, J. Org. Chem., 35, 70 (1970). However, the reaction shown 
below, in which N0 2 ~, a poor leaving group, departs, affords the product in 100 percent yield at 
25°C in benzene. Lack of base catalysis indicates that the first step is rate-determining. 

N0 2 

O a N' ^^ "N0 2 \^ 2 N' 

[F. Pietra and D. Vitali, J. Chem. Soc, Perkin II, 385 (1972).] 



398 Addition and Elimination Reactions 

Roberts elucidated a second mechanism for nuclophilic aromatic substitu- 
tion. Treatment of iodo-, bromo-, or chloro benzene with potassium amide yields 
aniline. In 1953 Roberts observed that when chlorobenzene-l- 14 C is the sub- 
strate, approximately 50 percent of the 14 C in the product is found in the 1- and 
approximately 50 percent in the 2-position. The overall substitution then must 
go by an elimination-addition mechanism in which the highly strained inter- 
mediate, benzyne, is formed as shown in Equation 7.93. 1Bi 

NH 2 


Comparison of the rates of formation of aniline from bromobenzene and 
bromobenzene-2-d gives ^ h /^d = 5.5; thus the proton is removed in the rate- 
determining step. 185 Fluorobenzene-2-d, however, exchanges its deuterium with 
solvent a million times faster than does deuterobenzene, but no aniline is 
formed. 186 Apparently, when the halogen is weakly electron-withdrawing but 
highly mobile, hydrogen abstraction is the slow step; when the halogen is 
strongly electron-withdrawing but unreactive as a leaving group, its expulsion is 
the slow step. 

The presence of benzyne has been more directly demonstrated by trapping 
experiments. For example, the generation of benzyne in the presence of anthra- 
cene gives the Diels- Alder adduct, triptycene (Equation 7.94). 187 


The third mechanism of nucleophilic aromatic substitution, specific for 
substitution on aromatic diazonium salts, is shown in Equation 7.95. 


+ N 2 



Apparently the leaving group must be as reactive as — N 2 in order that the 
strained intermediate 93 be formed. 

184 (a) J. D. Roberts, H. E. Simmons, Jr., L. A. Carlsmith, and C. W. Vaughan, J. Amer. Chem. 
Soc, 75, 3290 (1953); (b) J. D. Roberts, D. A. Semenow, H. E. Simmons, Jr., and L. A. Carlsmith, 
J. Amer. Chem. Soc, 78, 601 (1956); (c) J. D. Roberts, C. W. Vaughan, L. A. Carlsmith, and D. A. 
Semenow, J. Amer. Chem. Soc, 78, 61 1 (1956). 

185 See note 184(b). 

186 G. E. Hall, R. Piccolini, and J. D. Roberts, J. Amer. Chem. Soc, 77, 4540 (1955). 

187 (a) G. Wittig and K. Niethammer, Chem. Ber., 93, 944 (1960); (b) G. Wittig, H. Harle, E. 
Knauss, and K. Niethammer, Chem. Ber., 93, 951 (1960). 

Problems 399 


\J?. Hydrochlorination of 1,2-dimethylcyclohexene gives a mixture of the two pro- 
ducts shown in Equation 1 . The ratio of 1 to 2 depends on the solvent and decreases 
in the order MeOH > AcOH > AcCl. Explain. 

-^^ <H H,C> + <H Cl> O 

H 3 C CH 3 

/Z) The addition of 2,4-dinitrobenzenesulfenyl chloride to cis- and to <rara.r-2-phenyl- 
2-butene gives the products shown below. Propose a mechanism for these reactions. 

H 3 C x CH 3 H *\7 V,' CH 3 H 3C N " f,, c U 3 

C=C . + ArSCl > N C— C' + X C— C'' (2) 

4 H <f>* ^SAr ArS^ ^<f> 

mp h h r C1 CH3 H 3 C CI 

3 °\ / HaC \l I -'H h I I CH 

X C=C + ArSCl > C-C + H ^C_Cr- tH3 (3) 

^ CH 3 <f>* *SAr ArS* V 

(3/ (a) Additions of Br 2 and ArSCl to [2.2.1]-bicycloheptene give the products 
shown in Equations 4 and 5, respectively. Give a mechanism for the products of Reaction 
2 and explain why only the bromination gives rearrangement products. 


+ Br 2 — ► r\ >- Br + r\ >- Br + n >- Br ( 4 ) 

y + ArSCl > r)^y SAr (5) 


(b) ^^-CH = CH 2 reacts 1000 times faster than <£— CH=CH 2 with Br 2 -HOAc but only 

3.8 times faster with />C1-C 6 H 5 SC1 in HOAc at 25°C. Explain. 

r^QAddition of hypochlorous acid to 3 gives the three products shown in Equation 6. 

CH 2 =CH— CH 2 + HOC1 > 

36 C1 

3 CH 2 — CH— CH 2 + CH 2 — CH— CH 2 + CH 2 — CH— CH 2 

I I I I I I I I I (6) 

CI HO 36 C1 OH CI 36 C1 CI 36 C1 OH 


(a) Give a mechanism for the formation of 4. 

(b) Much less rearrangement of 36 C1 occurs if 3 is treated with HOBr instead of HC1. 

QL/Bromination of 2-butene in acetic acid gives dibromide addition product 

400 Addition and Elimination Reactions 

only. However, bromination of phenylethene under the same conditions gives the 
products shown in Equation 7. Explain the difference in behavior between 2-butene and 

Br AcO 

,/ = + Br 2 2°^- \m— CH 2 Br + \h— CH 2 Br (7) 

6. With what alkene would you begin and what synthetic method would you 
use to produce pure zAr«o-3-/>-anisyl-2-butanol ? Pure erythro ? 

7. In the reaction of Equation 8, if R = /-butyl, the rate of reaction is indepen- 
dent of the concentration of base if more than an equimolar amount of base is 
present. If R = CH 3 , however, the rate is dependent on added base up to high base 
concentrations. Explain. 

OMe o 2 n 

^^U / \ + HOMe (8) 

4> H <f> no 2 

<8j) Explain why bromination of benzene with Br 2 has a p value of —12.1, 
whereas bromination with HOBr has- a p value of only —6.2. 

\9y Decide for each of the compounds in Table 7. 1 7 whether the substituent is 
+ /or -/, +Ror -R. 

flO) By drawing resonance structures for the respective a complexes, decide 
whether attack is more likely at the 1- or the 2-position in electrophilic substitution on 

MJV Explain: The benzene halides undergo aromatic substitution more slowly 
than benzene but give predominantly ortho and para substitution. 

tQSp. Treatment of 1 -chloronapthalene with ethoxide ion gives no reaction. Treat- 
ment of 5 with ethoxide, however, gives the nucleophilic substitution product shown 
in Equation 9. Explain the difference in behavior between 1 -chloronapthalene and 5. 


+ "OEt > (9) 


f Predict the relative reactivities in nucleophilic substitution of CI - of: (a) 6a 
, 6b and 7b, 6c and 7c; (b) 6a, 6b, and 6c; (c) 6d and 6e. 


N0 2 ^\^NO 



a, X = CH 3 

b, X = CN 

c, X = NH 2 

d, X = N(CH 3 ) 3 

e, X =S0 2 CH 3 

References for Problems 401 

14. In 80 percent aqueous ethanol, 3-/9-tropanyl chloride gives the product shown 
in Equation 10 in 100 percent yield. Under the same conditions, 3-a-tropanyl chloride 
reacts at one twentieth the rate to give only the addition and elimination products 
shown in Equation 1 1. Formulate a mechanism for Reaction 10 and explain the dif- 
ference between the mode of reaction of Reactions 10 and 11. 

H 3 C. 




CH 3 

N + 

CH 2 CH=CH 2 


H 3 C 



H 3 C. 







1. R. C. Fahey and C. A. McPherson, J. Amer. Chem. Soc, 93, 2445 (1971). 

2. D. J. Cram, J. Amer. Chem. Soc. s 71, 3883 (1949). 

3. (a) R. Kwart and R. K. Miller, J. Amer. Chem. Soc, 78, 5678 (1956); (b) D. G. 

Garratt, A. Modro, K. Oyama, G. H. Schmid, T. T. Tidwell, and K. Yates, J. 
Amer. Chem. Soc, 96, 5295 (1974). 

4. C. A. Clarke and D. H. Williams, J. Chem. Soc, B, 1126 (1966). 

5. J. H. Rolston and K. Yates, J. Amer. Chem. Soc, 91, 1469 (1969). 

6. E. L. Allred, J. Sonnenberg, and S. Winstein, J. Org. Chem., 25, 26 (1960). 

7. F. G. Bordwell, M. M. Vestling, and K. C. Yee, J. Amer. Chem. Soc, 92, 5950 (1970). 

12. M.J. Perkins, Chem. Commun., 231 (1971). 

13. (a, b) W. Greizerstein, R. A. Bonelli, and J. A. Brieux, J. Amer. Chem. Soc, 84, 1026 

(1962); (c) J. F. Bunnett, F. Draper, Jr., R. R. Ryason, P. Noble, Jr., R. G. 
Tonkyn, and R. E. Zahler, J. Amer. Chem. Soc, 75, 642 (1953). 

14. G. A. Grob, Theoretical Organic Chemistry — Kekule Symposium, London: Butterworths, 

1959, p. 114. 

Chapter 8 



Carbonyl compounds comprise a large and important class of organic substances, 
and the chemistry of this functional group is essential to the understanding of 
many chemical and biochemical processes. 1 In this chapter we use a few funda- 
mental ideas of mechanism to correlate reactions of various carbonyl functional 
groups. We shall touch briefly on the closely related chemistry of carbon- 
nitrogen double bonds. 

Carbonyl reactions may be understood in terms of two basic processes: 
addition of a nucleophile to the carbonyl carbon (Equation 8.1) and removal of 
a proton from the carbon adjacent to the carbonyl group (Equation 8.2). In the 
first process the carbonyl molecule is acting as a Lewis acid, and in the second 

\ .. + I .. 

C=0 + :B . B^C— O:- (8.1) 



)c=6 + :B ^=± )c=6 < > J^—O-- + BH+ ( 8 -2) 

— C C C 

/•_• / 


(which is, of course, possible only if the molecule bears an a-hydrogen) as a 
Bransted acid. Both depend on the electron deficiency of the carbonyl carbon, 

1 Reviews of various aspects of carbonyl chemistry may be found in the following sources: (a) W. P. 
Jencks, Catalysis in Chemistry and Enzymology, McGraw-Hill, New York, 1969; (b) W. P. Jencks, 
Prog. Phys. Org. Chem., 2, 63 (1964) ; (c) R. P. Bell, Advan. Phys. Org. Chem., 4, 1 (1966) ; (d) S. Patai, 
Ed., The Chemistry of the Carbonyl Group, Vol. 1, and J. Zabicky, Ed., The Chemistry of the Carbonyl 
Group, Vol. 2, Wiley-Interscience, London, 1966 and 1970; (e) S. Patai, Ed., The Chemistry of Acyl 
Halides, Wiley-Interscience, London, 1972. 


Hydration and Acid-Base Catalysis 403 

which is in turn caused by the electronegativity of the oxygen and its ability to 
accept a negative charge. The second reaction is readily reversible, and the first 
under most circumstances is also. Coordination of the carbonyl oxygen with a 
proton or some other Lewis acid will make the oxygen more electrophilic 
and may be expected to facilitate both addition of a nucleophile to the carbonyl 
carbon and removal of a proton from the a position. Catalysis by acids and bases 
is thus a central theme of carbonyl reactions. 


We consider first the simple addition of a nucleophile to a carbonyl carbon, 
preceded, accompanied, or followed by addition of a proton to the oxygen, and 
the reverse. The overall process (Equation 8.3) amounts to addition of H — X 
to C=0. The reaction differs from the additions to C=C discussed in Chapter 7 
in two important respects. First, the nucleophile always becomes bonded to the 


C=0 + H^X , C^ (8.3) 

carbon and the proton to the oxygen, so there is no ambiguity concerning direc- 
tion of addition; and second, the C=0 group is much more susceptible to attack 
by a nucleophile than is C=C. 


Water adds to the carbonyl group of aldehydes and ketones to yield hydrates 
(Equation 8.4). For ketones and aryl aldehydes, equilibrium constants of the 

Ri R N OH 

C=0 + H a O ^^ ^C (8.4) 

R 2 R 2 OH 

Ri, R 2 = H, alkyl, aryl 
reaction as written are much less than unity, but aliphatic aldehydes are appreci- 
ably hydrated in water solution. The equilibrium constant is larger for the lower 
aldehydes and is largest for formaldehyde. Some representative values are given 
in Table 8. 1 . Bulky groups and groups that donate electron density to the electron- 
deficient carbonyl carbon stabilize the carbonyl form, whereas substituting 
electron-withdrawing groups, or incorporating the carbonyl carbon in a strained 
ring, 2 favors the hydrate. Equilibrium constants correlate with Taft inductive 
and steric parameters. 3 

Mechanistic questions in the hydration-dehydration equilibrium center 
around the acid-base relationships and the precise sequence of events in the 
addition or elimination of the water molecule. Investigations have relied pri- 
marily on kinetics of aldehyde hydration to elucidate the mechanistic details ; 

2 (a) H. G. Brown, R. S. Fletcher, and R. B. Johannesen, J. Amer. Chem. Soc, 73, 212 (1951); (b) 
J. F. Pazos, J. G. Pacifici, G. O. Pierson, D. R. Sclove, and F. D. Greene, J. Org. Chem., 39, 1990 
(1974); see also (c) N.J. Turro and W. B. Hammond, J. Amer. Chem. Soc, 88, 3672 (1966). 

3 (a) Y. Ogata and A. Kawasaki, in The Chemistry of the Carbonyl Group, Zabicky, Ed., Vol. 2, p. 1 ; 
(b) P. Greenzaid, Z. Luz, and D. Samuel, J. Amer. Chem. Soc, 89, 749 (1967). 

404 Reactions of Carbonyl Compounds 

Table 8.1 Approximate Equilibrium Constants at 25°C for the Reaction 
R 1 R 2 C=0 + H a O , R 1 R 2 C(OH) 2 

[RxRaCfOH).,] ° 
Carbonyl Compound /T[H a O] = — — — 



X C=0 2 x 10 3 

X C=0 1.3 

H 3 C / 
H 3 C 

C=0 2 x lO" 3 

H 3 C / 

C=0 37 

C1H 2 C 
X C=0 2.8 x 10* 

C1 3 C 
\.=0 0.71 

CH 3 — H 2 C 

H 3 C / P=° O- 44 " 

v c 

H 3 C /H 


H 3 C V C=0 0.24" 

\ / 
H 3 C-C 

HaC 7 

CHC1 2 

^C=0 2.9 

H 3 C 

CH 2 C1 


CH 2 C1 10 

" Except as noted, values are from R. P. Bell, Advan. Phys. Org. Chem., 4, 1 (1966). 
" P. Greenzaid, Z. Luz, and D. Samuel, J. Amer. Chem. Soc., 89, 749 (1967). 

rates of reaction in both directions have been measured by spectroscopic methods,* 
isotope exchange experiments, 5 heat of reaction, 6 volume change measure- 

4 (a) P. Greenzaid, Z. Luz, and D. Samuel, J. Amer. Chem. Soc, 89, 756 (1967); (b) M.-L. Ahrens 
and H. Strehlow, Disc. Faraday Soc, 39, 1 12 ( 1965) ; (c) R. P. Bell and M. B. Jensen, Proc Roy. Soc, 
A261, 38 (1961). 

5 M. Cohn and H. C. Urey, J. Amer. Chem. Soc, 60, 679 (1938). 

6 R. P. Bell, M. H. Rand, and K. M. A. Wynne-Jones, Trans. Faraday Soc, 52, 1093 (1956). 

Hydration and Acid-Base Catalysis 405 

merits, 7 and by scavenging liberated aldehyde. 8 The reaction is subject to general 
acid and general base catalysis. 9 

General Acid and Base Catalysis 

We have already encountered general catalysis in Section 7.1 (p. 340). Because 
it is so important to the understanding of carbonyl reactions, we shall consider 
it here in more detail. The discussion will be restricted to aqueous solutions, 
because these have been the most thoroughly studied. 

Suppose that acid catalyzes a reaction by forming the conjugate acid of the 
substrate in a rapid equilibrium preceding a slower step, as indicated in Scheme 1 . 

Scheme 1 


S + HA , SH+ + A" 

OTT-t *' 0W 1 

5>H * — t^-> products 

The reaction rate is given by Equation 8.5. Concentration [SH + ] is in turn 
determined by the preliminary equilibrium, for which we may write the equilib- 
rate = /t[SH + ] (8.5) 

K .. [SH + ][A-] 

K ~ [S][HA] (8 - 6) 

rium constant K (Equation 8.6). But concentrations [HA] and [A - ] are them- 
selves related to [H 3 + ] through the K a for the acid HA (Equation 8.7). Combi- 

K ^ = ™^m (8 . 7) 

K [SH + ][A-] [HA] 

K aaA ~ [S][HA] [A"][H 3 + ] 

K [SH + ] _ _J 

A^7" [S][H 3 + ] ~K^~ + 




[S][H 3 Q + ] (8.10) 

nation of Equations 8.6 and 8.7 shows that under these circumstances the con- 
centration of reactive species, SH + , is actually determined by the H 3 + con- 
centration and the K a of SH + (Equations 8.8 and 8.9). The reaction rate (Equa- 
tion 8.10) depends on the H 3 + concentration, and the reaction is said to be 
subject to specific acid catalysis. An entirely analogous argument can be made 
for a base-catalyzed reaction with a preliminary equilibrium to form the con- 
jugate base of the substrate. Such a reaction shows specific base catalysis. Note that 
the mechanism of Scheme 1 , which gives only specific catalysis, does not involve 
any proton transfer in the rate-determining step. 

Another possibility is that the proton transfer itself constitutes the rate- 
determining step, or that the rate-determining step consists of proton transfer 

7 R. P. Bell and B. de B. Darwent, Trans. Faraday Soc, 46, 34 (1950). 
R. P. Bell and P. G. Evans, Proc. Roy. Soc, A291, 297 (1966). 

8 Discussions of the acid-base catalysis may be found in the reviews cited in note 1 . 

406 Reactions of Carbonyl Compounds 

occurring simultaneously with some other process. An example is the deprotona- 
tion of carbon acids, which we discussed in Section 3.3 (p. 141), when we con- 
sidered the Bronsted catalysis law relating the effectiveness of the catalyst to its 
equilibrium acidity. Under these circumstances each individual acid (or base) 
present in the system can act as a proton donor (or acceptor) in the rate-deter- 
mining step, and the rate of this step then depends on each of these acids (bases) 
individually, as indicated in Equation 8. 1 1 for an acid-catalyzed process. 
A reaction that follows Equation 8.1 1 is said to be subject to general acid catalysis; 
the analogous situation with base catalysis is general base catalysis. 

rate = k oha + £„ + [H 3 + ] + ^[HAJ + A 2 [HA 2 ] + . . . (8.11) 

The Bronsted catalysis law states that the individual catalytic constants, 
k n , should be related to the equilibrium acidities by Equation 8. 1 2, or, for a base- 
catalyzed process, by Equation 8.13. (See Section 3.3, p. 141, for further dis- 

Acid catalysis : log k n = a log K an + log C or k n = CK% n (8.12) 

Base catalysis: log k n = -rj8 log K aBH + + log C" or i n = C'Q H+ (8.13) 

cussion of these relations.) The Bronsted slope a (/S for base catalysis) is a measure > 
of the sensitivity of the reaction to the acid strengths of the various catalysts. . 
If for a particular reaction a is near 1 .0, most of the catalysis will be by the 
strongest acid (H 3 + in aqueous solution) ; catalysis by weaker acids will then 
be difficult or impossible to detect, and the situation will be indistinguishable 
kinetically from specific catalysis. If a is near zero, all acids will be equally 
effective, but since the solvent is present in much higher concentration than any 
other acid, it will be the predominant catalyst and again the catalysis by other 
acids will be difficult to detect. 

The usual means of finding general catalysis is to measure reaction rate with 
various concentrations of the general acids or bases but a constant concentration 
of H 3 + . Since the pH depends only on the ratio of [HA] to [A - ] and not on the 
absolute concentrations, this requirement may be satisfied by the use of buffers. 
Catalytic rate constants have been measured for a number of acids and bases 
in aldehyde hydration-dehydration, notably by Bell and co-workers. 10 For 
formaldehyde, a = 0.24, /S = 0.40; earlier work 11 gave for acetaldehyde a = 
0.54, /3 = 0.45 and for symmetrical dichloroacetone a = 0.27, /S = 0.50. 

The observation of general catalysis means that proton transfer must be 
involved in the rate-determining step. 12 Much has been learned about kinetics 
of proton transfer from fast-reaction techniques developed largely by Eigen and 
co-workers; absolute rate constants for many proton transfers are known. 13 
The rates of simple proton transfers between oxygen atoms or oxygen and 
nitrogen are extremely fast, and become diffusion-controlled when the equilib- 
rium constant is favorable in the direction in which the proton is being trans- 
ferred. These observations have generally been considered to rule out a mech- 

10 See note 8, p. 405. 

11 See note 6, p. 404, and note 4(c), p. 404. 

12 It may, of course, happen that no one step is rate-determining. The requirement then is that proton 
transfer must be part of at least one of the group of steps that together constitute the rate-determining 

13 M. Eigen, Angew. Chem. Int. Ed., 3, 1 (1964). 

Hydration and Acid-Base Catalysis 407 

anism for carbonyl hydration in which simple proton transfer is the rate-deter- 
mining step (Scheme 2). Such a process would have to proceed faster than is 

Scheme 2 

\ slow \ 

C=0 + HA , C=OH + + A" 

N fast, \ / OH 

C— OH+ + H 2 , C 

7 x 6h 2 

\ /° H _^ \ /° H 

C + A -=± C +HA 

OH 2 OH 

observed in order to be consistent with Eigen's data. There do, nevertheless, 
appear to be reactions in which simple proton transfer to or from a highly 
reactive intermediate is rate-determining, but which are nevertheless slow simply 
because the concentration of that intermediate is very small. 14 

Simultaneous Proton Transfer and Attack of Nucleophile 

The alternative that appears to offer a consistent explanation for hydration is 
that proton transfer occurs simultaneously with addition of the nucleophile. 

Scheme 3 

C=0 + HA . C=^0---H— A 

v P H 

\ slow \ / 

C=0-"HA + H 2 . C + A" 

7 OH 2 + 


\ / fast , \ / 

C + A" ^^ C + HA 


The mechanism shown in Scheme 3 envisions an association by hydrogen bonding 
between the catalyst and the carbonyl compound, followed by rate-determining 
attack of the nucleophile (H 2 0) and simultaneous transfer of the proton. The 
rate of this step will depend on the nature and concentration of HA, and the 
mechanism is consistent with general catalysis. It should be noted that the 
reverse process consists of a specific acid plus a general base catalysis. A possible 
general base catalysis mechanism is shown in Scheme 4. The reverse is a specific 
base plus a general acid catalysis. 

Scheme 4 fast 

H 2 + :B . B-HOH 


\ slow \ / 

B-HOH + C=0 , C + BH + 

/ / X OH 

C + BH + ^=^ C + :B 


14 R. E. Barnett, Accts. Chem. Res., 6, 41 (1973). 

408 Reactions of Carbonyl Compounds 




ApK a 

Figure 8.1 Logarithm of the rate of a simple proton transfer of the type 

HA + B- v A- + HB 

as a function of the relative strength of the acids HA and HB. When equilibrium 
lies toward the right (log [A' a(HA )/A' a(HB) ] positive), k± is diffusion-controlled 
and a = 0; when equilibrium lies toward the left (log[/f a(HA) /X a(HB) ] negative), 
k_i is diffusion-controlled and j8 = 0. From M. Eigen, Angew. Chem., Int. Ed., 
3, 1 (1964). See also J. N. Bronsted and K. Pedersen, Z. Phys. Chem., 108, 185 
(1924). (Angewandte Chemie, International Edition in English, Vol. 3 (1964), from 
the paper by M. Eigen beginning on p. 1. Reproduced by permission of Verlag 
Chemie, GMBH.) 

The mechanism with simultaneous proton transfer and nucleophile attack 
helps account for another phenomenon observed by Eigen. 15 He found that, for 
simple proton transfers between oxygen atoms or between oxygen and nitrogen 
atoms, the proton transfer rate responds as shown in Figure 8.1 to changes in 
relative acidity of the two acids. 16 In Reaction 8.14, suppose that the structure of 
acid HA is varied so as to change its strength, but HA is kept substantially 

HA + B" . A" + HB (8.14) 

log/ti - logA_! = \o%K = log 



Ap* a 


stronger than HB. Then the rate (k x ) of proton transfer from HA to B" will be 
diffusion-controlled (k x = k max ) and will not change as HA changes. Interpreted 
from the point of view of the Bransted catalysis law, a rate that is independent 
of acid strength means that a = [k^ curve, right-hand side of Figure 8.1). 
The reverse reaction in this same region of relative acid strength would be 
considered a base catalysis by bases A" of varying strength. Equation 8.15 
shows that, with k x = £ max > l°g ^-i wu l De linearly related, with a slope of unity, 
to ApK a when the latter is varied by changing A ~ . Hence /? = 1 , as shown by the 
k_ 1 curve on the right side of Figure 8.1. The same reasoning, this time with HB 
as the stronger acid, generates the left side of the figure. Each curve changes 
slope from unity to zero over a relatively narrow range. These results are in 
accord with the interpretation based on the Hammond postulate in Section 3.3 
(p. 141). Eigen's data suggest that in an acid-catalyzed reaction in which the 

15 See note 13, p. 406. 

16 If the acids are of different charge types, the curve is modified somewhat. See note 13. 

Hydration and Acid-Base Catalysis 409 



\ +\ ^ 

C = OH + A"~ 

/ +Nuc A 

' "^ -A — 


/ 1 
/ 1 
/ \ 

s j 

y 1 



C = O + HA + Nuc 


si / 


/ \ + 

+ Nuc 

C — Nuc distance 

C = OH + A~ + Nuc 

decrease ■ 

\/ OH 

C + A" 

/ \ + 


Figure 8.2 Energy surface for addition of nucleophile Nuc to a carbonyl with concerted 
proton transfer from an acid HA. The lowest-energy path is indicated by the 
heavy line from point A to point B. Points C and D are the high-energy inter- 
mediates of the two possible stepwise paths. The circled point is the transition 

rate-determining step is a simple proton transfer between oxygens, the a relating 
rate [k t ) to strength of catalyst {K aaA ) should be either zero or unity if the cata- 
lyst, HA, is a much stronger or a much weaker acid than the protonated sub- 
strate, HB. Intermediate values of a should be found when the two are of similar 

Bronsted anticipated this kind of behavior when he originally proposed the 
catalysis law, 17 but investigators in intervening years lost sight of the prediction 
because in many cases, as in carbonyl hydration, a is found to be constant and 
different from unity over quite a wide range of catalysts. The reason is that in 
these reactions some other process is occurring simultaneously with proton 
transfer. Figure 8.2 gives a schematic representation of the energy surface for a 
concerted addition and proton transfer; Figure 8.3 is the projection of the reac- 
tion coordinate in the horizontal plane. 18 In the figures, the reaction begins with 
carbonyl compound, nucleophile, and acid catalyst (point A) and proceeds 
directly to point B by simultaneous addition of nucleophile and transfer of proton, 
thereby avoiding the higher-energy stepwise alternatives through points C and D. 

17 J. N. Bronsted and K. Pedersen, Z. Phys. Chem., 108, 185 (1924). 

18 For further discussion of three-dimensional reaction coordinate diagrams for these processes, 
see Section 5.4, p. 246, and (a) W. P. Jencks, Chem. Rev., 72, 705 (1972). (b) M. Choi and E. R. 
Thornton, J. Amer. Chem. Soc, 96, 1428 (1974), have suggested the possibility of more complex 
reaction paths with two consecutive transition states not separated by any energy minimum and 
with reaction coordinates perpendicular to each other on the potential energy surface. 

410 Reactions of Carbonyl Compounds 




C = O + HA + Nuc 


\ + 

C = OH + \~ + Nuc 

Figure 8.3 

C-Nuc distance 
-increase decrease- 

\ /OH 

Nuc + A" 

P «-H 





O «-H 



P H- 





P H- 


Projection in the horizontal plane of the reaction path shown in Figure 8.2. An 
increase in the strength of HA will facilitate motions R 1 and J^, causing shift 
of the transition state to * and change of the reaction path from the solid curve 
to the dashed curve. 

In order to relate the Bronsted coefficient a to the reaction coordinate dia- 
grams, we interpret a as a measure of the position of the proton at the transition 
state, a near zero (HA very strong) indicating an earlier transition state with 
little proton transfer and a near unity (HA very weak) indicating a late transition 
state with proton nearly completely transferred. We have already given a partial 
justification for this interpretation of a in the discussion in Section 3.3; we shall 
return to this point again later. It is nevertheless important to emphasize here 
that in a process involving simultaneous proton transfer and nucleophilic addi- 
tion, a measures only the degree of proton transfer at the transition state (location 
along the back-to-front coordinate in Figure 8.2 and along the top-to-bottom 
coordinate in Figure 8.3) and not the degree of bonding of the nucleophile. 

As the proton is partly transferred at the transition state in Figure 8.3, a will 
have a value intermediate between zero and one. We may use the reacting bond 
rule discussed in Section 2.6 (p. 104) to find the effect of a change in strength of 
the catalyzing acid HA on the position of the transition state. Recall that reacting 
bond Rule 1 (equivalent - to the Hammond postulate) states that a change in 
reactants that facilitates motion along the reaction coordinate (motion R 1} 

Hydration and Acid-Base Catalysis 411 

Figure 8.3) will move the transition state to an earlier point. Since strengthening 
acid HA facilitates motion R 1 (transfer of proton from HA to carbonyl oxygen 
coupled with attack of nucleophile), the transition state will tend to come earlier 
with respect to this motion ; that is, it will be shifted in the direction indicated by 
the arrow R 2 in Figure 8.3. But proton motion is also involved in the vibration 
designated by _\_ 1 and _|_ 2 in Figure 8.3; reacting bond Rule 2 states that change 
in structure will shift the transition state in the direction indicated by the change. 
Here, strengthening acid HA aids motion J_ 1 . 

The composite result of the tendencies for transition state shift in the 
mutually perpendicular directions R 2 and _J_! is to move it to the point designated 
by * in Figure 8.3. The extent of proton transfer is thus not much changed from 
what it was before, despite the stronger acid HA. Therefore a will be relatively 
little affected by changes in strength of catalyzing acid and will not pass as 
quickly through the transition region (near ApA^ a = in Figure 8.1) as it would 
have had the proton transfer not been coupled to nucleophile attack. 

In some cases of general catalysis it is found that the final rapid proton 
transfer (for hydration, the last step of Scheme 3 or Scheme 4) occurs at a rate 
faster than would be possible if the conjugate base (or conjugate acid in a base 
catalysis) of the catalyst actually moved away from the immediate solvation shell 
of the substrate to become part of the general solution. Eigen has proposed that 
this last step may be accomplished simultaneously with the rate-determining 
step by means of a cyclic transition state that includes one or more extra water 
molecules, as indicated in the hydration case by Structure l. 19 When the catalyst 
is a carboxylic acid, the proton transfer from the catalyst may occur at one of the 
carboxylate oxygens while the other accepts the proton from the attacking 


HA (8.16) 

The Bronsted a and /S as Measures of Transition State Location 

We have made use above of the idea that the magnitude of a (or j8) measures 
the extent of proton transfer at the transition state or, equivalently, of the position 
of the transition state along the proton-transfer reaction coordinate. Figures 
8.4 and 8.5 show, respectively, the reaction coordinate diagrams drawn according 
to the Hammond postulate for Reaction 8. 1 7 in the extreme cases where HX is a 

HX + Y" ^^ X- + HY (8.17) 

much weaker or a much stronger acid than HY. In the former case (Figure 8.4), 
x t close to unity, small structural changes that alter the free energy of products, 
Gp, will cause a similar change in transition state free energy, G i , whereas 
changes in reactant free energy, G°,/will have little effect. This case corresponds 

19 (a) M. Eigen, 'Due. Faraday Soc, 39, 7 (1965); (b) R. P. Bell, J. P. Millington, and J. M. Pink, 
Proc. Roy. Soc, A303, 1 (1968). 

412 Reactions of Carbonyl Compounds 

Free energy 

X" +HY 

* = 

X = X* X - 

Reaction coordinate 

Figure 8.4 Reaction coordinate diagram for the proton transfer HX + Y 
HY, where HX is a weaker acid than HY. 

=± x- + 

Free energy 

HX + Y" 

X + HY 

;Q x 


Reaction coordinate 

Figure 8.5 Reaction coordinate diagram for the proton transfer HX + Y ~ 
HY, where HX is a stronger acid than HY. 

to a = 1, /J = in Figure 8.1, that is, reverse reaction diffusion-controlled. 
Figure 8.5 depicts the opposite extreme, x t close to zero, where G* depends on 
G° and not G£; this case corresponds to forward reaction diffusion-controlled, 
a = and /? = 1 in Figure 8.1. In the intermediate region (center part of Figure 
8.1), a varies from 1 to as the transition state moves from being near products 
(Figure 8.4) to near reactants (Figure 8.5). If we let the symbol 8 be an operator 
designating change in a thermodynamic quantity caused by structural change in 


Hydration and Acid-Base Catalysis 413 

the molecules involved, 20 the predictions of the Hammond postulate may be 
roughly quantified by using a and /} as the parameters relating G* to G° and G\ 
as shown in Equation 8.18, where <: a < 1 and < fi < l. 21 If we also assume 
that jS = 1 - a (see Figure 8.1) and remember that AG* = G* - G° and 
AG° = Gp - G°, we obtain Equation 8.19 by subtracting SG° from both sides of 

8G* = a 8G° + p 8G° r (8.18) 

8G* - 8G° = a8G° p + (1 - a) 8G° - 8G° r (8.19) 

8G* - 8G? = a{8G° - 8G°} (8.20) 

8AG* = a8AG° (8.21) 

Equation 8.18 and find relation 8.21 between activation free energy, AG*, 
and standard free energy change, AG°. This equation is equivalent to the 
Bransted catalysis law as was shown in Section 3.3 (Equations 3.49 and 3.53), 
and we may conclude that an interpretation of a as a measure of the position of 
the transition state is consistent with the Hammond postulate. 

It should be emphasized again that these arguments apply only to the 
proton transfer coordinate, and do not give information about the progress of 
another process that may be concerted with it. 22 Another complication can arise 
when the proton transfer is to or from a soft center and accompanied by con- 
siderable redistribution of charge, as in a carbon acid with an anion-stabilizing 
group. Bordwell and co-workers have found values of a greater than unity and 
less than zero for deprotonation and protonation of nitroalkanes ; the simple 
interpretation of this parameter that we have outlined clearly does not apply to 
such cases. 23 An alternative measure of position of transition state is the deuterium 
isotope effect; in a simple proton transfer, £ H /£ D should be at a maximum for a 
transition state in which the proton is midway between the two basic centers. 24 
Again, however, the situation is more complex if another process is concerted 
with proton transfer. 

The Mechanistic Ambiguity in General Catalysis 

In addition to the problems of interpretation of a and /?, certain other difficulties 
remain. We have assumed that the observation of general acid catalysis implies 
proton transfer from acid catalyst to substrate in the rate-determining step 
(Mechanism T, Scheme 5). Mechanism II in Scheme 5 shows that preliminary 
fast equilibrium yielding the conjugate acid of the substrate followed by a rate- 
determining step in which a proton is transferred from the protonated substrate 
to the conjugate base of the catalyst predicts the same dependence on substrate, 
catalyst, and nucleophile concentrations. Furthermore, the catalysis law (Equa- 
tions 8.12 and 8.13) shows that when HA is changed, the observed rate constant 
of Mechanism I, k u is proportional to K% aA . In Mechanism II, k[ is proportional 

20 J. E. Leffler and E. Grunwald, Rates and Equilibria of Organic Reactions, Wiley, New York, 1963, 
p. 26. 

21 (a) Leffler and Grunwald, Rates and Equilibria of Organic Reactions, p. 156; (b) M. Bender, Mech- 
anisms of Homogeneous Catalysis from Protons to Proteins, Wiley-Interscience, New York, 1971, p. 85. 
32 For a discussion, see G. F. Lienhard and W. P. Jenclcs, J. Amer. Chem. Soc, 88, 3982 (1966). 

23 F. G. Bordwell, W. J. Boyle, Jr., and K. C. Yee, J. Amer. Chem. Soc, 92, 5926 (1970). 

24 (a) R. P. Bell, Disc. Faraday Soc, 39, 16 (1965) ; (b) R. A. More O'Ferrall and J. Kouba, J. Chem. 
Soc B, 985 (1967); (c) F. H. Westheimer, Chem. Rev., 61, 265 (1961); see Section 2.7, p. 108. 

414 Reactions of Carbonyl Compounds 


C = O + HA + Nuc H 


\ + 

C = OH + A~ + Nuc H 

C ■■■ Nuc distance 
— increase decrease- 

\ / OH 
C ^ + A" 

/ \ + 


Figure 8.6 









O <-H 

J-i c 



P H- 





Projection in the horizontal plane of the three-dimensional reaction coordinate 
of the rate-determining step for Mechanism I, Scheme 5. Increasing nucleo- 
philicity of Nuc will facilitate motions R ± and _\_ 2 , causing shift of transition 
state to *. 

Scheme 5 25 

Mechanism I 

Mechanism II 


ti -y 


'C=P + HA + H 2 P . . _ 

/ slow / \ 

S v OH 2 


+ A" 


C=0 + HA — 

/ fast / 


C=PH + + A" 



+ A" 

PH 2 


fast \ / 

— - c 
/ \ 


+ HA 

rate = *![S][HA][H 2 0] 

\ *'i \ / 

C=OH + + A" + H 2 -: — *■ C + HA 

/ • • ■* ,| OW / N. 

SH + OH 

rate = yti[SH + ][A-][H z O] 

SH+=X [S][HA] 
^ H [A"] 

rate = ^X[S][HA][H 2 0] 

25 The mechanisms are abbreviated by incorporating the hydrogen bonding equilibria of Schemes 3 
and 4 into the proton-transfer step, and simplified by neglecting reverse reactions in the slow steps. 

Hydration and Acid-Base Catalysis 415 

\ + 

C = OH + Nuc H + A' 

\ + 

C = OH + Nuc~ 



+ A" 


+ H 

C ■■■ Nuc distance 
-increase decrease- 

/ c x +HA 


Figure 8.7 




-Li C 


Nuc H- 






Nuc *-H A 



Projection of the reaction coordinate for the rate-determining step of Mechanism 
II, Scheme 5. Increasing nucleophilicity of Nuc will facilitate motions /?! and J_ 2 , 
shifting transition state to *. 

to K~^ A whereas K is equal to •^ aHA /A^ aaH + , and the observed rate constant, 
k[K, is therefore proportional to K\~£ = ^a HA . The mechanisms therefore also 
predict the same dependence of rate on strength of the acid catalyst. The funda- 
mental reason for this kinetic equivalence is that the stoichiometric composition 
of the transition states in the rate-determining steps are the same in both mech- 
anisms. We may summarize this conclusion by stating that general acid catalysis 
is not distinguishable by kinetic measurements alone from specific acid plus 
general base catalysis. The reader may show by similar reasoning (Problem 13) 
that general base catalysis cannot be distinguished from specific base plus general 
acid catalysis. 

One method of deciding between Mechanisms I and II is to look at the 
trend of a in acid-catalyzed additions of various nucleophiles to a carbonyl 
group. 26 It follows from the reacting bond rules that in true general acid catalysis 
(Mechanism I), the sensitivity of the rate to acidity of the catalyst, and therefore 
also a, should decrease as the species adding is made more nucleophilic. The 
reason is that this variation will cause the change in reaction coordinate shown in 

2a Jencks, Catalysis in Chemistry and Enzymology, pp. 195-197. 

416 Reactions of Carbonyl Compounds 

Table 8.2 Dependence of Bronsted Coefficient a on Basicity of the Nucleophile 
in Additions to C=0 


P"a(NH + ) 

Addition to 



<£NHNH 2 

H 2 NCNH 2 








C1C 6 H 4 CH 



CH 3 CH 




CH 3 CH 


CH 3 CH 


C1C 6 H 4 CH 





Source: W. P. Jencks, Catalysis in Chemistry and Enzymology, McGraw-Hill, New York, 1969, p. 198, 
where a more extensive table may be found. Reproduced by permission of McGraw-Hill. 

Figure 8.6, so that in the transition state the proton will be transferred from the 
catalyst to a smaller extent and the acidity of the catalyst will not be so strongly 
felt. If, on the other hand, the reaction is actually specific acid- plus general 
base-catalyzed, (Mechanism II, Scheme 5), then analysis of Figure 8.7 shows 
that the sensitivity of rate to basicity of A - , and therefore also /3, should decrease 
as the adding species is made more nucleophilic. But if this latter alternative were 
the correct mechanism and the reaction were erroneously regarded as a true 
general acid catalysis, one would find experimentally that a ( = 1 - /8) would 
increase with more nucleophilic adding reagents. 

The experimental evidence favors the conclusion that in addition of nucleo- 
philes to carbonyl groups the observed catalysis is true general acid catalysis. 
Table 8.2 presents selected data; a decreases with increasing nucleophilicity of 
the addend. More specific techniques applicable to particular reactions lead to 
the same conclusion. 27 For hydration, Mechanism I of Scheme 5, with true 
general acid catalysis in the forward direction and specific acid plus general 
base catalysis in the reverse direction, thus appears to be the most reasonable one. 


The previous section considered the simple single-step addition of water to the 
carbonyl group. Certain other nucleophiles undergo similar simple additions. 

See, for example, W. P. Jencks, Prog. Phys. Org. Chem., 2, 63 (1964), p. 90. 

Other Simple Additions 417 

Addition of Cyanide and Sulfite 

Aldehydes and unhindered aliphatic ketones or arylalkyl ketones add hydrogen 
cyanide to form cyanohydrins (Equation 8.22). As with hydration, the equilib- 


N C-=0 + HCN , N C (8.22) 

X ' CN. 

rium lies farther to the right for aldehydes than for ketones. The equilibrium 
constant K is decreased by electron-donating groups, which stabilize the electron- 
deficient carbonyl carbon, and by the presence of bulky groups, which will be 
pushed closer together by the change to tetrahedral cyanohydrin. Table 8.3 
gives selected equilibrium constants. The reaction is of considerable synthetic 
utility, since the cyano group is readily hydrolyzed to yield an a-hydroxy acid. 
The cyanide addition was one of the first organic reactions to be elucidated 
mechanistically. In 1903 Lapworth found that whereas a high concentration of 
undissociated HCN is desirable to assure a high yield of cyanohydrin, the reaction 

Table 8.3 Equilibrium Constants at 20°C in 96 percent Ethanol for the Reaction 

x c=o + 


- V 




HCN .r- 



R 2 



C 6 H 5 




/>-CH 3 C 6 H 5 




C 6 H 5 

CH 3 



CH 3 

CH 3 



CH 3 

C 2 H 5 



CH 3 

i-C 3 H 7 



CH 3 



i-C 4 H 9 







"J. W. Baker, Tetrahedron, 5, 135 (1959). 

6 A. Lapworth and R. H. F. Manske, J. Chem. Soc, 1976 (1930). 

c V. Prelog and M. Kobelt, Helv. Chim. Acta, 32, 1187 (1949). 

418 Reactions of Carbonyl Compounds 

rate depends on concentration of cyanide ion according to Equation 8.23. 28 
His mechanism was essentially the same as the one accepted today (Scheme 6) . 29 


*[^C=o][CN-] (8.23) 

Scheme 6 


HCN + A" , HA + CN" 


\ slow \ / 

C=0 + CN- ;=± C 

O- OH 

\ / fast \ / 

C + HA . C + A" 

/ \ / \ 


The reaction clearly should be subject to specific base catalysis, as is indeed ob- 
served. There is a possibility of general acid catalysis also ; this process seems to 
be of only minor importance. 30 

Sulfite ions also undergo simple addition to aldehydes and unhindered 
ketones. No evidence for significant general catalysis exists, although a thorough 
search does not appear to have been made. Stewart and Donnally have investi- 
gated the mechanism in some detail ; the situation is complicated by the multiple 
acid-base equilibria possible, but the reaction appears to follow the general 
pattern of other simple additions. 31 Equilibrium constants again show that the 
addition is more favorable with aldehydes than with ketones. The equilibrium 
constants (Table 8.4) correlate with the Taft a* inductive parameters. 32 The bi- 

Table 8.4 Equilibrium Constants at 0°C for the Reaction 
R! R! OH 

\ \ / 

C=0 + HS0 3 - ;=t C 

/ / \ 

R 2 R 2 SO3- 

Ri R 2 K a 


CH 3 

CH 3 

CH 3 

CH 3 _ . 

" Calculated from data of K. Arai, Nippon Kagaku Zasshi, 82, 955 (1961) [Chem. Abstr., 56, 5623g 

28 A. Lapworth, J. Chem. Soc, 83, 995 (1903). 

29 The observation of a low yield of chiral cyanohydrin when certain optically active amines are 
present requires a minor modification of the mechanism to allow for coordination of the carbonyl 
oxygen with a cation. See V. Prelog and M. Wilhelm, Helv. Chim. Acta, 37, 1634 (1954); H. Hustedt 
and E. Pfeil, Justus Liebigs Ann. Chem., 640, 15 (1961). 

30 (a) W.J. Svirbely and J. F. Roth, J. Amer. Chem. Soc, 75, 3106 (1953); (b) W.J. Svirbely and 
F. H. Brock, J. Amer. Chem. Soc, 77, 5789 (1955). 

31 (a) T. D. Stewart and L. H. Donnally, J. Amer. Chem. Soc, 54, 2333, 3555, 3559 (1932); (b) see 
also D. A. Blackadder and C. Hinshelwood, J. Chem. Soc, 2720 (1958). 

32 K. Arai, Nippon Kagaku Zasshi, 82, 955 (1961) [Chem. Abstr., 56, 5623g (1962)]. 

CH 3 


CH 3 


C 2 H 5 


t-C 3 H 7 




Other Simple Additions 419 

sulfite adducts have been demonstrated by synthesis, 33 Raman spectroscopy, 3 * 
and isotope effect measurements 35 to have the hydroxy sulfonic acid structure (2) 

R lx JDH R 1n 7 OH 

r/ X S=0 r/ X 0— S^ 

o- x o- 

rather than the alternative hydroxy sulfite ester structure (3) . Note that the softer 
sulfur center rather than the harder oxygen of the ambident sulfite prefers to be 
bonded to carbon. 

Addition of Organometallics 

Addition of organometallics will not be considered in detail here; we wish merely 
to note that additions of organolithium and organomagnesium compounds are 
analogous to the processes that have been considered up to this point. 36 Although 
the detailed structure of these organometallics may vary from one compound to 
another, and may in some cases be unknown, they consist essentially of a strong, 
soft carbon Lewis base coordinated to a hard metal ion Lewis acid. 37 Combination 

Ri x Ri P- M + 

RM + C=0 > C (8.24) 

R 2 r/ N R 

with a carbonyl compound (Equation 8.24) yields a bonding situation of so 
much lower energy that equilibrium constants are usually very large and the 
additions are for practical purposes irreversible. Acid-base catalysis of the type 
we have been considering is clearly out of the question here, as the reactions must 
be conducted under rigorously aprotic conditions if the organometallic reagent 
is not to be destroyed. 

It should be noted that despite equilibria favorable to the adduct, the 
reactions are not without complications ; because of the strongly basic properties 
of the organometallic, side reactions can occur. If the carbonyl compound bears 
a hydrogens, an enolate ion may result (Equation 8.25) ; the negative charge 

33 (a) W. M. Lauer and C. M. Langkammerer, J. Amer. Chem. Soc, 57, 2360 (1935); (b) R. L. 
Shriner and A. H. Land, J. Org. Chem., 6, 888 (1941). 

34 C. N. Caughlan and H. V. Tartar, J. Amer. Chem. Soc, 63, 1265 (1941). 

35 W. A. Sheppard and A. N. Bourns, Can. J. Chem., 32, 4 (1954). 

36 The mechanisms are complex, particularly in the organomagnesium (Grignard) reactions. 
Several reactive species are present, and the product metal alkoxide can complex with unreacted 
organometallic. Furthermore, trace transition metal impurities in the magnesium used to prepare 
Grignard reagents appear to facilitate electron transfer and may cause the reaction to proceed at 
least partly by a radical pathway. See (a) J. Laemmle, E. C. Ashby, and H. M. Neumann, J. Amer. 
Chem. Soc, 93, 5120 (1971); (b) E. C. Ashby, J. Laemmle, and H. M. Neumann, Accts. Chem. Res., 
7,272 (1974). 

37 In some other organometallics, for example the soft acid-soft base organomercury compounds, 
the carbon-metal bond has a high degree of covalent character and is sufficiently strong that these 
substances are considerably less reactive than substances of the organolithium or organomagnesium 

420 Reactions of Garbonyl Compounds 

then prevents addition. An a hydrogen in the organometallic may be trans- 
ferred to the carbonyl carbon (Equation 8.26), giving reduction. 38 


RM 4- C— C=0 

/ I 

p- .O 

X —X 


M + + RH 


\l I \ X / \/°" M + 

C— C— M + C=0 > fi=C^ + C (8.26) 

/ | / / \ / \ R 

Oxidations and Reductions 39 

Addition of hydride to the carbonyl carbon to form an alcohol, or the reverse, 
changes the oxidation state and so is usually classified separately from other 
carbonyl reactions. Some of these processes are nevertheless fundamentally 
similar to the ones we have been considering. Reductions by complex metal 
hydrides, such as lithium aluminum hydride or sodium borohydride, are addi- 
tions of H : " (Equation 8.27) ; the metal hydride ion is simply a convenient source 
of this extremely basic species. The carbonyl oxygen takes the place of the hy- 
dride in coordination with the boron (or aluminum in the case of an alumino- 

OBH 3 - 
Na + BH 4 " + X C=0 >- c/ (8.27) 


hydride), and the other hydrogens still available can add to carbonyl groups of 
other molecules. The additions are effectively irreversible and usually free of 
side reactions. Many useful variations of these reagents are available for accom- 
plishing specific synthetic tasks. 40 

A reduction that also consists of hydride addition but in which the hydride 
donor is an alkoxide ion has found some synthetic use. 41 Equation 8.28 shows this 
process, referred to as the Meerwein-Ponndorf-Verley reduction. The alkoxide 
M + .. 

R, H O:- M + 

z=^ C=0 + C (8.28) 

R 2 R3 R 4 

38 For detailed discussions, see: (a) G. E. Coates, M. L. H. Green, and K. Wade, Organometallic 
Compounds, 3rd ed., Methuen, London, 1967, Vol. 1 ; (b) M. S. Kharasch and O. Reinmuth, Grignard 
Reactions of Non-Metallic Substances, Prentice-Hall, New York, 1954; (c) M. Cais and A. Mandel- 
baum, in The Chemistry of the Carbonyl Croup, S. Patai, Ed., Vol. 1, Wiley-Interscience, London, 
1966, Vol. l.chap. 6. 

39 (a) Oxidations and reductions are considered in detail by H. O. House, Modern Synthetic Reactions, 
2nd ed., W. A. Benjamin, Menlo Park, Calif., 1972; (b) reductions with borohydrides and alumino- 
hydrides are discussed by H. C. Brown, Boranes in Organic Chemistry, Cornell University Press, 
Ithaca, N.Y., 1972; see also (c) C. F. Cullis and A. Fish, in The Chemistry of the Carbonyl Croup, S. 
Patai, Ed., Vol. 1, chap. 2 (oxidations); (d) O. H. Wheeler, in The Chemistry of the Carbonyl Group, S. 
Patai, Ed., Vol. 1, chap. 11 (reductions); (e) N. G. Gaylord, Reduction with Complex Metal Hydrides, 
Wiley-Interscience, New York, 1956. 

40 See note 39(a), (b). 

41 (a) Note 39(a); (b) A. L. Wilds, Org. Reactions, 2, 178 (1944); (c) C. Djerassi, Org. Reactions, 6, 
207 (1951). 

Other Simple Additions 421 

undergoes a reverse carbonyl addition and hence is oxidized; when looked at 
from this point of view, the transformation is called the Oppenauer oxidation. 
The equilibrium may be shifted in the desired direction by using an excess of 
one of the reagents. 

An alternative and more generally used oxidation method employs chromic 
acid. This process is an exception to our general theme, because here the alcohol 
is transformed to a carbonyl group by removal of electron density from oxygen 
rather than from carbon. The first step has been shown to be a rapid equilibrium 
between the alcohol and its chromate ester, followed by rate-determining de- 
composition of the ester in the manner shown in Scheme 7. 42 It will be noted that 
the species eliminated from the carbon that becomes the carbonyl carbon is a 
Lewis acid, not a Lewis base. 

Scheme 7 


R, OH R O— Cr— OH 

y C^ + HCr0 4 " + H 3 + ^^ C^ Q + 2H 2 

R 2 H • R 2 H 



Ri \ /°TLir r "~ OH Ri \ 

/V* O + Hz0 > / C=( ? + H 3 Q+ + HCr °3 

Ro H Rn 

Stereochemistry of Addition 

When an effectively irreversible addition, such as that of an organometallic or 
hydride, occurs in a cyclic structure or in a molecule that contains a chiral center, 
two isomers may form. Under these circumstances, the additions are stereo- 
selective, and one of the isomers is formed in greater amount than the other. 
Cram and his collaborators have provided a rationalization for the observed 
isomer distribution that is useful in predicting the outcome of reactions of this 
type. 43 They proposed that the carbonyl oxygen in the substrate is coordinated 
to the Lewis acid part of the attacking reagent so that it has a large effective size. 
The preferred conformation of the carbonyl substrate will therefore be 4, where 
L, M, and S are, respectively, the large, medium, and small groups on the chiral 

S R— M S R' M + 

R'_ M---Q — (— V T R > -O— (— ( ) — L (8.29) 

42 (a) A. Leo and F. H. Westheimer, J. Amer. Chem. Soc, 74, 4383 (1952); (b) M. Cohen and F. H. 
Westheimer, J. Amer. Chem. Soc, 74, 4387 (1952); (c) K. B. Wiberg, Ed., Oxidation in Organic Chem- 
istry, Academic Press, New York, 1965; (d) R. Stewart, Oxidation Mechanisms, W. A. Banjamin, 
Menlo Park, Calif., 1964, chap. 4. 

« (a) D.J. Cram and F. A. Abd Elhafez, J. Amer. Chem. Soc, 74, 5828 (1952); (b) D.J. Cram and 
F. D. Greene, J. Amer. Chem. Soc, 75, 6005 (1953). 

422 Reactions of Garbonyl Compounds 


(CH 3 ) 3 C 


(CH 3 ) 3 C 

(CH 3 ) 3 C 


Figure 8.8 (a) Steric approach control. R' enters from the less hindered direction, giving 
the axial alcohol. This behavior is observed for bulky R', such as Grignard 
reagents, LiAlH(OCH 3 ) 3 , or when axial groups in the 3-position are large. 
(b) Product development control. R' enters from the axial direction, giving 
equatorial alcohol. Observed with small R', such as LiAlH 4 , and small axial 
groups in the 3-position. 

a carbon, and the incoming R' group will approach from the less hindered face 
onto the carbonyl carbon. 

The Cram interpretation successfully predicts the results of a number of 
additions; it cannot, however, be readily applied to cyclic systems where con- 
formational possibilities are limited. Dauben and co-workers 44 proposed that, 
depending upon the bulk of the entering reagent and the presence or absence of 
axial substituents on the ring two carbons removed from the site of attack, 
addition to a cyclohexanone could be subject to either steric approach control or 
product development control. Steric approach control directs the entering group to the 
less hindered equatorial position (Figure 8.8a). Product development control 
requires the nucleophile to enter from the more hindered axial direction so that 
the developing hydroxy group will be in the less hindered equatorial position 
(Figure 8.8b) . 45 The proposal is designed to explain the predominant formation of 
the product with equatorial hydroxyl in metal hydride reductions of relatively 
unhindered ketones and of the product with axial hydroxyl from hindered 
ketones and when the entering group is bulky. 

The Dauben proposal assumes implicitly that, in those reactions subject to 
steric approach control the transition state is close to reactants, whereas in those 
subject to product development control, it is close to product. Various investi- 
gators have pointed out that because additions of hydride and organometallics 
are highly exothermic, a reactantlike transition state is expected. 46 It seems 
unlikely that the transition state would undergo such a large change in response to 
a relatively minor change in structure, the fundamental nature of the process being 

" W. G. Dauben, G.J. Fonken, and D. S. Noyce, J. Amer. Chem., Soc, 78, 2579 (1956). 

45 The terms steric strain control and product stability control are preferred by H. C. Brown and H. R. 
Deck, J. Amer. Chem. Soc, 87, 5620 (1965). 

46 (a) D. M. S. Wheeler and M. M. Wheeler, J. Org. Chem., 27, 3796 (1962); (b) E. L. Eliel and Y. 
Senda, Tetrahedron, 26, 2411 (1970). 

Other Simple Additions 423 

the same in all cases. Eliel and Senda found evidence to support their view that 
product development control is of little importance. 47 Other critics have pro- 
posed alternative explanations that permit one to suppose that the position of the 
transition state is approximately constant. They suggest that the stereochemistry 
is determined by a balance between steric interference with the approach of the 
reagent and the tortional, or eclipsing, effects that are introduced as new bonds 
form and that are not strongly dependent on the bulk of the groups. 48 Geneste, 
Lamaty, and Roque, on the other hand, have found independent evidence from 
linear free-energy correlations that the position of the transition state may indeed 
be significantly different for the various additions. 49 The matter is clearly more 
complex than it appeared initially, and the definitive theory has yet to be given. 

Relative Affinity of Various Nucleophiles for the Carbonyl Group 

It is appropriate at this point to summarize the tendency of various nucleo- 
philes to add to the carbonyl group. In general, the strong bases (organometallics, 
hydrides, negative ions) are most effective; among the neutral nucleophiles, the 
soft ones, for example the sulfur bases, tend to be more effective in addition than 
the hard ones, for example the oxygen bases. 

The strong nucleophiles are also the ones that Table 8.2 shows do not require 
general catalysis to accompany the addition. A general acid or base catalyst 
enters where it is needed to avoid formation of highly unstable intermediates. 50 
Addition of a strongly basic nucleophile will lead to a relatively stable inter- 
mediate of the type 5. There is no large pK change, and no general catalysis is 

V:=0 + :Nuc~ ^=t \/ (8.30) 

expected. A weak nucleophile, as for example a water molecule, would produce 
a high-energy intermediate (6) with the new basic site, — O", much more basic 
than the original Nuc — H was. Concerted acid catalysis (Equation 8.32) circum- 

^=0 + :Nuc— H ^=^ tr (8.31) 


Nuc + - 



v OH 


/ C =° + -Nuc—H + HA , p[ + A" (8.32) 

47 See note 46(b). 

48 (a) J.-C. Richer, J. Org. Chem., 30, 324 (1965); (b) M. Cherest, H. Felkin, and N. Prudent, 
Tetrahedron Lett., 2199 (1968); (c) M. Cherest and H. Felkin, Tetrahedron Lett., 2205 (1968); (d) M. 
Cherest, H. Felkin, and C. Frajerman, Tetrahedron Lett., 379 (1971); (e) M. Cherest and H. Felkin, 
Tetrahedron Lett., 383 (1971); see also (f) R. A. Auerbach and C. A. Kingsbury, Tetrahedron, 29, 
1457 (1973). 

49 (a) P. Geneste, G. Lamaty, and J.-P. Roque, Tetrahedron Lett., 5007, 5015 (1970) ; (b) P. Geneste, 
G. Lamaty, C. Moreau, and J.-P. Roque, Tetrahedron Lett., 501 1 (1970) ; (c) P. Geneste, G. Lamaty, 
and J.-P. Roque, Tetrahedron, 27, 5539, 5561 (1971). See also (d) D. C. Wigfield, D.J. Phelps, R. E. 
Pottie, and R. Sander, J. Amer. Chem. Soc, 97, 897 (1975). 

60 (a) W. P. Jencks, J. Amer. Chem. Soc, 94, 4731 (1972) ; (b) W. P. Jencks, Chem. Rev., 72, 705 (1972). 

424 Reactions of Carbonyl Compounds 

vents this unfavorable situation. It is important to realize that these remarks 
apply only to simultaneous addition and proton transfer, and not to cases where 
general catalysis is the result of rate-determining proton transfer unaccompanied 
by another change. 


Many carbonyl additions yield intermediates that undergo further transforma- 
tions that restore the original carbonyl carbon to a doubly bonded state. These 
changes are fundamentally the same as the reverse steps of the additions consider- 
ed in the previous sections, and differ only in that departure of some group other 
than the original nucleophile is possible. Equations 8.33 and 8.34, where Nuc 
and Nuc' are generalized nucleophiles, illustrate two possibilities. 

R \ R \ / OH h+ R 

C— O + Nuc— H , C , " ' \:= Nuc + + H 2 (8.33) 

R R Nuc R 


Nuc Nuc O " 

C^O + Nuc'~ , \/ , :■'■ C + Nuc- (8.34) 

R R X Nuc' R Nuc' 

The product of the elimination step may still contain a highly electrophilic 
doubly bonded carbon, as would be the case in Equation 8.33. In that case, a 
third step may follow in which a second molecule of the nucleophile adds to 
yield a final product in which the original carbonyl carbon is tetrahedrally 
bonded (Equation 8.35). In this section we consider reactions of this kind, and in 
Sections 8.4 and 8.5 we take up reactions that stop at the stage indicated by 
Equation 8.33 or 8.34. 

R R Nuc 

\ \ / 

C=Nuc + + Nuc—H . C + H + (8.35) 

R R ^Nuc 

Acetals and Ketals 

Addition of an alcohol to a carbonyl group is the most straightforward extension 
of the hydration process. The first product formed will be a hemiacetal (7) ; 
in the presence of an acid catalyst this intermediate may eliminate the OH 

Ri Ri OH 

\ ^ \ / 

C=0 + R'OH , _J. C (8.36) 

/ / \ 

R 2 R 2 OR' 

R! OH R x R x 

\ / ^ \ \+ ■• 

C + H + v C=0— R' « > C— O— R' + H 2 (8.37) 

R 2 OR R 2 R 2 

Addition Followed by Elimination 425 



R 2 

C=0— R' + R'OH 

Ri OR' 

\ / 
C + H A 

/ \ 


R 2 


group to return to a structure with trigonal carbon, stabilized carbocation 8. 
This ion will then react with a second molecule of the alcohol to yield the acetal 
or ketal. Hemiacetals and hemiketals, with a few exceptions, are not sufficiently 
stable to isolate in pure form ; their presence in solution has been demonstrated 
by various physical measurements. 51 Acetals and ketals are stable under neutral 
or basic conditions, although they undergo reaction back to alcohol and aldehyde 
or ketone in the presence of aqueous acid. 

Since rapid conversion of hemiacetal to acetal requires more acidic con- 
ditions than does formation of the hemiacetal, it is possible to measure the rate 
of hemiacetal production without complication from the second stage of the 
reaction. 52 As might be expected, the hemiacetal formation displays character- 
istics similar to those of hydration; general acid and general base catalysis are 
observed. 53 

Cyclic hemiacetals and hemiketals with five- and six-membered rings 
formed by hydroxy aldehydes or hydroxy ketones are considerably more stable 
than their acyclic counterparts. The most important examples are the sugars. 54 
Glucose exists largely in the pyranose form, of which there are two possible 
structures (9 and 10), called, respectively, a-glucose and /9-glucose. The /3 form, 
having all hydroxyl groups equatorial, is slightly more stable. In neutral solution, 
the open-chain free aldehyde 11 accounts for only about 0.003 percent of the 
total at equilibrium, 55 although in 50 percent sulfuric acid it is the predominant 











CH 2 OH 


species. 56 The rate of interconversion of the a and /? modifications is readily 
measured by following the change in optical rotation (mutarotation) . The 
reaction must proceed through the open-chain hydroxy aldehyde, and so serves 
as a conveniently studied example of hemiacetal formation. Mutarotation of 
glucose was one of the early reactions to be investigated using modern ideas of 

51 See, for example, G. W. Meadows and B. de B. Darwent, Can. J. Chem., 30, 501 (1952). 

52 G. W. Meadows and B. de B. Darwent, Trans. Faraday Soc, 48, 1015 (1952). 

53 See note 52. For further references, see Y. Ogata and A. Kawasaki, in The Chemistry of the Carbonyl 
Group,}. Zabicky, Ed., Wiley-Interscience, London, 1970, Vol. 2, p 1. 

64 See B. Capon, Chem. Rev., 69, 407 (1969) for a comprehensive discussion of mechanism in carbo- 
hydrate chemistry. 

55 J. M. Los and K. Wiesner, J. Amer. Chem. Soc, 75, 6346 (1953). 
58 E. Pacsu and L. A. Hiller, Jr., J. Amer. Chem. Soc, 70, 523 (1948). 

426 Reactions of Carbonyl Compounds 

acid-base catalysis; it is subject to general acid catalysis with a = 0.27 and to 
general base catalysis with /? = 0.36. 57 The fact that a is not equal to 1 — ^ 
indicates that the acid- and base-catalyzed mechanisms differ by more than just a 
proton. 58 The acid catalysis is probably true general acid catalysis (see Section 
8.1, p. 413), and base catalysis is true general base catalysis rather than specific 
base-general acid catalysis. 59 

A possibility that was proposed quite early for the glucose mutarotation, 
and that could conceivably be of importance for other reactions, is simultaneous 
catalysis by an acid and a base. It will be recalled from Section 8.1 that hydra- 
tion requires addition of a proton at one site and removal of a proton from 
another. If both these processes were to occur in one step, either by means of 
separate acid and base molecules acting together or by action of a single molecule 
containing both an acidic and a basic center, we would designate the process as a 
concerted acid and base catalysis (Equation 8.39). 60 Swain found that the rate of 

N C=0 — H— A OH 

7 ^ —^ ,C + A- + BH + (8.39) 

C : 0— H.---.B OR 



mutarotation of tetramethylglucose in benzene containing pyridine and phenol is 
third-order overall (Equation 8.40) ; he interpreted this result as showing 

rate = k [Me 4 glucose] [pyridine] [phenol] (8.40) 

the importance of the concerted mechanism 8.39 in aprotic solvents. 61 Subse- 
quent work has cast some doubt on this interpretation; 62 and Bell and co- 
workers have shown that the proposal of concerted acid and base catalysis 
does not apply as generally as Swain had expected. 63 On the other hand, con- 
certed catalysis does occur with substances that have an acidic and a basic site in 
the same molecule and in which the sites have a tautomeric relationship to 
each other. 64 An example of such a catalyst is 2-pyridone, which can catalyze a 


n-^ o: ^N" 

>• I " (8-41) 

X ,. H H 

R cLo: Ro x H 

7 //C- 0: 

67 (a) J. N. Bronsted and E. A. Guggenheim, J. Amer. Chem. Soc, 49, 2554 (1927) ; (b) T. M. Lowry, 
J. Chem. Soc, 2554 (1927). 

58 W. P. Jencks, Prog. Phys. Org. Chem., 2, 63 (1964). 

59 See note 58. 

90 T. M. Lowry and I. J. Faulkner, J. Chem. Soc, 127, 2883 (1925). 

61 (a) C. G. Swain, J. Amer. Chem. Soc, 72, 4578 (1950); (b) C. G. Swain and J. F. Brown, Jr., J. 

Amer. Chem. Soc, 74, 2534 (1952). 

93 H. Anderson, C-W. Su, and J. W. Watson, J. Amer. Chem. Soc, 91, 482 (1969). 

63 R. P. Bell and J. G. Glunie, Proc. Roy. Soc, A212, 33 (1952). 

64 (a) C. G. Swain and J. F. Brown, Jr., J. Amer. Chem. Soc, 74, 2538 (1952); (b) P. R. Rony, 
J. Amer. Chem. Soc, 91, 6090 (1969); (c) P. R. Rony and R. O. Neff, J. Amer. Chem. Soc, 95, 2896 

Addition Followed by Elimination 427 

nucleophile addition in the manner shown in Equation 8.41. 85 Carboxylic acids 
can also function in this way. 66 The evidence for such a process is the acceleration 
of reaction rate compared with what one would expect on the basis of the 
catalyst pK a and the Bronsted a of the reaction being catalyzed. These examples 
of concerted acid and base catalysis have been found in nonaqueous solvents ; 
although there is little evidence for it in aqueous reactions, it remains a possi- 
bility for catalysis by enzymes. 67 It should be noted that this concerted catalysis 
by two separate molecules, or by two separate sites on the same molecule, is not 
the same as the one-encounter process, discussed in Section 8.1 (p. 41 1), in which 
a single molecule acts successively as acid and base catalyst during the same en- 
counter before the reaction partners can diffuse apart. 

The second stage of acetal and ketal formation, the acid-catalyzed elimina- 
tion of the hydroxyl group as a water molecule and addition of a second alcohol 
molecule to the resulting carbocation (Equations 8.37 and 8.38), is most conve- 
niently investigated in the reverse direction starting from the acetal or ketal. 88 
As Structures 12 and 13 indicate, it is conceivable that either of two bonds could 
be broken in the hydrolysis. One method of settling the ambiguity is to hydrolyze 

H + 

\ x 0_R \ 

CQ > C + + HOR (8.42) 



H + . 

\ /H R \ /° H 

C > C + R + (8.43) 



acetals in which R is bonded to oxygen at an asymmetric carbon; such experi- 
ments consistently show retained configuration, demonstrating cleavage of 
oxygen-carbonyl carbon bond (12) rather than oxygen-alkyl bond. 69 This type 
of cleavage is preferred even when R is chosen deliberately so as to make R + 
a good cation. 70 A second type of experiment is to use 18 as a tracer; these 
investigations lead to the same conclusion. 71 

A somewhat more difficult question is that of the precise mechanism by 
which the carbonyl carbon-oxygen bond is cleaved. Scheme 8 illustrates three 

66 See note 64(a). 

86 See note 64(b), (c). 

67 (a) W. P. Jencks, Catalysis in Chemistry and Enzymology, McGraw-Hill, New York, 1969, pp. 211- 
217. (b) A report of concerted acid and base catalysis of an esterification has appeared: S. Milstien 
and L. A. Cohen, J. Amer. Chem. Soc, 91, 4585 (1969). (c) See also J. P. Fox and W. P. Jencks, 
J. Amer. Chem. Soc, 96, 1436 (1974), who have reported negative results in a case that should be 
favorably disposed toward concerted catalysis. 

68 E. H. Cordes, Prog. Phys. Org. Chem., 4, 1 (1967), has reviewed hydrolysis of acetals, ketals, and 
ortho esters. 

69 (a) J. M. O'Gorman and H.J. Lucas, J. Amer. Chem. Soc, 72, 5489 (1950) ; (b) H. K. Garner and 
H.J. Lucas, J. Amer. Chem. Soc, 72, 5497 (1950); (c) E. R. Alexander, H. M. Busch, and G. L. 
Webster, J. Amer. Chem. Soc, 74, 3173 (1952). 

70 J. D. Drumheller and L. J. Andrews, J. Amer. Chem. Soc, 77, 3290 (1955). 

71 F. Stasiuk, W. A. Sheppard, and A. N. Bourns, Can. J. Chem., 34, 123 (1956). 

428 Reactions of Carbonyl Compounds 


Figure 8.9 Possible mechanisms for cleavage of acetals and ketals. I: A-l, Mechanism I; 
II: A-2, Mechanism II; III: S £ 2, Mechanism III. 

reasonable possibilities; these mechanisms are further clarified by schematic 
reaction coordinate diagrams in Figure 8.9. Mechanism I is a unimolecular 
S A 1 ionization of the acetal conjugate acid. It is designated the A-l (acid- 
catalyzed unimolecular) mechanism. Mechanism II is an Sjv2 displacement of 
ROH by H a O, designated A-2, and Mechanism III is essentially a bimolecular 
electrophilic substitution by proton on the oxygen. Mechanisms I and II both 
predict specific acid catalysis, whereas Mechanism III leads to general acid 

Specific acid catalysis, but not general catalysis, is found for acetal and 

Addition Followed by Elimination 429 



. ^ 






f* X 



\ / 





1 Pi 


/ \ 



■ -, / 







/ \ 















Pi pi 




\ / 













at ei 
-O J=> 






+ \ 

1 1 

* S X 

x— o. 9 o 

Pi X 





, X 

/ \ 








x-p x 







(* ct! 


X— 0, 



+ \ / 









/ \ 











Pi Pi 

<* Pi 


Q. ,0 




\ / 

+ \ / 









oi X 






430 Reactions of Carbonyl Compounds 

ketal hydrolysis. 72 (Exceptions to this statement for particular structures will be 
discussed below.) Mechanisms I and II therefore remain as possibilities. Of 
these, the A-l process, Mechanism I, appears on the basis of a number of criteria 
to be the correct one for most acetals and ketals. Strong acceleration by electron 
donation in the carbonyl portion of the molecule has been demonstrated by 
Hammett a-p and Taft a*-p* correlations. For example, in hydrolysis of 14, p 
is in the neighborhood of —3.3, and in hydrolysis of 15, p* is near — 3.6. 73 

R2 OC 2 H 5 


Entropies and volumes of activation, 74 though less reliable criteria, are in the 
range usually found for unimolecular reactions and do not agree with values 
expected for the A-2 process. Solvent isotope effects also are in agreement with 
the A-l mechanism. 75 

A criterion of mechanism based on the Hammett acidity function, H 
(Section 3.2, p. 130), has long been used to decide the type of question raised 
by the choice between Mechanisms I and II in Scheme 8. Since in strongly 
acidic media the concentration of the protonated substrate should be pro- 
portional to h , the reaction rate for a unimolecular decomposition of this proto- 
nated substrate (Mechanism I) should also be proportional to k , whereas if a 
water molecule is required (Mechanism II), the rate should follow H 3 + 
concentration instead. This test, known as the Zucker-Hammett hypothesis, 76 
when applied to acetal and ketal hydrolysis, appears to confirm the A-l mech- 
anism, since a linear relationship is found between rate constant and h at high 
acidity. 77 Inconsistencies have nevertheless been found in application of the 
Zucker-Hammett hypothesis, for example failure of the plots of log k vs. — H 
to have the theoretical slope of unity in a number of cases, and failure to predict 
consistent mechanisms for forward and reverse reactions ; the method is therefore 
now considered to be of doubtful validity. 78 Bunnett has devised a more successful 
treatment (Equation 8.45), in which the parameter w measures the extent of 

log k + H = w log a H20 (8.44) 


log k = w log a H2 o - H (8.45) 

72 (a) K. Koehler and E. H. Cordes, reported in ref. 68, p. 32; (b) J. N. Bronsted and W. F. K. 
Wynne-Jones, Trans. Faraday Soc, 25, 59 (1929); (c) M. M. Kreevoy and R. W. Taft, Jr., J. Amer. 
Chem. Soc, 77, 3146 (1955); (d) T. H. Fife and L. K. Jao, J. Org. Chem., 30, 1492 (1965). 

73 (a) Note 72(d); (b) M. M. Kreevoy and R. W. Taft, Jr., J. Amer. Chem. Soc, 77, 5590 (1955). 

74 E. H. Cordes, Prog. Phys. Org. Chem., 4, 1 (1967), pp. 13, 14. 

75 (a) C. A. Bunton and V.J. Shiner, Jr., J. Amer. Chem. Soc, 83, 3207 (1961); (b) M. Kilpatrick, 
J. Amer. Chem. Soc, 85, 1036 (1963). 

76 L. Zucker and L. P. Hammett, J. Amer. Chem. Soc, 61, 2791 (1939). 

77 F. A. Long and M. A. Paul, Chem. Rev., 57, 935 (1957). 

78 For a discussion and references, see M. L. Bender, Mechanisms of Homogeneous Catalysis from Protons 
to Proteins, Wiley-Interscience, New York, 1971, p. 45. 

Addition Followed by Elimination 431 

participation of the water molecule in the transition state. The low value of w 
found in acetal hydrolysis agrees with the A-l mechanism. 79 

General Catalysis in Acetal Hydrolysis 

Increasing knowledge of enzyme mechanisms has spurred a renewed search for 
general acid catalysis in acetal hydrolysis. The active site in the enzyme lysozyme, 
which catalyzes hydrolysis of the acetal link in glycosides, has a carboxylic acid 
and a carboxylate anion in favorable positions to interact with the acetal group, 
one presumably by general acid catalysis and the other by electrostatic stabiliza- 
tion of the intermediate carbocation. 80 The proposed general catalysis in the 
enzyme would be more convincing if analogies could be found. Further in- 
vestigation has led to discovery of general acid catalysis in a number of acetals 
and ketals in which either the carbocation stability is enhanced or oxygen basicity 
suppressed. Structures with phenol leaving groups constitute the majority of these 
cases. 81 The mechanisms are presumably S E 2. 82 There has been only limited 
success in the search for general catalysis and neighboring carboxylate stabiliza- 
tion in systems chosen as models for. the lysozyme active site. 83 

Thioacetals and Thioketals 

As we pointed out in the previous section, thiols have a markedly greater ten- 
dency to add to carbonyl groups than do water and alcohols. The equilibrium 
constant for the exchange reaction 8.46 is estimated 84 to be about 2.5 x 10 4 . 


C + RSH ^^ \/ + H 2 (8.46) 


Addition of hydrogen sulfide and thiols is qualitatively similar to reaction with 
alcohols in that there are two stages, formation of hemithioacetal (or hemithio- 
ketal) followed by acid-catalyzed elimination of the hydroxy group and sub- 
stitution of a second — SR (Equations 8.47 and 8.48). The transformation has 
been studied less extensively than hydration and acetal formation, and relatively 
little information on mechanism is available. The initial addition appears to be 
specific base-catalyzed, an observation that implies that RS ~ is the species that 
adds. The situation is thus similar to cyanide addition. General acid catalysis 
has, however, been found at pH 1 to 2 for addition of weakly acidic alkyl thiols, 
and the reaction rate as a function of pH has a minimum and rises both on the 

79 J. F. Bunnett, J. Amer. Chem. Soc, 83, 4956 (1961), and following papers. 

80 (a) T. H. Fife, Accts Chem. Res., 5, 264 (1972) ; (b) B. M. Dunn and T. C. Bruice, J. Amer. Chem. 
Soc, 92, 2410, 6589 (1970). (c) See, however, G. M. Louden, C. K. Smith, and S. E. Zimmerman, 
J. Amer. Chem. Soc, 96, 465 (1974), who find that electrostatic stabilization contributes only a small 
rate acceleration in a model system. 

81 (a) A report of general acid catalysis of benzophenone diethylketal has appeared: R. H. DeWolfe, 
K. M. Ivanetich, and N. F. Perry, J. Org. Chem., 34, 848 (1969). (b) Ring strain can also make pos- 
sible general acid catalysis. See R. F. Atkinson and T. C. Bruice, J. Amer. Chem. Soc, 96, 819 (1974). 

82 See note 80(a). 

83 (a) See note 80; (b) B. Capon, M. C. Smith, E. Anderson, R. H. Dahm, and G. H. Sankey, 
J. Chem. Soc. B, 1038 (1969). 

84 W. P. Jencks, Prog. Phys. Org. Chem., 2, 63 (1964), p. 104. 

432 Reactions of Carbonyl Compounds 

basic and on the acidic side. General base catalysis was not found. 85 The acid 
catalysis presumably represents addition of undissociated RSH by a mechanism 
similar to the H 2 and ROH additions. 

\ . \ / OH 

C=0 + RSH . C (8.47) 


. P H s , SR 

\ / H+ \ / 

C + RSH ^=rt C + H 2 (8.48) 



A number of important chemical and biochemical processes are initiated by 
addition of a nitrogen nucleophile to a carbonyl group. 86 These processes have 
been the subject of extensive study, and we shall not attempt to do more than 
outline the main features. 

Addition of Nitrogen Nucleophiles to C=0 

Addition of primary amines to carbonyl groups follows the pattern we have 
established for other nucleophiles with formation of a carbinolamine (Equation 
8.49). These compounds are sufficiently stable to be isolated in some cases, 87 

\ . \ / OH 

C=0 + H 2 NR , C (8.49) 


\ / OH , \ .. 

C ;=± /C^N + H 2 (8.50) 



but they usually undergo an elimination to an imine (Equation 8.50). Note that 

this reaction is analogous to the elimination of H 2 in the second stage of acetal 

formation, except that here, because the nitrogen bears a proton that is lost to a 

base, a neutral molecule results rather than an ion. The imine structure 16 is 

usually unstable if the substituents on carbon and nitrogen are all alkyl or 

hydrogen. Imines with hydrogen attached to nitrogen have been demonstrated 

spectrophotometrically, 88 but they cannot ordinarily be isolated, as they undergo 

further condensations. 89 The imine is stabilized by one or more aryl groups 

65 G. E. Lienhard and W. P. Jencks, J. Amer. Chem. Soc, 88, 3982 (1966). 

86 Discussions of mechanisms of addition of nitrogen nucleophiles may be found in the following 
sources: (a) W. P. Jencks, Catalysis in Chemistry and Enzymology, McGraw-Hill, New York, 1969, p. 
490ff; (b) W. P. Jencks, Chem. Rev., 72, 705 (1972); (c) W. P. Jencks, Prog. Phys. Org. Chem., 2, 63 
(1964); (d) R. L. Reeves, The Chemistry of the Carbonyl Group, S. Patai, Ed., Wiley-Interscience, 
London, 1966, Vol. 1, p. 567; (e) M. L. Bender, Mechanisms of Homogeneous Catalysis from Protons to 
Proteins, Wiley, New York, 1971; (f) L. P. Hammett, Physical Organic Chemistry, 2nd ed., McGraw- 
Hill, New York, 1970, p. 336. 

87 (a) P. K. Chang and T. L. V. Ulbricht, J. Amer. Chem. Soc, 80, 976 (1958); (b) E.J. Poziomek, 
D. N. Kramer, B. W. Fromm, and W. A. Mosher, J. Org. Chem., 26, 423 (1961). 

88 R. K. McLeod and T. I. Crowell, J. Org. Chem., 26, 1094 (1961). 

89 F. Sachs and P. Steinert, Ber., 37, 1733 (1904). 

Addition of Nitrogen Nucleophiles 433 

& ob5 .(min ) 

Figure 8.10 Dependence of rate on pH for the reaction 

H 3 C 



C=0 + HoNOH 




H 3 C 


+ H 2 Q 


Reprinted with permission from W. P. Jencks, J. Amer. Chem. Soc, 81, 475 
(1959). Copyright by the American Chemical Society. 

attached to carbon or nitrogen, in which case the compounds are easily isolated 
and are called Schiff bases. Stabilization is also achieved if a hydroxyl or a second 
nitrogen is attached to the nitrogen. The most common of these structures are 
the oximes (17), semicarbazones (18), and hydrazones (19). 











N— C— NH 2 


>= N \ 

N— R 



Another possible reaction of the carbinolamine, observed in the addtion of 
amide or urea nitrogen, is substitution of the hydroxyl by a second molecule of 
the nucleophile (Equation 8.51). Addition of secondary amines leads to carbinol- 

v OH ? 



+ NH 2 C- 







amines which cannot attain a neutral structure having a carbon-nitrogen double 
bond ; if there is a hydrogen on the a carbon, elimination of water can occur in 
this direction to yield a product with a carbon-carbon double bond (Equation 

434 Reactions of Carbonyl Compounds 

8.52), a process similar to that which occurs in aldol-type condensations (see 
Table 8.8). The vinyl amines (20) are referred to as enamines; they find applica- 



/ C \/ OH N " 

C ► / C=C \ < 8 - 52 > 

N— R N— R 

I I 

R R 


tion in synthesis. 90 In addition of tertiary amines, the carbinolamine is ionic and 
there is no possibility of formation of a neutral addition compound. 

Addition of primary amines to carbonyl groups has been the subject of 
extensive study, notably by Jencks and co-workers. 91 The most striking feature 
of these reactions is the characteristic maximum in the graph of reaction rate as a 
function of pH. 92 Figure 8.10 illustrates the observations for the reaction of 
hydroxylamine with acetone. It is also found that the sensitivity of rate to acid 
catalysis, 93 and to substituent effects, 94 is different on either side of the maximum in 
the pH-rate curve. These phenomena may be understood in terms of the two-step 
nature of the reaction. In acetal formation, we saw in Section 8.3 that the second 
step is rate-limiting in the overall process, and it is relatively easy to study the 
two steps separately; here, the rates of the two steps are much more closely 
balanced, so that one or the other is rate-determining depending on the pH. 

It is convenient for further analysis to divide the nitrogen nucleophiles 
into two categories: the strongly basic hydroxylamine and aliphatic amines, 

Scheme 9 

C— O + H 2 NR : 


v OH 

/ \ 





/C=N^ + H 2 + A 




C — N + A " 



C=N + HA 


y X R 


= alkyl or OH 

90 See, for example, (a) J. Szmuszkovicz, Advances in Organic Chemistry: Methods and Results, Wiley- 
Interscience, New York, 1963, vol. 4, p. 1; (b) S. F. Dyke, The Chemistry of Enamines, Cambridge 
University Press, Cambridge, 1973. 

91 See, for example, W. P. Jencks, J. Amer. Chem. Soc, 81, 475 (1959), and notes 86(a), (c), p. 432. 

92 (a) See note 91 ; (b) E. Barrett and A. Lapworth, J. Chem. Soc, 93, 85 (1908) ; (c) J. B. Conant 
and P. D. Bartlett, J. Amer. Chem. Soc, 54, 2881 (1932); (d) J. C. Powers and F. H. Westheimer, 
J. Amer. Chem. Soc, 82, 5431 (1960). 

93 (a) See note 92(d) ; (b) E. H. Cordes and W. P. Jencks, J. Amer. Chem. Soc, 84, 832 (1962). 

94 (a) See note 93(b); (b) B. M. Anderson and W. P. Jencks, J. Amer. Chem. Soc, 82, 1773 (1960). 

Addition of Nitrogen Nucleophiles 435 

pK aBH+ roughly 6 to 10, and the weakly basic semicarbazide and aryl amines, 
pK aBH+ about 4. Considering the former class first, we find good evidence that 
in neutral solution, which is on the basic side of the maximum in the pH-rate 
curve, the second step (dehydration) is rate-determining. For example, it is 
observed that when the nucleophile and carbonyl compound are mixed in rela- 
tively concentrated solution, the characteristic absorption spectrum of the 
carbonyl group disappears rapidly, and the spectrum of the final product, the 
imine, appears much more slowly. The overall reaction is subject to general acid 
catalysis, and, as we show below, it is true general acid catalysis and not specific 
acid plus general base catalysis. The general catalysis must apply to the rate- 
determining dehydration step, and the mechanism must therefore be that shown 
in Scheme 9. 95 The value of a is 0.75 and of £ is 0.27 ; the proton being donated by 
HA is thus probably close to the oxygen of the carbinolamine at the transition 
state of the slow step. 96 This evidence also establishes the mechanism for the 
reverse reaction, addition of water to C=N ; note that it differs from addition to 
C=0 in that an equilibrium protonation precedes the addition. 

The fact that true general acid catalysis is correct for the slow step in 
Scheme 9 is established for the hydrolysis of benzylidene-i-butylamine (21) 
at pH 4 to 5, conditions sufficiently basic that hydration is still the rate-deter- 
mining step, as shown in Scheme 9, but acidic enough that essentially all of the 
imine exists in the protonated form. Under these circumstances, the hydrolysis 
(reverse of Scheme 9) is subject to general base catalysis by acetate ion. 97 This 


H C(CH 3 ) 3 


observation means that if the mechanism is that shown in Scheme 9, the base A - 
is assisting in the reverse of the slow step by removing a proton from the attacking 
water molecule. If the true mechanism of the dehydration step had been specific 
acid plus general base catalysis in the forward direction (Scheme 10), the 
reverse reaction would have had to involve donation of a proton by the protonated 

Scheme 10 

\ / OH _j^ x / 6h * 

C + HA ^^ C + A" 


A" + C ^^ H 2 + /C=N V + HA 


96 (a) See note 93(b); (b) E. H. Cordes and W. P. Jencks, J. Amer. Chem. Soc, 85, 2843 (1963). 

96 (a) J. E. Reimann and W. P. Jencks, J. Amer. Chem. Soc, 88, 3973 (1966); (b) K. Koehler, W. 
Sandstrom, and E. H. Cordes, J. Amer. Chem. Soc, 86, 2413 (1964). 

97 See note 95(b). 

436 Reactions of Carbonyl Compounds 

catalyst HA to the nitrogen, and such a process can be ruled out in this instance 
because the nitrogen is already fully protonated at these pH values. 98 

In more strongly basic solutions, above about pH 9, a pathway subject to 
neither acid nor base catalysis (Scheme 11) is observed." 

Scheme 11 

w OH , \ ♦ 

,G , C=N— R + OH" 



)c=N-R ^=± ) C=N \ + H 3° + 
H R 

One might inquire at this point about the addition of a secondary amine, 
which cannot yield a stable neutral product by dehydration as the primary amine 
can. Diebler and Thorneley measured rate constants of the addition step for 
reaction of piperazine (22) with pyridine-4-aldehyde in the pH range 5.8-10.8, 
a range in which the addition step is very fast so that, for primary amines, the 
kinetics would be determined by the rate-limiting dehydration. 100 They were 



able to show, by use of fast-reaction measurement techniques, that the general 
base catalysis observed is a result of a simple rate-determining proton transfer in 
step 2 of Scheme 12. The rate constant for the actual addition (step 1) is on the 
order of 10 7 m _1 sec -1 . Note that this reaction is in the category mentioned in 
Section 8.1, p. 407, in which a simple proton transfer involving a species present 
in low concentration is rate-determining. When no base catalyst is present, step 2 
is still rate-determining, but it now consists of an intramolecular proton transfer 
from nitrogen to oxygen. 

Returning now to primary amines, one finds that as the solution is made 
more acidic, the rate increases as a result of the acid catalysis of the dehydration 
step, until the maximum rate is attained, usually at pH between 2 and 5. 101 
The decrease of rate that occurs on further decrease of pH can be explained by 
assuming that whereas greater acidity facilitates the dehydration, it inhibits 
the addition step (Equation 8.49) because only the unprotonated amine is re- 
active. The first step then becomes rate-determining. In this pH region there is no 

98 See note 95(b), p. 435. 

99 See note 95(b), p. 435. 

100 H. Diebler and R. N. F. Thorneley, J. Amer. Chem. Soc, 95, 896 (1973). 

101 See note 92(d), p. 434 and note 95(b), p. 435. 


Addition of Nitrogen Nucleophiles 437 

Scheme 12 

\ / fast \ / 

1. /C =0 + HN^ ^ C 

O" O" 

\ / rate-determining \ / 

^ + » _ ^ + BH + 


3. C + H + , C 

general catalysis with the more strongly basic aliphatic amines, and only a minor 
general acid catalysis for hydroxylamine addition. 102 These bases, like cyanide 
ion, are strong enough not to require assistance by proton transfer in the rate- 
determining step; the mechanism is as shown in Equation 8.54. The intramolec- 

\ X S>~ 

C=0 + RNH 2 . C (8.54) 

/ / \ + 

NH 2 R 

ular proton transfer from nitrogen to oxygen in intermediate 23 is presumed to 
be fast compared to the addition under these circumstances, although as we have 
noted above, it can be rate-determining above pH 5 when structural features 
cause the reaction to stop at the carbinolamine stage. The entire mechanism is 
shown in Scheme 13. 

Scheme 13 

slow below pH 4 
\ fast above pH 4 

c=o + rnh 2 : 

/ \ + 

NH 2 R 






\ + 

NH 2 R 








OH fast below p h 4 

\ / slow above pH 4 \ + 

C + HA _ C = N— R + A- + H 2 

/ \ / I 



\ + fast \ 

C=N— R + A" _ C=N + HA 

/ I / \, 


1 See note 86(c), p. 432. 


438 Reactions of Carbonyl Compounds 

The general pattern we have outlined holds true also for the more weakly 
basic nitrogen nucleophiles such as semicarbazide or aryl amines. The electron- 
withdrawing groups retard the addition step, in which the nitrogen unshared 
pair attacks carbon, but they also retard the dehydration, where again the 
unshared pair is acting in a nucleophilic manner to expel the hydroxyl group. 
The change from rate-determining addition to rate-determining dehydration is 
observed at roughly the same pH as for the more basic amines. The weaker bases, 
however, require more help from acid catalysts. In the addition step, general 
acid catalysis is found 103 with a about 0.25; in dehydration, general acid catalysis 
with the partial proton transfer (a = 0.75) found with the more basic amines is 
no longer sufficient, a approaches 1.0, and the general catalysis gives way to 
specific hydronium ion catalysis. 104 By the same token, in the reverse process, 
starting from the imine structure, the protonated imine is so strongly electro- 
philic that it can be attacked by a water molecule with no help from a base 
catalyst. The detailed mechanism is given in Scheme 14. 
Scheme 14 / 

slow below pH 4 OH 

\ fast above pH 4 \ / 

C=0 + RNH 2 + HA - C + A" 

NH 2 R 


+ A" 

NH 2 R 



C X + HA 

/ \ 



+ HA 


\ / 

/ \ 



C=N— R + A" 




fast below pH 4 
slow below pH 4 


+ A" 







R + H a O 

+ HA 

In strongly basic solution, pH roughly 10 to 12, the rate for additions of all 
but the strongly basic alkyl amines is observed to increase again. 105 In this case 
one is presumably dealing with the process shown in Scheme 15, which should be 
favored by electron-withdrawing groups on nitrogen. 106 And finally, it appears 
that in some cases at high pH this base-catalyzed dehydration becomes sufficiently 
fast that the initial addition is again rate-determining, but now, as in the case of 
addition of the secondary amine piperazine discussed above (Scheme 12), the 

103 E. H. Cordes and W. P. Jencks, J. Amer. Chem. Soc., 84, 4319 (1962). 

104 See note 94(b). 

105 (a) See note 92(b), p. 434; (b) see note 93(b), p. 434; (c) see note 94(b), p. 434; (d) A. Wil- 
liams and M. L. Bender, J. Amer. Chem. Soc, 88, 2508 (1966). 

106 See note 94(b), p. 434. 

Carboxylic Acid Derivatives 439 

Scheme 15 

OH v OH 

^C^ + OH" ^=r± ^C + H 2 


\ / OH . X .. 

C . C=N + OH- 

N— R R 

rate-determining step is not the actual addition but rather the proton transfer 
that follows it. 107 

Nucleophilic Catalysis 

It has been found that amines frequently are effective catalysts for addition of 
other nucleophiles to carbonyl groups. 108 The reason for this catalysis is that 
amines can add rapidly to the carbonyl compound to form an imine; the imine 
in turn is subject to the same kinds; of addition reactions as are carbonyl com- 
pounds, but reacts faster because it is more easily protonated. Scheme 16 illus- 
Scheme 16 

\ \ 

C=0 + RNH 2 v C=N + H 2 

/ / \ 


k x + / H 

C=N + HA , C=N + A" 

R R 


\ +/ \ / 

C=N + :QH , C 

/ \ / \i 


C , C=Q + RNH 2 


trates this process, which is referred to as nucleophilic catalysis. In order for nucleo- 
philic catalysis of addition of Q to occur, it is necessary that (1) the rate of 
addition of the catalyst to the carbonyl group be greater than the rate of addition 
of Q; (2) that the protonated imine be more reactive than the carbonyl com- 
pound toward Q; and (3) that the equilibrium favor the Q addition more than 
amine addition. 


When the carbonyl group bears as one substituent a group that can potentially 
depart as a Lewis base, the most common result of addition of a nucleophile to the 
carbonyl carbon is elimination to regenerate a carbon-oxygen double bond 

107 J. M. Sayer and W. P. Jencks, J. Amer. Chem. Soc., 95, 5637 (1973). 

los jr or a di scuss ion, see Bender, Mechanisms of Homogeneous Catalysis from Protons to Proteins, p. 165. 

440 Reactions of Carbonyl Compounds 
Scheme 17 




=0 + :Y 


/ \ 
X Y + 

R O- 

/ \ 
X Y + 


x c=o + 



(Scheme 17). The starting material, intermediates, and products may be in 
various states of protonation, depending on the acidity of the medium and the 
nature of X and Y. An alternative mechanism, observed much less commonly, 
is a unimolecular S^l dissociation (Chapter 5) to an acylium ion (25, Scheme 
18), which then reacts with a nucleophile to yield the same final result. 

Scheme 18 


N c=o , r_c=o + x- 


R— C=0 + Y y C=0 




Structures 24 are conveniently thought of as derivatives of carboxylic acids, 
and include acids, esters, anhydrides, acyl halides, and amides. These structures 
(and others less commonly encountered) can be readily interconverted, either 
directly or indirectly; the number of different reactions is therefore large. 109 
Because these processes occupy an important place in organic chemistry and 
because carboxylic acid derivatives are of central importance in biochemical 
systems and therefore of considerable interest in the study of enzyme action, they 
have been the subject of intensive investigation. 110 We shall outline briefly the 
main features, and in order to give an idea of the kinds of mechanistic questions 
involved, we consider ester hydrolysis in somewhat greater detail. 

The Addition Mechanism 

The main feature of interest is the question whether, in the replacement of X by Y 
in Reaction 8.55, the substitution is an ordinary nucleophilic substitution, either 
S#2 (Reaction 8.56), or S^l (Scheme 18), or a two-step process with addition of 
the nucleophile to give an approximately tetrahedral intermediate (26) followed 

109 Surveys outlining the general features of many of the reactions may be found in: (a) J. March, 
Advanced Organic Chemistry: Reactions, Mechanisms, and Structure, McGraw-Hill, New York, 1968; 
(b) D. P. N. Satchell, Quart. Rev. (London), 17, 160 (1963). 

110 Comprehensive discussions are to be found in: (a) M. L. Bender, Mechanisms of Homogeneous 
Catalysis from Protons to Proteins, Wiley, New York, 1971 ; (b) W. P. Jencks, Catalysis in Chemistry and 
Enzymology, McGraw-Hill, New York, 1969; (c) M. L. Bender, Chem. Rev., 60, 53 (1960). For more 
specialized treatments of particular aspects, see: (d) W. P. Jencks, Chem. Rev., 72, 705 (1972), 
general acid-base catalysis; (e) S. L.Johnson, Advan. Phys. Org. Chem., 5, 237 (1967), ester hydrolysis; 
(f) L. P. Hammett, Physical Organic Chemistry, 2nd ed., McGraw-Hill, New York, 1970, chap. 10, 
acid— base catalysis. 

Carboxylic Acid Derivatives 441 

by elimination of the leaving group. The latter process, to which we shall refer 
as the addition mechanism or stepwise mechanism, is the one we would expect by anal- 
ogy with the carbonyl reactions considered earlier in this chapter. Bender 



C=0 + :Y 





C=0 + :X 





C=0 + :Y 







C=0 + :X 




R O- R OH 

\ / \ / 

C or C s 

/ * / ** 

X Y X Y 


introduced an isotopic labeling method to demonstrate the presence of inter- 
mediate 26 in hydrolysis reactions. 111 Addition of water to a carbonyl oxygen- 
labeled substrate (Scheme 19) would yield an intermediate with two oxygens 
bonded to carbon ; a simple proton transfer, which should be very rapid, would 
make these oxygens equivalent. Reversal of the addition step would then exchange 
the oxygen. A similar process, with one less proton, can be written for addition of 

Scheme 19 




C= 18 + H 2 

R la O- 


X OH 2 

R 18 OH 2 

x o- 



x c 



OH 2 





} 8 OH 2 





=o + 

H 2 



hydroxide ion. Bender found significant exchange in ester hydrolysis; exchange 
has also been found in hydrolysis of amides, acyl chlorides, and anhydrides. 112 
Although oxygen exchange implies the existence of an intermediate, the con- 
verse is not necessarily true; the intermediate might continue on to product by 
elimination of X much faster than it reverts to starting material by elimination of 
H 2 (or OH-). 113 

Another way to demonstrate an intermediate is to show that there are two 
steps, one rate-determining under some conditions and the other under other 

111 M. L. Bender, J. Amer. Chem. Soc, 73, 1626 (1951). 

112 D. Samuel and B. L. Silver, Advan. Phys. Org. Chem., 3, 123 (1965). 

113 Strictly speaking, the observation of exchange shows only that tetrahedral intermediate is 
present, not that it necessarily lies on the reaction path leading to product. But the possibility that 
the intermediate would be readily and reversibly formed yet not go on to product seems unreason- 

442 Reactions of Carbonyl Compounds 

conditions. It is now generally agreed that except in certain types of ester hydro- 
lysis, which we consider in more detail below, and in certain reactions of acid 
halides, 114 the addition mechanism applies. 115,116 

The other important mechanistic question is one of catalysis by acids and 
bases. The situation is complicated because of the several possible sites of proto- 
nation. The substrate may be protonated on carbonyl oxygen and also on X if 
that group has unshared pairs, as it does in all the common cases; the nucleo- 
phile :Y may be protonated or not; the tetrahedral intermediate may be 
protonated in various possible ways; and either of the two steps may be 
rate-determining. It is therefore not suprising that the details are still under 

The general features of catalysis for hydrolysis, the most thoroughly studied 
of the many possible reactions, are as follows. The nucleophile : Y must have 
available an unshared pair of electrons. This requirement usually presents no 
problem in hydrolysis, where there is always plenty of H 2 0, but in concentrated 
acids, where a significant portion of the water is converted to H 3 + , the rate 
decreases. 117 Because hydroxide ion is a much more effective nucleophile than 
water, bases catalyze the hydrolysis ; this catalysis can take the form of general 
base catalysis and in some cases also nucleophilic catalysis. 

Acids also catalyze the reaction by transferring a proton to the carbonyl 
group. It has generally been considered that the site of protonation is the car- 
bonyl oxygen, 118 but this point is by no means well established, and evidence 
for protonation of nitrogen in amide hydrolysis has appeared. 119 In those special 
cases that do react by an S w l process (Scheme 18) rather than by the stepwise 
mechanism, acid catalysis presumably operates by protonation of the leaving 
group. Acid catalysis is expected to be effective for the less reactive carbonyl 
groups, as in esters and amides; for acid chlorides the electron-withdrawing 
halogen makes the unprotonated carbonyl so reactive that acid catalysis is not 
usually observed, except again in those cases where an S^l mechanism is being 
followed. 120 

Nucleophilic catalysis is a process of particular significance in reactions of 
carboxylic acid derivatives. As an example we may cite hydrolysis catalyzed by a 
tertiary amine (Scheme 20). The catalysis is effective because initial attack of the 
amine will be faster than attack by the less nucleophilic water ; the amine addi- 
tion yields the intermediate 27 which, because of the positive charge, has an 
extremely reactive carbonyl group and is attacked by water much faster than the 
original compound. The fact that a given base is acting by nucleophilic catalysis 

114 (a) M. L. Bender and M. C. Chen, J. Amer. Chem. Soc, 85, 30 (1963); (b) D. P. N. Satchell, 
J. Chem. Soc, 558, 564 (1963). 

116 Addition intermediates have been observed directly in favorable cases. See (a) M. L. Bender, 
J. Amer. Chem. Soc, 75, 5986 (1953); (b) G. A. Rogers and T. C. Bruice, J. Amer. Chem. Soc, 95, 
4452 (1973) ; (c) N. Gravitz and W. P. Jencks, J. Amer. Chem. Soc, 96, 489, 499, 507 (1974). 

118 C. R. Smith and K. Yates, J. Amer. Chem. Soc, 94, 8811 (1971), have reported evidence that 
amides may not always hydrolyze by the addition mechanism. 

117 See, for example: (a) K. Yates, Accts. Chem. Res., 4, 136 (1971) (esters); (b) J. T. Edward and 
S. C. R. Meacock, J. Chem. Soc, 2000 (1957) (amides). 

118 See note 110(c), p. 440. 

119 See note 116. 

120 See note 114(a). 

Carboxylic Acid Derivatives 443 

Scheme 20 


R R O- 

C=0 + NR 3 ^ C + 


R O- R 

\ / ,. \ 

c , c=o + x 

/ \+ +/ 

X NR 3 R 3 N 


R x R^ OH 

C=0 + H 2 ;=± C 

+ / +/ \ 

R 3 N R 3 N OH 


C , N C=0 4- NR 3 + H + 

+ / \ / 

R 3 N OH HO 

rather than by general base catalysis (removal of a proton from attacking H 2 0) 
can be established by noting deviations from the Bransted catalysis correlation 
that demonstrate that a given substance is markedly more effective as a catalyst 
than its proton basicity would indicate, or by structural variations that show the 
effectiveness as a catalyst to be more sensitive than proton basicity to steric 
effects. 121 

Electrophilic catalysis by Lewis acids is also observed; here no ambiguity 
arises with general acid catalysis, as Lewis acids and proton acids are not the 
same. An interesting example is the strong catalysis of thiolester hydrolysis by 
mercuric and silver ions. These soft acids presumably coordinate with the sulfur 
and, by virtue of the consequent electron withdrawal, make the carbonyl group 
much more susceptible to attack in the addition mechanism, or, in favorable 
cases, promote unimolecular S w l cleavage of the sulfur-carbon bond. 122 

Ester Hydrolysis 

We close this section with a somewhat more detailed consideration of ester 
hydrolysis as an example of the kinds of questions that arise in study of reactions 
of acid derivatives. 123 

Ingold 124 classified the possible mechanisms of ester hydrolysis according 
to the scheme shown in Table 8.5. To his original eight categories a ninth, 
E1 CB , has been added more recently, and has been included in the table. The 
primary subdivision is made on the basis of whether the acyl-oxygen or the alkyl- 
oxygen bond is cleaved. This information may be obtained by isotope tracer 
studies using 18 (Equation 8.57), 125 or by hydrolyzing an ester with an asym- 

121 See, for example, Bender, Mechanisms of Homogeneous Catalysis from Protons to Proteins, chap. 6. 

122 D. P. N. Satchell and I. I. Secemski, Tetrahedron Lett., 1991 (1969). 

123 For reviews, see: C. H. Bamford and C. F. H. Tipper, Eds., Ester Formation and Hydrolysis 
(Comprehensive Chemical Kinetics, Vol. 10), American Elsevier, New York, 1972, chap. 2 (A. J. 
Kirby) and 3 (R. E.J. Talbot). 

124 C. K. Ingold, Structure and Mechanism in Organic Chemistry, 2nd ed., Cornell University Press, 
Ithaca, N.Y., 1969, p. 1131. 

125 See note 112, p. 441. 

444 Reactions of Carbonyl Compounds 
Table 8.5 Mechanisms of Ester Hydrolysis 








A AC 2" 




A AC 1 


B AC 1 









A AI 2 

B AI 2 






B AL 1 

" C. K. Ingold, Structure and Mechanism in Organic Chemistry, 2nd ed., Cornell University Press, Ithaca, 
N.Y., 1969, p. 1131. 

6 A or B : acid or base catalysis ; AC or AL : acyl-oxygen or alkyl-oxygen fission ; 1 or 2 : unimolecular 
or bimolecular. E1 0B designates unimolecular elimination through the conjugate base. 

metric carbon bonded to oxygen in the alcohol portion (Equation 8.58). 126 The 
reactions proceeding by alkyl-oxygen cleavage are, of course, nucleophilic 
substitutions at saturated carbon with carboxylate or carboxylic acid leaving 
groups; these processes have been considered in Chapters 4 and 5. They require 
the leaving group to be a particularly weak base (for example, />-nitrobenzoate) 
or the carbocation R + to be well stabilized. Thus £-butyl esters usually hydrolyze 
by alkyl-oxygen cleavage. 

126 (a) B. Holmberg, Ber., 45, 2997 (1912). For other methods see (b) E. H. Ingold and C. K. 
Ingold, J. Chem. Soc, 756 (1932); (c) O. R. Quayle and H. M. Norton, J. Amer. Chem. Soc, 62, 

Carboxylic Acid Derivatives 445 




C=OH + H,0 





C=0 + OH- 



/ \ + 
R'O OH 2 

R O- 

V ; 

/ \ 





C_OH + R'OH 




0=O + R'OH 






C^O . R— C=0 + R'OH , 

/ + +H a o +/ 

R'— O H 2 

H + 

C=-0 + R'OH 

Not observed 



-> RO^ + C=C=0 






,C— O— C— + OH- 

Not observed 

\ I 

// / \ 



-► C— O- + C— OH 

o / '\ 

\ H + 
C— O— R ^ 





C— OR 




\ H 3 \ 

C— OH + R + , C— OH + ROH + H + 

O O 

X H a O \ 

C— O- + R + — -^ C— OH + ROH 

° Mechanisms are schematic and do not show initial and final proton transfers that may occur between 

acid and base sites within an intermediate. 

* A A c2 and B AC 2 are the most common ester hydrolysis mechanisms. 

» R. F. Pratt and T. C. Bruice, J. Amer. Chem. Soc, 92, 5956 (1970). 

The most common ester hydrolyses involve acyl-oxygen cleavage and 
proceed by the A AC 2 mechanism under acid catalysis or the B AC 2 mechanism 
under base catalysis. These are the processes that involve the tetrahedral inter- 
mediate, demonstrated by the methods mentioned earlier. The third mechanism, 
A AC 1, occurs under special circumstances as we note below. The B AC 1 process 
presumably does not occur because it would require unimolecular departure of 
RO ~ , which is not a sufficiently good leaving group. Hydrolyses in basic medium 
are for practical purposes not reversible. The acid formed is immediately con- 
verted to the carboxylate ion, which has an unreactive carbonyl carbon on ac- 
count of the negative charge. 

446 Reactions of Carbonyl Compounds 

R— C ^ 18 + R'OH 

acyl-oxygen jf \ ( 

fission ^^"^ OH 

R— C + H a 18 ^or (8.57) 

\>R' ^^. o 

alkyl-oxygeii*--.^^ ^ 

fi» s ion R— C + R'— 18 OH 


R— C + HO-C-4 

acyl-oxygen ^^>r \ 

.~ fission ^^^ Oil 

J^ ^. — retained 


R— CT a + h z O -T or 

V „' K ^\ ( 8 - 58 ) 

O-C-b ^ 


R— C + HO— C— b 


racemized or 

In base-catalyzed hydrolyses, general base catalysis is well established. 127 
In a general base-catalyzed reaction of alcohols with ethyl trifluoroacetate 
(Scheme 21) it is possible to establish for pyridine catalysis that Mechanism I 
(true general base catalysis) is correct rather than the kinetically equivalent 
Mechanism II (specific base plus general acid catalysis). From the rate of the 
reaction and the pK of pyridine, one can show that the initial addition of RO ~ 
in Mechanism II would have to occur with a rate constant of 7 x 10 9 Af _1 
sec -1 , nearly diffusion-controlled and unreasonably high for such a process. 128 
It is therefore also likely that the general base-catalyzed hydrolysis proceeds by 
the true general base-catalyzed route. The points for hydroxide and for various 
other strong nucleophiles do not lie on the Bronsted law general base catalysis 
correlation line established for weaker nucleophiles; these strong nucleophiles 
are presumably entering as nucleophilic catalysts, by direct attack on the 
carbonyl group, rather than as general bases by removal of a proton from an 
attacking water molecule as in Mechanism I. 129 

Ester hydrolysis would be expected to be subject to general acid catalysis, 
but this catalysis appears to have been conclusively demonstrated in relatively 
few cases. 130 Rather more is known about hydrolysis in strong acid solutions. 
Yates, 131 for example, has reported data on hydrolysis of several acetates in 
strong acid solution and uses a modified Bunnett plot according to Equation 
8.59 (or, for regions of acidity where a significant portion of the ester is proton- 
ated, Equation 8.60). In these equations, mH , with m = 0.62, is an acidity func- 

127 (a) W. P. Jencks and J. Carriuolo, J. Amer. Chem. Soc, 83, 1743 (1961); (b) S. L. Johnson, 

Advan. Phys. Org. Chem., 5, 237 (1967). 

126 S. L. Johnson, J. Amer. Chem. Soc, 86, 3819 (1964). 

129 (a) See note 127; (b) Bender, Mechanisms of Homogeneous Catalysis from Protons to Proteins, p. 

130 For an example, see: S. Milstien and L. A. Cohen, J. Amer. Chem. Soc, 94, 9158 (1972). 

131 See note 117(a), p. 442. 

Carboxylic Acid Derivatives 447 

Scheme 21 

Mechanism I 
General Base Catalysis 

CF 3 CF 3 O- 

\ slow \ / 

B-H— O + C=0 , BH + + C 

y / v 



CF 3 ^ O- CF 3 ^ 

C r . X 0=O + R'O- 

R'o' X OR RO 7 

R'O + BH + , R'OH-B 

Mechanism II 
Specific Base plus General Acid Catalysis 


B + ROH > RO" + BH + 

CF 3 CF 3 OH 

\ slow \ / 

RO" + C=0-HB+ , C + B 


CF 3 OYl CF 3 

C + B . X C=0-HB + + R'O" 


R'O" + BH + . ROH + B 

tion appropriate to ester protonation. Figure 8.1 1 shows plots of rate as a function 
of percent sulfuric acid in the medium and plots of Equation 8.59 for four 
different types of esters (28). In Types I and II, the initial increase of rate followed 
by a drop reflects the ordinary A AC 2 mechanism, catalyzed by acid but requiring 
as nucleophile free H a O, which begins to become less available as the proportion 
of sulfuric acid increases. The final rise, which occurs for Type I and Type II 
esters, corresponds to a change to a mechanism not requiring nucleophilic 
participation of water, as shown by the break in the acidity function graph, for 
Type I presumably to A AC 1 and for Type II esters probably to A AL 1. For the 

log k + mH = rloga H20 + Const. (8.59) 


log k - log — — — = r log a H20 + Const. (8.60) 

a sh + + n 

N c=o 



Type I Type II Type III Type IV 

R = primary alkyl R = secondary alkyl, R = vinyl, R = /er/-butyl, 

benzyl, allyl phenyl /j-methoxyphenyl 


10 - 

5 - 

40 60 80 

Percent H 2 S0 4 


15 r 



Percent H 2 S0 4 



10 2 k (min~') 

5 - 



80 100 


Percent H 2 S0 4 

10 - 

5 - 

J L 


J I 

J L 


40 60 
Percent H 2 S0 4 



-.5 - 

-1 -1.5 
log <*H 2 o 

Figure 8.11 (a) Hydrolysis rates of esters of Types I through IV as a function of percent 
H 2 S0 4 . (b) Graphs of Equation 8.59 for esters of Types I through IV. 

h m 
A = lo g™ T1S 

- /V SH+ + "0 

Reprinted with permission from K. Yates, Accts. Chem. Res., 4, 136 (1971). 
Copyright by the American Chemical Society. 

Enols, Enolates, and Carbon Nucleophiles 449 

Type III esters, the acidity function plots demonstrate clearly that in these 
cases also a change in mechanism occurs ; this fact is not evident from the graphs 
of rate vs. percent sulfuric acid, because the change occurs before the acid 
concentration becomes high enough to cause the decrease found with Types I 
and II. Since vinyl and phenyl cations are unlikely, Yates proposes a change to 
the A AC 1 mechanism, or, for the vinyl case, to a mechanism involving protonation 
of the carbon-carbon double bond. The f-butyl acetate, Type IV, hydrolyzes by 
the A AL 1 route over the whole range, a fact confirmed by isotope tracers, 132 
but uncertainty remains about the />-methoxyphenyl acetate, because although it 
behaves like the f-butyl ester, most of the reaction proceeds with acyl-oxygen 
cleavage. 133 

Questions of general catalysis by the various acidic species present in strongly 
acid media such as sulfuric acid-water mixtures are beginning to be explored. 134 


The second main aspect of reactions of carbonyl compounds is one we have 
already touched upon in Chapter 3. The carbonyl group increases the acidity of 
C — H bonds on a carbon directly attached to it by many powers of ten over an 
unactivated carbon-hydrogen bond. Removal of such a proton leaves the 
conjugated ambident enolate ion (29), which can be reprotonated either at the 
carbon, to give back the original keto tautomer, or at oxygen to give the enol 
(Equation 8.61). 135 Acid also promotes interconversion between enol and keto 

H O 

^C-C/ + :B 
/ \ 

y o , o- 

/ \ / \ 


+ BH H 

C=C + :B (8.61) 

/ X 

forms (Equation 8.62). In some cases it has proved possible by careful exclusion 
of acids and bases to isolate enol and keto forms, 136 but under ordinary circum- 
stances there are sufficient acids or bases present to cause rapid interconversion. 

Ho H OH* OH 

\ S X / ^ X / 

— C— C + HA , — C— C + A" v C=C + HA 

/ \ / \ / \ 


132 C. A. Bunton and J. L. Wood, J. Chem. Soc, 1522 (1955). 

133 See note 117(a), p. 442. 

134 R. A. Cox, J. Amer. Chem. Soc, 96, 1059 (1974). 

135 (a) For a discussion of enolization, see S. Forsen and M. Nilsson, in The Chemistry of the Carbonyl 
Group, J. Zabicky, Ed., vol. 2, Wiley-Interscience, London, 1970, p. 157. (b) Preparative aspects of 
enols and particularly enolate ions are discussed in detail with numerous references to the literature 
in H. O. House, Modern Synthetic React