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PROFESSOR: All right, so
we started talking about

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transition metals, and at the
end of last time we'd given an

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introduction to all the sort of
nomenclature and things you

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need to know, and we had just
gotten up to d orbitals, and

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when you're talking about
transition metals you're

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talking about d orbitals.
 

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So, we're going to start with a
little review of d orbitals,

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some of you have seen this
before, maybe some

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of you have not.
 

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But here is what you're
going to need to know

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about the d orbitals.
 

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You need to know the names of
all the d orbitals, you should

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be able to draw the shapes of
the d orbitals, and so the bar

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is not too high for this.
 

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You see the drawings that are
in your handouts, you should be

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able to do about that well, it
doesn't have to be super fancy.

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But you should be able to draw
their shapes, and you should

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also be able to recognize which
d orbital it is -- if you have

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a picture of different d
orbitals, you should be able

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to name that d orbital.
 

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So let's just review what
the d orbitals look like.

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And in this class, we're always
going to have the same

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reference frame, so we're
always going to have the z-axis

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up and down, the y-axis is
horizontal, and the x-axis is

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coming out of the board
and going into the board.

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So, we'll always use
that same description.

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It'll often be given, but if
it's not, you can assume that's

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what we're talking about.
 

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So, the first d orbital we'll
consider is d z squared.

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It has its maximum amplitude
along the z-axis, and it also

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has a little donut
in the x y plane.

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So, d x squared minus y squared
has its maximum amplitude along

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the x and the y axis, so
directly on-axis for this

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particular d orbital.
 

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The next sets of d orbitals
have their maximum amplitudes

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off-axis, so they don't
correspond directly to the axes

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that I just mentioned, they're,
in fact, 45 degrees off-axis.

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So we have the d y z shown
here, d x z shown here, so

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maximum amplitude 45 degrees
off z and x axes, and then z --

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these pictures are a little bit
complicated to see -- d x y, so

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it's 45 degrees off
of the x and the y.

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And so, here I tried to
draw them all in the same

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orientation of axes, which
is a little bit difficult.

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So now let's look at them in
terms of where they're drawn so

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you can kind of see them a
little bit better, and so why

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don't you try to learn to
recognize all of these.

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So, what is this one
called? d z squared.

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What is this one, so its
maximum amplitude is along

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x and y? d x squared
minus y squared.

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I think this picture might be a
little -- you might have

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somewhat aversion later on, but
this is just good practice for

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you in recognizing them.
 

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So here we have one 45 degrees
off-axis, which one is this?

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Yup.
 

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And this one over here?
 

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Yup.
 

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So, y z.
 

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And this last one here?
 

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Yup, we have the x z, so
it's going up and down

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for the for z-axis.
 

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So, a little more practice now.
 

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To show what these look like
again, you want to think in

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three dimensions, and on paper
and in most the time in

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Powerpoint you're not in three
dimension, so here's a little

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movie in three dimensions.
 

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Here you can really see that
donut, so this is d x squared

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-- see the maximum amplitude
along z-axis here, and

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down here, and the little
donut in the x y plane.

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So this one is d x
squared minus y squared.

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The maximum amplitudes are
right directly along axis,

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so that allows you to
distinguish it from d x y.

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So when it's on-axis here, it's
the x squared minus y squared.

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So moving along here, so this
is d x y, so you see that it's

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in that axis but it's not
directly on-axis -- the maximum

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amplitude is 45 degrees
off, so the orbitals are in

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between the axes there.
 

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Now we're looking at one that
has a z in it, and it looks

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like it's x z, so that's where
our maximum amplitude is

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between the x and the
z-axes, 45 degrees off.

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And our last one, we
have y and z here.

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Again, 45 degrees off-axis
between the y-axis and z-axis.

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So, hopefully these little
movies will help cement in

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your brain, what the shapes
of these d orbitals are.

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All right, so that's d
orbitals, and we're going to be

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mentioning d orbitals in every
lecture in this, and you have

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to be thinking about what the
shapes of the d orbitals are to

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talk about today's topic, which
is crystal field theory.

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So, there are two types of
theories that you may hear of

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and that your book mentions --
crystal field theory, and

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ligand field theory, and like
most things that you learn

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about in freshman chemistry,
the theories were developed to

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explain experimental
information.

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So there are special properties
of coordination complexes, so

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that's where you have a
transition metal in the middle

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and you have ligands all
around it, so you have these

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coordination complexes and they
have special properties.

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And so people wanted to try to
rationalize these special

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properties and they came up
with these two theories.

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So, the basic idea behind these
theories is that when you place

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a metal ion with the particular
oxidation number in the center

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of a coordination sphere, and
you have all these ligands,

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these donor ligands, all
surrounding them, that the

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energy of the d orbitals is
going to be altered by the

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position of those ligands.
 

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So it's all about the d
orbitals, and the d orbitals

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are going to experience some
influence from these ligands,

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these donor ligands that
are surrounding the metal.

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So then, between these two
theories that are used to

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explain how these d orbitals
are being affected.

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The crystal field theory is
based on an ionic description,

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so it considers the ligands
as negative point charges.

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It's a very simplified model,
whereas as the ligand field

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theory considers covalent, as
well as ionic aspects

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of coordination.
 

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It's more powerful it's more
useful, but it's also a bit

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more complex, and so we don't
cover it in this of course, and

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if you go on and take the first
level of inorganic chemistry,

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which is 503, then
you'll hear about this.

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But for this course, we're
just going to talk about

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crystal field theory.
 

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Even though it's very much
of a simplified model, it

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00:08:25 --> 00:08:26
actually works very well.
 

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You can explain quite a few
properties of coordination

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complexes just using
this simplified method.

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So, crystal field theory,
again, very simple.

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It's just considering the ionic
interactions, it considers the

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ligands as negative
point charges.

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And so, the basic idea is that
ligands, as negative point

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charges, are going to have
repulsive effects if they get

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close to the d orbitals.
 

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So here is a drawing of a
metal, and so this is metal

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abbreviated m, its oxidation
number is m plus here, and it

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has ligands all around it.
 

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What is the geometry here?
 

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It's octahedral geometry.
 

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And so we have ligands up and
down along z, ligands along y,

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and a ligand going back
along x, and a ligand

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coming out along x.
 

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And so here's another picture
of the same thing, the metal is

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in the middle, and the ligands
-- in this case, you have these

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ammonia ligands or these little
negative point charges, which

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are all along the axes.
 

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You have four along the
equatorial, and one up and

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one down, so this is the
octahedral geometry.

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And so you can just think about
each of these ligands as

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negative point charges.
 

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And so, if the negative point
charge is pointing right

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toward a d orbital,
that'll be very repulsive.

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If it's not it's
less repulsive.

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00:10:00 --> 00:10:04
That's the whole idea behind
this crystal field theory.

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00:10:04 --> 00:10:09
So, here again, is just another
little picture, so you can kind

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of get the idea that we're
going to be thinking about the

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all the shapes of the d
orbitals, and we're going to

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think about where
the ligands are.

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Today we're going to talk about
octahedral geometry, but we're

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also going to go on and talk
about tetrahedral

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geometry later.
 

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So here in octahedral geometry,
you can think about the

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positions of all of these
negative point charges

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surrounding your d orbitals.
 

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And when the d orbitals are on
axis, like the ligands, there's

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going to be more repulsion, so
you can see here that would be

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quite repulsive -- you have a
negative point charge

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00:10:41 --> 00:10:42
by that d orbital.
 

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When the d orbitals are
off-axis and the ligands are

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on-axis, that's less repulsive.
 

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And that's the basic idea.
 

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So, let's look at each one of
these orbitals now in detail

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and think about how a ligands
that's pointing directly toward

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it is going to be affected.
 

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So we have the ligands, l, as
these point charges directed

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toward the d z squared, and the
d x squared minus y squared

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orbitals, and these would
result in quite a

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bit of repulsion.
 

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So if you had a ligand right up
here along z, and so that would

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be a very close interaction.
 

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In this case, you're going to
have ligands along x and y,

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again pointing directly toward
the orbitals, that would

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be quite repulsive.
 

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And I'll just mention, we'll
come back to this later, that

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one can think about the case
where you have the octahedral

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geometry where the ligands are
in a definite position, and you

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can also think about this sort
of hypothetical case where you

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have a metal in the middle and
you have the ligands, here are

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the little ligands, and they're
everywhere, there's ligands

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everywhere all around.
 

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And so, in this case where you
have ligands everywhere all

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around your metal, then all
your d orbitals would have the

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same energy, but if you take
the ligands and you isolate

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them in particular positions,
then you can consider how the

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different shapes of the d
orbitals will be affected.

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We'll come back to
that in a minute.

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All right, so here we have a
case where our ligands are

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on-axis, our orbitals on-axis,
this is a large repulsion.

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So, I will tell you that d x
squared and d z squared and d x

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squared minus y squared
orbitals are destabilized, and

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they are destabilized
by the same amount.

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So there's repulsion now, and
so they're destabilized, and

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they're destabilized by the
same amount of energy.

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00:12:47 --> 00:12:50
So what's it called
when orbitals are

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of the same energy?
 

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Yup.
 

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So, d z squared and d x squared
minus y squared are degenerate.

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00:13:02 --> 00:13:07
So, d z squared and d x squared
minus y squared orbitals are

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destabilized more than the
other three orbitals, and let's

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consider now why that is true.
 

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00:13:15 --> 00:13:18
So here are our other sets of
orbitals, and remember, here

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00:13:18 --> 00:13:22
the maximum amplitude of these
orbitals are 45 degrees

217
00:13:22 --> 00:13:27
off-axis, whereas our
ligands are all on-axis.

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00:13:27 --> 00:13:31
So, the ligand negative charges
are directed in between these

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00:13:31 --> 00:13:34
orbitals, not directly
toward them.

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00:13:34 --> 00:13:40
So that is stabilized compared
to this hypothetical case where

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the ligands are everywhere, so
some of them will be pointing

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00:13:43 --> 00:13:47
toward them, and also
stabilized compared to the

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00:13:47 --> 00:13:49
other sets of orbitals
where the ligands are now

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00:13:49 --> 00:13:54
pointing directly at them.
 

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So these three sets of orbitals
are stabilized relative to the

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00:13:57 --> 00:14:01
d z squared and the d x squared
minus y squared orbitals,

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00:14:01 --> 00:14:04
and they're stabilized
by the same amount.

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So these three orbitals
are also degenerate with

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respect to each other.
 

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So then to sort of summarize
this set of orbitals, we have

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for d z squared and d x squared
minus y squared, we have large

232
00:14:24 --> 00:14:27
repulsions by those negative
point charges, they're pointing

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00:14:27 --> 00:14:31
directly at the orbitals, and
so they're destabilized, higher

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00:14:31 --> 00:14:38
in energy than the other --
the d x y, d y z and d x z.

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00:14:38 --> 00:14:46
For the d y z, d x z and d x y,
they're smaller repulsion,

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00:14:46 --> 00:14:49
because these orbitals are
off-axis, and so the negative

237
00:14:49 --> 00:14:51
point charges aren't
pointing directly at them.

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00:14:51 --> 00:14:56
So they're stabilized relative
to these guys up here.

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00:14:56 --> 00:15:00
So that's the whole idea
behind an octahedral case

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00:15:00 --> 00:15:04
of crystal field theory.
 

241
00:15:04 --> 00:15:07
And we can look at this
just one other way,

242
00:15:07 --> 00:15:08
if pictures help you.
 

243
00:15:08 --> 00:15:11
Here it's a little clearer that
those negative point charges

244
00:15:11 --> 00:15:14
are pointing directly toward
the orbitals, here I think you

245
00:15:14 --> 00:15:18
can see that the negative point
charges are not directly

246
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pointing toward any
of the orbitals.

247
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So I'll show you a bunch of
different figures, this all

248
00:15:23 --> 00:15:26
shows you the same thing,
but some might help you see

249
00:15:26 --> 00:15:30
this relationship better.
 

250
00:15:30 --> 00:15:34
OK, so now we're going
to draw some diagrams.

251
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I'm going to start over here.
 

252
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So we're going to draw what's
called a crystal field

253
00:15:46 --> 00:16:00
splitting diagram, and this
is for an octahedral case.

254
00:16:00 --> 00:16:03
And the diagrams are going
to look different depending

255
00:16:03 --> 00:16:07
on what the geometry is.
 

256
00:16:07 --> 00:16:12
So when we draw this diagram,
energy is going up, and we're

257
00:16:12 --> 00:16:19
going to start with our 5 d
orbitals, and so this is going

258
00:16:19 --> 00:16:27
to be the average energy, the
average energy of

259
00:16:27 --> 00:16:32
our d orbitals.
 

260
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And so, this is then with a
spherical crystal field.

261
00:16:41 --> 00:16:46
So that's where the ligands are
distributed around uniformly.

262
00:16:46 --> 00:16:50
So it's all spherical, they
aren't set up in the octahedral

263
00:16:50 --> 00:16:53
case yet, our octahedral
diagram's going to be over

264
00:16:53 --> 00:16:58
here, but this is the case
that this represents.

265
00:16:58 --> 00:17:03
If you have all your ligands
spherically distributed around

266
00:17:03 --> 00:17:05
your metal, then the energy of
all the d orbitals are

267
00:17:05 --> 00:17:08
identical, because every d
orbital has the same amount of

268
00:17:08 --> 00:17:11
ligands, it's uniform,
it's symmetrical all

269
00:17:11 --> 00:17:12
around the metal.
 

270
00:17:12 --> 00:17:15
And I just want to tell you
that this is was very exciting

271
00:17:15 --> 00:17:17
to me when I saw this.
 

272
00:17:17 --> 00:17:20
I've been teaching this class
for a while, and I never had a

273
00:17:20 --> 00:17:24
real spherical crystal field
around my metal before.

274
00:17:24 --> 00:17:28
And then I walked into
Walgreens one day, and I was

275
00:17:28 --> 00:17:32
very excited to see that
Walgreens sold spherical

276
00:17:32 --> 00:17:33
crystal fields.
 

277
00:17:33 --> 00:17:35
I mean you never know what
you're going to get.

278
00:17:35 --> 00:17:37
I'm a big fan of Walgreens,
I've found a lot of good stuff,

279
00:17:37 --> 00:17:42
toys for my dog, etcetera,
but this was really amazing.

280
00:17:42 --> 00:17:46
So I asked the cashier on the
way out whether they knew they

281
00:17:46 --> 00:17:50
were selling spherical
crystal fields, and

282
00:17:50 --> 00:17:53
they did not actually.
 

283
00:17:53 --> 00:17:56
So, you just never know
what you're going to get.

284
00:17:56 --> 00:18:02
OK, so in that case, where the
ligands are uniform all around,

285
00:18:02 --> 00:18:07
the energy is the same.
 

286
00:18:07 --> 00:18:10
But now, if we have an
octahedral crystal field over

287
00:18:10 --> 00:18:23
here, so we have our octahedral
crystal field, then we

288
00:18:23 --> 00:18:26
get some splitting.
 

289
00:18:26 --> 00:18:30
So some of our orbitals are
going to be destabilized,

290
00:18:30 --> 00:18:32
and they'll be higher
in energy here.

291
00:18:32 --> 00:18:37
So we have the d x squared
minus y squared, and d z

292
00:18:37 --> 00:18:40
squared over here are going
to be higher in energy.

293
00:18:40 --> 00:18:47
And we're going to have three
that lower in energy, so we'll

294
00:18:47 --> 00:18:55
have our d x y, our d y z, and
our d x z over here, will

295
00:18:55 --> 00:18:58
be lower in energy.
 

296
00:18:58 --> 00:19:05
This difference is called the
octahedral field splitting

297
00:19:05 --> 00:19:09
energy, because it's the
amount of energy that the

298
00:19:09 --> 00:19:11
octahedral field is split.
 

299
00:19:11 --> 00:19:20
So over here, we can put this
is for the octahedral case,

300
00:19:20 --> 00:19:34
crystal field splitting energy.
 

301
00:19:34 --> 00:19:38
And again, some of the orbitals
go up in energy, some of the

302
00:19:38 --> 00:19:42
orbitals go down in energy,
and the overall energy

303
00:19:42 --> 00:19:44
needs to be conserved.
 

304
00:19:44 --> 00:19:55
So, if two orbitals go up in
energy, and three go down in

305
00:19:55 --> 00:20:02
energy, then to have everything
add up, you can say that three

306
00:20:02 --> 00:20:07
go up in energy by 3/5, and
two, these three orbitals are

307
00:20:07 --> 00:20:09
going to go down by 2/5.
 

308
00:20:09 --> 00:20:16
So overall, the energy of
the system is maintained.

309
00:20:16 --> 00:20:19
OK, so that's a crystal field
splitting diagram for an

310
00:20:19 --> 00:20:23
octahedral case, and now let's
look at some examples of this.

311
00:20:23 --> 00:20:29
So let's look at an example,
and we're going to have a

312
00:20:29 --> 00:20:34
chromium system that has
three n h 3 ligands

313
00:20:34 --> 00:20:38
and three b r ligands.
 

314
00:20:38 --> 00:21:34
Now, you tell me what
the d count of that is.

315
00:21:34 --> 00:21:52
Let's just take
10 more seconds.

316
00:21:52 --> 00:21:55
They're not as high overall,
but still more people

317
00:21:55 --> 00:21:56
got the right answer.
 

318
00:21:56 --> 00:22:00
So, let's take a look at this.
 

319
00:22:00 --> 00:22:04
What's the oxidation
number of bromium?

320
00:22:04 --> 00:22:11
What is it?
 

321
00:22:11 --> 00:22:13
Bromium?
 

322
00:22:13 --> 00:22:17
What's 1 b r minus?
 

323
00:22:17 --> 00:22:19
What's its oxidation number.
 

324
00:22:19 --> 00:22:21
Minus 1.
 

325
00:22:21 --> 00:22:22
There are three of them.
 

326
00:22:22 --> 00:22:25
What about ammonia?
 

327
00:22:25 --> 00:22:25
0.
 

328
00:22:25 --> 00:22:27
So, 3 times 0.
 

329
00:22:27 --> 00:22:31
And the overall charge of
this is 0, so there's

330
00:22:31 --> 00:22:32
nothing up there.
 

331
00:22:32 --> 00:22:35
So what does that
mean about chromium?

332
00:22:35 --> 00:22:38
Plus 3.
 

333
00:22:38 --> 00:22:41
All right, so now we have
to figure out the d count.

334
00:22:41 --> 00:22:47
So the d count is going to
equal the -- and the periodic

335
00:22:47 --> 00:22:50
table, the group number, so if
you switch to my slides,

336
00:22:50 --> 00:22:52
we can see what that is.
 

337
00:22:52 --> 00:22:55
So what is that for chromium?
 

338
00:22:55 --> 00:22:56
6.
 

339
00:22:56 --> 00:23:00
And then we have 6 minus 3,
because our oxidation number is

340
00:23:00 --> 00:23:08
3, and so we have a d 3 system.
 

341
00:23:08 --> 00:23:10
So, did some of you get
this wrong because you

342
00:23:10 --> 00:23:13
stopped too early?
 

343
00:23:13 --> 00:23:17
Here, the answer, if you had
3, you could have stopped

344
00:23:17 --> 00:23:20
with oxidation number and
still gotten it correct.

345
00:23:20 --> 00:23:26
So that's a d 3 system.
 

346
00:23:26 --> 00:23:29
So, we're going to worry about
three d electrons, and we're

347
00:23:29 --> 00:23:35
going to put three d electrons
into our splitting diagram.

348
00:23:35 --> 00:23:38
OK, so if you had a
hypothetical spherical crystal

349
00:23:38 --> 00:23:43
field, you would have your
one's in here, but now let's

350
00:23:43 --> 00:23:46
consider what happens in
the octahedral case.

351
00:23:46 --> 00:23:48
So we can come down here.
 

352
00:23:48 --> 00:23:53
Am I going to put my first
electron down here or up here?

353
00:23:53 --> 00:23:54
Down.
 

354
00:23:54 --> 00:23:56
Oh, I just realized that I
didn't put two things on this

355
00:23:56 --> 00:24:01
diagram, so these are in your
notes, but these diagrams have

356
00:24:01 --> 00:24:06
little abbreviations in them
for the orbital levels.

357
00:24:06 --> 00:24:10
So we have an e g and t 2 g,
and that's an abbreviation

358
00:24:10 --> 00:24:12
for the names of the ts of
orbitals, which you'll see

359
00:24:12 --> 00:24:16
later is very convenient in
terms of writing things out.

360
00:24:16 --> 00:24:18
All right, so we're going
to put them down here.

361
00:24:18 --> 00:24:22
Am I going to put two of them
together with the spins

362
00:24:22 --> 00:24:23
up in the first orbital?
 

363
00:24:23 --> 00:24:24
No.
 

364
00:24:24 --> 00:24:27
So you know that that is not
good, give you the same

365
00:24:27 --> 00:24:30
four quantum numbers, you
don't want to do that.

366
00:24:30 --> 00:24:32
So, we can put them in.
 

367
00:24:32 --> 00:24:37
What about just putting in a
paired set over here yet?

368
00:24:37 --> 00:24:37
No.
 

369
00:24:37 --> 00:24:41
They have the same energies
here, so we're going to

370
00:24:41 --> 00:24:45
put them in all singly,
and then we're done.

371
00:24:45 --> 00:24:49
So we put three electrons
in these three orbitals.

372
00:24:49 --> 00:24:54
Now we can introduce a couple
other terms, which is where I

373
00:24:54 --> 00:24:58
realized I forgot to
put the labels on.

374
00:24:58 --> 00:25:08
So, you'll often be asked for
-- OK, you'll often be asked

375
00:25:08 --> 00:25:21
for something called the d
n electron configuration.

376
00:25:21 --> 00:25:26
And so here you can use the
abbreviations for the orbitals,

377
00:25:26 --> 00:25:31
so we point three electrons in
to the t 2 g orbitals, so we

378
00:25:31 --> 00:25:35
can just say that's t 2
g raised to the three.

379
00:25:35 --> 00:25:41
So that let's someone know that
you have three electron in the

380
00:25:41 --> 00:25:44
set of orbitals that
are stabilized in an

381
00:25:44 --> 00:25:48
octahedral crystal field.
 

382
00:25:48 --> 00:25:56
Then we can consider something
else that's called c f s e,

383
00:25:56 --> 00:26:05
and I think I should have --
OK, so I'll write that out.

384
00:26:05 --> 00:26:19
So, this is the crystal
field stabilization energy.

385
00:26:19 --> 00:26:22
So it's not the crystal field
splitting energy, it's the

386
00:26:22 --> 00:26:26
stabilization energy, which
indicates how much those

387
00:26:26 --> 00:26:30
electrons are stabilized by
being in an octahedral field,

388
00:26:30 --> 00:26:35
rather than this hypothetical
spherical crystal field.

389
00:26:35 --> 00:26:39
And so what we can do there is
you see that you have three

390
00:26:39 --> 00:26:44
electrons in those lower sets
of orbitals, and those orbitals

391
00:26:44 --> 00:26:49
are stabilized by 2/5 times the
octahedral crystal field

392
00:26:49 --> 00:26:51
splitting energy.
 

393
00:26:51 --> 00:26:58
And so that gives an answer of
minus 6/5 times the octahedral

394
00:26:58 --> 00:27:00
crystal field splitting energy.
 

395
00:27:00 --> 00:27:03
So that's how much those
electrons are stabilized.

396
00:27:03 --> 00:27:07
So they are lower in energy --
see, the average energy is

397
00:27:07 --> 00:27:11
much, much higher in this
hypothetical case, but because

398
00:27:11 --> 00:27:15
of having this octahedral
geometry, and there are only

399
00:27:15 --> 00:27:21
three electrons to consider,
they all go into the stabilized

400
00:27:21 --> 00:27:25
energy, and so they're
stabilized by minus 6/5 times

401
00:27:25 --> 00:27:28
whatever the octahedral crystal
field splitting energy is

402
00:27:28 --> 00:27:34
for this particular case.
 

403
00:27:34 --> 00:27:40
So, now let's look
at another example.

404
00:27:40 --> 00:27:45
So let's look at an example of
a coordination complex -- you

405
00:27:45 --> 00:27:52
have manganese and you have
six water ligands and some

406
00:27:52 --> 00:27:55
chlorides hanging around.
 

407
00:27:55 --> 00:27:59
So why don't you tell me what
the oxidation number is for

408
00:27:59 --> 00:28:27
this now -- not the d count,
but the oxidation number?

409
00:28:27 --> 00:28:46
OK, so let's just take
10 more seconds.

410
00:28:46 --> 00:28:49
OK, so let's just look at that
one for a minute, people

411
00:28:49 --> 00:28:51
did very well on that.
 

412
00:28:51 --> 00:28:57
So, what's the overall charge
in this coordination complex?

413
00:28:57 --> 00:29:03
So we can write this out here.
 

414
00:29:03 --> 00:29:08
Our six ligands and we say that
here it's plus 3 overall,

415
00:29:08 --> 00:29:11
because we have three chloride
ions hanging around with

416
00:29:11 --> 00:29:12
a negative charge.
 

417
00:29:12 --> 00:29:16
So this tells us that the
overall charge on the

418
00:29:16 --> 00:29:19
coordination complex
had to be plus 3.

419
00:29:19 --> 00:29:24
And this again is 0, so
that means that is plus 3.

420
00:29:24 --> 00:29:26
So, people did very
well on that.

421
00:29:26 --> 00:29:31
All right, so then
what is the d count?

422
00:29:31 --> 00:29:32
What is it?
 

423
00:29:32 --> 00:29:34
4, right.
 

424
00:29:34 --> 00:29:41
So we have 7 minus 3 is 4,
so we have a d 4 system.

425
00:29:41 --> 00:29:46
All right, so now, if you look
up there, we have to make a

426
00:29:46 --> 00:29:50
decision about that fourth
electron. three electrons were

427
00:29:50 --> 00:29:52
easy, four makes
it complicated.

428
00:29:52 --> 00:29:55
Do we put the fourth
one down in the lower

429
00:29:55 --> 00:29:57
set or do we go up?
 

430
00:29:57 --> 00:30:00
So there are two
possibilities here.

431
00:30:00 --> 00:30:03
So I have two diagrams
drawn over here.

432
00:30:03 --> 00:30:07
And you might be in a case
where you have a small crystal

433
00:30:07 --> 00:30:10
field splitting energy, or you
might be in a case where

434
00:30:10 --> 00:30:15
you have a large crystal
field splitting energy.

435
00:30:15 --> 00:30:21
And so, there are two different
ways the electrons can go.

436
00:30:21 --> 00:30:26
So over here where you have a
small crystal field splitting

437
00:30:26 --> 00:30:31
energy, that's called
a weak field.

438
00:30:31 --> 00:30:33
And when you have a
big splitting energy,

439
00:30:33 --> 00:30:40
that's a strong field.
 

440
00:30:40 --> 00:30:45
So, with the weak field there's
not that much of an energy

441
00:30:45 --> 00:30:47
difference between them.
 

442
00:30:47 --> 00:30:51
And so, when you're putting
in, you do your first three

443
00:30:51 --> 00:30:54
electrons, that's always
going to be the same.

444
00:30:54 --> 00:30:58
But then the fourth electron,
in this case, if there's not a

445
00:30:58 --> 00:31:01
big difference in the energy,
if it's pretty small, if it's

446
00:31:01 --> 00:31:05
a weak field, you can put
that fourth one up there.

447
00:31:05 --> 00:31:10
Because it takes energy to pair
the electrons up, and so you're

448
00:31:10 --> 00:31:13
asking the question, does it
take more energy to pair them,

449
00:31:13 --> 00:31:17
or does it take more energy
to put one in the upper set?

450
00:31:17 --> 00:31:20
And for a weak field you say
that the crystal field

451
00:31:20 --> 00:31:25
splitting energy is smaller
than the pairing energy or p e,

452
00:31:25 --> 00:31:27
so p e is the pairing energy.
 

453
00:31:27 --> 00:31:31
And so it takes more energy to
pair than it does to bump one

454
00:31:31 --> 00:31:34
electron up to the
higher level.

455
00:31:34 --> 00:31:38
So that's what a weak field
situation would look like.

456
00:31:38 --> 00:31:43
Now in a strong field
situation, boy, there's a big

457
00:31:43 --> 00:31:46
splitting difference, a big
energy difference here.

458
00:31:46 --> 00:31:52
So in this case, the crystal
field splitting is much larger

459
00:31:52 --> 00:31:56
than p e, that pairing
energy for the electron.

460
00:31:56 --> 00:31:59
So it's better to pair,
then to put one up.

461
00:31:59 --> 00:32:03
I can't even reach those,
that's really far up.

462
00:32:03 --> 00:32:07
So I'm not going to do
that, I'm just going

463
00:32:07 --> 00:32:07
to put them in here.
 

464
00:32:07 --> 00:32:11
I'll put the first three in,
and then the fourth one is

465
00:32:11 --> 00:32:13
going to go down where
I can reach it.

466
00:32:13 --> 00:32:15
I don't have the energy
to put it up there.

467
00:32:15 --> 00:32:18
So that's a strong field.
 

468
00:32:18 --> 00:32:21
Weak field I can handle,
strong field I'm going

469
00:32:21 --> 00:32:26
to try pair them all up.
 

470
00:32:26 --> 00:32:31
So, now we can write the
different d n electron

471
00:32:31 --> 00:32:34
configurations for these two.
 

472
00:32:34 --> 00:32:51
So, in this case, if we have
our d n electron configuration,

473
00:32:51 --> 00:32:57
so we have three in the
t 2 g, we have three.

474
00:32:57 --> 00:33:02
And in the e g set we
have one, so that is our

475
00:33:02 --> 00:33:06
electron configuration
for this weak field case.

476
00:33:06 --> 00:33:09
And for the strong field case,
we didn't put any up in the e

477
00:33:09 --> 00:33:16
g, so we just have t 2 g, four
electrons in that

478
00:33:16 --> 00:33:20
set of orbitals.
 

479
00:33:20 --> 00:33:28
OK, so let's just put up what
we've done here, and introduce

480
00:33:28 --> 00:33:32
another term, which are
high spin and low spin.

481
00:33:32 --> 00:33:35
So we have these two cases
here, and again, we're

482
00:33:35 --> 00:33:40
considering how big is this
octahedral crystal field

483
00:33:40 --> 00:33:43
splitting energy compared
to a pairing energy.

484
00:33:43 --> 00:33:46
The energy involved in
pairing electrons together.

485
00:33:46 --> 00:33:49
In a weak field, the splitting
energy is small, so electrons

486
00:33:49 --> 00:33:54
are placed singly with spins
parallel to the fullest extent

487
00:33:54 --> 00:33:57
in all the sets of orbitals.
 

488
00:33:57 --> 00:34:00
In this other case with the
strong field, the pairing

489
00:34:00 --> 00:34:04
energy is smaller than the
splitting energy -- strong

490
00:34:04 --> 00:34:07
field you have a big
splitting energy.

491
00:34:07 --> 00:34:11
And so, in that case, with the
splitting energy is large,

492
00:34:11 --> 00:34:14
you're going to put all your
electrons in and pair them up

493
00:34:14 --> 00:34:18
in t 2 g and don't put any
electrons in the e g sets of

494
00:34:18 --> 00:34:22
orbitals until you completely
filled your t 2 g set.

495
00:34:22 --> 00:34:27
So, the net result of this is
for a weak field, you have the

496
00:34:27 --> 00:34:31
maximum number of unpaired
electrons, so see, you have a

497
00:34:31 --> 00:34:34
maximum number, you have four
electrons, all four

498
00:34:34 --> 00:34:35
are unpaired.
 

499
00:34:35 --> 00:34:38
So that's the maximum number of
unpaired electrons, and this

500
00:34:38 --> 00:34:40
is referred to as high spin.
 

501
00:34:40 --> 00:34:44
And in the other case, you have
the minimum number of unpaired

502
00:34:44 --> 00:34:47
electrons that you can have,
and so you have this one set

503
00:34:47 --> 00:34:50
that's paired here, so that
would be considered

504
00:34:50 --> 00:34:54
a low spin case.
 

505
00:34:54 --> 00:35:00
We can also talk about the
stabilization energy of

506
00:35:00 --> 00:35:05
these two cases, and so we
have the crystal field

507
00:35:05 --> 00:35:08
stabilization energy.
 

508
00:35:08 --> 00:35:10
So why don't you go ahead
and tell me for a weak

509
00:35:10 --> 00:36:42
field case, what is our
stabilization energy?

510
00:36:42 --> 00:36:57
Let's just take
10 more seconds.

511
00:36:57 --> 00:36:59
OK, pretty good.
 

512
00:36:59 --> 00:37:01
So let's work this out.
 

513
00:37:01 --> 00:37:05
So, first we consider how many
electrons we have in the

514
00:37:05 --> 00:37:09
lower set of orbitals,
so we have three.

515
00:37:09 --> 00:37:14
Those three are
stabilized by 2/5.

516
00:37:14 --> 00:37:22
And then we have one in the
upper set, so we have one at

517
00:37:22 --> 00:37:26
3/5 times the octahedral
crystal field splitting energy.

518
00:37:26 --> 00:37:32
So this ends up with minus 3/5
times the octahedral crystal

519
00:37:32 --> 00:37:34
field splitting energy.
 

520
00:37:34 --> 00:37:40
And notice why a is not correct
-- you don't have the symbol

521
00:37:40 --> 00:37:43
for the octahedral crystal
field splitting energy.

522
00:37:43 --> 00:37:47
On a test, you need to make
sure that you remember to write

523
00:37:47 --> 00:37:52
this term, so this was a little
test so that you hopefully

524
00:37:52 --> 00:37:57
emphasize that you want
to have that there.

525
00:37:57 --> 00:37:59
All right, so that's
for this one.

526
00:37:59 --> 00:38:06
Let's look at the low spin
case, the strong field case,

527
00:38:06 --> 00:38:11
and do our crystal field
splitting energy for that.

528
00:38:11 --> 00:38:19
So in this case we're going to
have four electrons times minus

529
00:38:19 --> 00:38:24
2/5 times the octahedral
crystal field splitting energy,

530
00:38:24 --> 00:38:30
so that's equal to minus 8/5
times the octahedral crystal

531
00:38:30 --> 00:38:36
field splitting energy, and
some books will also indicate,

532
00:38:36 --> 00:38:42
and they'll say plus p e to
indicate that there's pairing

533
00:38:42 --> 00:38:44
energy that's associated there.
 

534
00:38:44 --> 00:38:49
So it's not quite as beneficial
as one might think.

535
00:38:49 --> 00:38:55
You do have a lot of electrons
in these in lower energy

536
00:38:55 --> 00:38:59
orbitals, but you did have to
pair some of them, so you had

537
00:38:59 --> 00:39:01
one, and if two of them are
paired, you can see

538
00:39:01 --> 00:39:02
sometimes 2 p e.
 

539
00:39:02 --> 00:39:05
So, some books will do
that, some books will not.

540
00:39:05 --> 00:39:09
So I just wanted to
mention that both are OK.

541
00:39:09 --> 00:39:13
And whether you're asked to
write that or not, and the

542
00:39:13 --> 00:39:16
question will say include the
pairing energy, so you know

543
00:39:16 --> 00:39:20
whether you're supposed to do
that or not, that there is that

544
00:39:20 --> 00:39:29
energy associated with pairing
in this strong field case.

545
00:39:29 --> 00:39:33
OK, so let's look at another
example, and then you should be

546
00:39:33 --> 00:39:41
all set to do these problems
for an octahedral field.

547
00:39:41 --> 00:39:44
So we'll take our
electrons down.

548
00:39:44 --> 00:39:53
All right, so let's at a
case of cobalt plus 2.

549
00:39:53 --> 00:39:59
So let's consider how many
we're going to put in,

550
00:39:59 --> 00:40:02
the oxidation number is?
 

551
00:40:02 --> 00:40:03
Plus 2.
 

552
00:40:03 --> 00:40:07
And what is the d count then?
 

553
00:40:07 --> 00:40:14
What group number?
 

554
00:40:14 --> 00:40:20
9 minus 2 is 7, so we're
doing a d 7 system.

555
00:40:20 --> 00:40:24
All right, so now for the weak
field case here, why don't you

556
00:40:24 --> 00:41:12
tell me what is the correct
electron distribution.

557
00:41:12 --> 00:41:28
OK, let's just take
10 more seconds.

558
00:41:28 --> 00:41:30
OK, very good.
 

559
00:41:30 --> 00:41:36
This is the weak field case, so
in this case, we are going to

560
00:41:36 --> 00:41:40
fill up singly all of the
orbitals, because the splitting

561
00:41:40 --> 00:41:43
energy is less than the pairing
energy, so we're going to put

562
00:41:43 --> 00:41:45
them to the fullest
extent possible before

563
00:41:45 --> 00:41:47
we have to pair.
 

564
00:41:47 --> 00:41:54
So we have 7, so we're going
to do 1, 2, 3, 4, 5, and

565
00:41:54 --> 00:41:55
now we have to pair.
 

566
00:41:55 --> 00:41:59
We have no -- we've used up all
our orbitals, so we're going to

567
00:41:59 --> 00:42:03
start pairing down here in
the lower energy, so

568
00:42:03 --> 00:42:06
that would be 6, 7.
 

569
00:42:06 --> 00:42:10
So we had no choice, we had to
pair them, but because it was a

570
00:42:10 --> 00:42:13
weak field, we filled them
all up singly first

571
00:42:13 --> 00:42:15
before we paired.
 

572
00:42:15 --> 00:42:18
So now let's consider what
we're going to do down here.

573
00:42:18 --> 00:42:21
Now remember, this is a strong
field, so there's a big

574
00:42:21 --> 00:42:26
splitting energy, so it takes
less energy to pair them than

575
00:42:26 --> 00:42:29
to reach this higher level.
 

576
00:42:29 --> 00:42:33
So first we put them in the
same way -- 1, 2, 3, but now

577
00:42:33 --> 00:42:36
that we have the 3 in, it's
better to pair than to

578
00:42:36 --> 00:42:38
bring them up here.
 

579
00:42:38 --> 00:42:42
So we'll do 1, 2, 3,
we'll pair them all up.

580
00:42:42 --> 00:42:50
Now it's all filled, we have no
other choice but to go up here.

581
00:42:50 --> 00:42:53
So, we have these very
different cases depending

582
00:42:53 --> 00:42:55
on the splitting energy.
 

583
00:42:55 --> 00:42:57
So what controls the
splitting energy?

584
00:42:57 --> 00:43:00
Well, what controls the
splitting energy is nature of

585
00:43:00 --> 00:43:02
the ligands, so we're going to
be talking about that next

586
00:43:02 --> 00:43:06
time, and you'll recognize for
certain kinds of ligands you're

587
00:43:06 --> 00:43:08
going to have a strong field,
and other kinds you'll

588
00:43:08 --> 00:43:10
have a weak field.
 

589
00:43:10 --> 00:43:12
But right now we're not talking
about that, we're just showing

590
00:43:12 --> 00:43:15
those two possibilities.
 

591
00:43:15 --> 00:43:18
So, for this system, is this
going to be a high spin

592
00:43:18 --> 00:43:21
or a low spin system?
 

593
00:43:21 --> 00:43:24
So, this will be high spin,
because we have the maximum

594
00:43:24 --> 00:43:27
amount of unpaired electrons.
 

595
00:43:27 --> 00:43:30
And over here we're going
to have a low spin system.

596
00:43:30 --> 00:43:34
We have the minimum
number possible of the

597
00:43:34 --> 00:43:36
unpaired electrons.
 

598
00:43:36 --> 00:43:43
All right, so let's finish this
up now, and do our d n electron

599
00:43:43 --> 00:43:47
configurations and our crystal
field splitting energies.

600
00:43:47 --> 00:43:51
So, for this case, we're
going to have in our t

601
00:43:51 --> 00:43:55
2 g system, how many?
 

602
00:43:55 --> 00:43:56
5.
 

603
00:43:56 --> 00:43:58
And in e g?
 

604
00:43:58 --> 00:44:00
2.
 

605
00:44:00 --> 00:44:06
And for our splitting energy,
we have 5 times minus 2/5 times

606
00:44:06 --> 00:44:11
the octahedral crystal field
splitting energy plus 2 times

607
00:44:11 --> 00:44:16
plus 3/5, and what does
that end up equaling?

608
00:44:16 --> 00:44:22
Minus 4/5 times the octahedral
crystal field splitting energy.

609
00:44:22 --> 00:44:26
And we could also optionally
put 2 p e because we

610
00:44:26 --> 00:44:28
have two sets paired.
 

611
00:44:28 --> 00:44:31
All right, so let's look at
our strong field system.

612
00:44:31 --> 00:44:35
How many do we have
in our e 2 g set?

613
00:44:35 --> 00:44:36
6.
 

614
00:44:36 --> 00:44:39
What about e g?
 

615
00:44:39 --> 00:44:40
1.
 

616
00:44:40 --> 00:44:44
And for our splitting energy
then, we have 6 times minus 2/5

617
00:44:44 --> 00:44:49
times the octahedral crystal
field splitting energy plus 1

618
00:44:49 --> 00:44:55
times 3/5, and what is
that going to equal?

619
00:44:55 --> 00:44:57
Minus what?
 

620
00:44:57 --> 00:44:59
9/5.
 

621
00:44:59 --> 00:45:05
And how many pairing energies?
three pairing energies, great.

622
00:45:05 --> 00:45:07
I think you have
that part down.

623
00:45:07 --> 00:45:09
Next time we get more
complicated, we're going to

624
00:45:09 --> 00:45:12
talk about types of ligands,
we're going to talk about

625
00:45:12 --> 00:45:16
tetrahedral, we're going to
talk about square planar, and

626
00:45:16 --> 00:45:20
that's, of course, after
the exam on Wednesday.

627
00:45:20 --> 00:45:23
So, good luck, everyone,
with the exam on Wednesday.

628
00:45:23 --> 00:45:24