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We have been talking about the
properties of transition metal

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complexes, coordination
complexes, in the context of a

7
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simple crystal field theory
model.

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And I just wanted to make
reference at the beginning,

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today, to state diagrams.

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00:00:34 --> 00:00:40


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And, in the context of
octahedral complexes,

12
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you saw that an array of six
ligands surrounding a central

13
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metal ion would lead to a t two
g and what we are

14
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calling an eg star
manifold of orbitals on the

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metal in which we can populate
with the number of d electrons

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that we have present.
And the graph that I am making

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00:01:10 --> 00:01:17
here is related to the idea that
for a system with only a single

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electron, so this could be,
for example,

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titanium OH two six times three
plus.

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00:01:26 --> 00:01:32
This is a d one system.
And it can go from a ground

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00:01:32 --> 00:01:37
state configuration of t two g
one eg star zero.

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And then, upon absorption of

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light, it can be promoted from
the ground state,

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00:01:44 --> 00:01:48
represented here,
into the excited state.

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00:01:48 --> 00:01:53
And the excited state has the
configuration t two g zero eg

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00:01:53 --> 00:01:58
star one,
showing that that electron has

27
00:01:58 --> 00:02:04
been promoted through absorption
of a photon.

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00:02:04 --> 00:02:09
And this gap here between t(2g)
and eg star,

29
00:02:09 --> 00:02:12
of course, is our delta O
value.

30
00:02:12 --> 00:02:19
And the axis on the bottom,
here, is ligand field strength.

31
00:02:19 --> 00:02:30


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00:02:30 --> 00:02:34
This is supposed to tell you
that different ligands give rise

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00:02:34 --> 00:02:39
to different values of delta O
accounting for the fact that

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00:02:39 --> 00:02:44
this d one titanium
three ion in a field

35
00:02:44 --> 00:02:47
of water molecules has one
color, whereas,

36
00:02:47 --> 00:02:51
if you, in fact, look at
Ti Cl six three minus,

37
00:02:51 --> 00:02:55
you will be able to tell that

38
00:02:55 --> 00:02:59
that also is a titanium three
plus or d one

39
00:02:59 --> 00:03:04
system.
But they do not have the same

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00:03:04 --> 00:03:07
color.
And the one absorption band

41
00:03:07 --> 00:03:11
that you find in the visible
part of the spectrum that

42
00:03:11 --> 00:03:16
corresponds to promotion of an
electron from t two g

43
00:03:16 --> 00:03:21
into eg star is just
moving around a little bit in

44
00:03:21 --> 00:03:26
energy because these ligands
behave differently with respect

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00:03:26 --> 00:03:30
to what we call their ligand
field strength that they exert,

46
00:03:30 --> 00:03:35
that leads to a particular
energy gap between t(2g) and

47
00:03:35 --> 00:03:40
e(g)*.
I will get into this a little

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bit further in the moment,
but the point here is that d

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one or d nine
are special electron counts.

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00:03:54 --> 00:04:05


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00:04:05 --> 00:04:10
And the reason that they are
special is that these have a

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single absorption peak due to
what we call d-d transitions.

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They have a single d-d
transition.

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00:04:25 --> 00:04:29
And that means there is a
ground state and then just one

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excited state that the system
can be promoted to in the

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presence of impinging photons of
the right energy.

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And what happens is that if you
have more d electrons than just

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one, or d nine is
special because we treat that

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using a whole formalism,
like there is just one electron

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missing from a complete
manifold, a completely full d

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shell minus one.
With d^n systems,

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for example,
d two is much more

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complex.
And this is beyond the scope of

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5.112, but it is something that
they are treating in 5.04,

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for example.
If you go on in organic

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chemistry, you will learn how
come different states can arise,

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multiple states arise when you
have more than just a one

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electron picture.

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For example,
if you have a vanadium three

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plus ion,
there are three bands observed.

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And so the simple picture that
you have, just a t(2g) level and

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an e(g) level is correct and
maps onto the picture of the

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electronic states that are
available, as long as we are

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just talking about a one
electron picture.

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With more electrons in play,
depending on just which of the

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orbitals they go into,
they will have inter-electron

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repulsion terms that come into
play and give rise to more

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00:06:09 --> 00:06:12
excited states.
Here, with three bands being

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observed in the visible,
that means there are three

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possible transitions and three
possible excited states that can

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be accessed.
So it is a very complicated

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picture.
And so we are going to be,

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for the purposes of this,
focusing on the one electron

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picture.
But I just wanted you to be

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aware that it does get a lot
more complex as soon as you go

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to many electron systems.
Now, let's talk just briefly

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about pairing energy.

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In the case of 3d system,
we typically find that the

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pairing energy is around 15
to 18,000 reciprocal

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centimeters, the typical energy
unit given for pairing energy.

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But then if we go to heavier
transition elements,

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to the 4d or the 5d elements,
then typically the pairing

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energy is about 8,000 to 12
reciprocal centimeters.

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And what that says is that it
is easier to pair up electrons

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00:07:31 --> 00:07:37
in 4d or 5d orbitals than it is
to put two electrons in the same

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3d orbital.
And the reason for that is just

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what the radial extension is of
these orbitals.

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In effect, these orbitals are
larger than the 3d orbitals.

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And it means that if you put
two electrons into the same 4d

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or 5d orbital,
much of the time they can stay

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farther apart from each other
than if they are in a 3d

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orbital.
And so this has the practical

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consequence that 4d and 5d
systems often are low spin.

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00:08:13 --> 00:08:19
And so this high spin/low spin
issue that we talked about last

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time is mostly focused on
complexes of the 3d ions.

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00:08:24 --> 00:08:28
So then we are talking about
titanium, vanadium,

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chromium, etc.
And, if we come over here,

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we can ask, what is the effect
of charge on delta O?

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This is all pointing back to
the state diagram that I showed

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you over there in this kind of
sliding scale,

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where you can change things
like just what type of metal ion

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you have, 3d,
4d, or 5d.

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Or you can change the nature of
the ligands.

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Or you can even change the
charge on the metal as a way of

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changing delta O.
And so we can look at,

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for example,
chromium hexaaquo two plus

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versus chromium
hexaaquo three plus.

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The first is a d four ion.

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And then, the second is a d

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three ion.
You should practice going from

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a formula into the d^n count.
And then we can look at what

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delta O does.
This is roughly 14,000 wave

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numbers.
And then, when we oxidize from

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2+ to 3+, higher charge on the
central metal,

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delta O shoots up to about
approximately 17,000.

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00:10:04 --> 00:10:07
And this is in reciprocal
centimeters.

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00:10:07 --> 00:10:13
We see that putting a higher
charge on the metal center leads

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to a larger value of delta O.
And that is also true if we

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look at some other metal systems
along these lines.

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00:10:23 --> 00:10:27
For example,
there are just a number of

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different metals for which the
hexaaquo systems can be

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generated in both the 2+ and the
3+ state of charge.

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And here, we go from about
12,000 and then oxidize,

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00:10:45 --> 00:10:52
and we get up to about 18,000,
so even a larger increase in

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the value of delta O on going
from the 2+ to the 3+ oxidation

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state of the metal.
And then in the notes you will

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00:11:05 --> 00:11:10
find that I put in another
example that behaves similarly

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based on cobalt.
If you go from cobalt two to

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cobalt three hexaaquo,
you go from about 9,000 up to

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18,000 reciprocal centimeters.
So almost doubling the value of

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00:11:22 --> 00:11:26
delta O by removing one electron
from the system.

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What is going on here is that
the greater charge --

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-- pulls the ligands in closer
to the metal.

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00:11:42 --> 00:11:48


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00:11:48 --> 00:11:51
And if the ligands are in
closer to the metal,

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00:11:51 --> 00:11:54
then what that ends up saying
is you will see in a moment

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because we are going to get to
the MO picture for octahedral

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coordination complexes,
is that putting electrons in e

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g star becomes more
difficult.

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Delta O is larger.
The ligands come in closer,

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and that is effectively
shrinking that value of r when

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00:12:12 --> 00:12:16
we talked about our spherical
coordinates as applied to the

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00:12:16 --> 00:12:20
angular parts of the d-orbital
wavefunctions and looking at

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00:12:20 --> 00:12:22
that.
So we are changing r.

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00:12:22 --> 00:12:26
The ligands are coming in
closer to the more positively

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charged metal ion in that case.
And then we can also look at

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the effect of changing the
ligand.

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In the system on the left,
we were looking at pairs of

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metal complexes with the same
ligand and changing the charge.

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And now we are just going to
say, what happens if you change

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the ligand?
And this will be a series of

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00:13:04 --> 00:13:08
vanadium complexes.
We have five of them.

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00:13:08 --> 00:13:12
We have the vanadium hexaaquo.

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00:13:12 --> 00:13:16


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00:13:16 --> 00:13:21
This one is 3+.
We have the vanadium with six

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urea molecules.
And this is also 3+.

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We have vanadium hexafluoride
three minus.

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00:13:35 --> 00:13:40
And these are all vanadium in
the +3 oxidation state.

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00:13:40 --> 00:13:44
Then we have vanadium
hexachloride three minus,

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00:13:44 --> 00:13:49
and down here the fifth one

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will be vanadium with six
cyanide ligands and three minus.

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So these are all d two

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systems with vanadium in the +3
oxidation state.

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00:14:05 --> 00:14:12
And here, we are going from
18,000 reciprocal centimeters to

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the hexafluoride.
And we drop down to 16,000.

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00:14:18 --> 00:14:25
And this is all approximate.
And six urea on vanadium,

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00:14:25 --> 00:14:31
we go up to about 17,0000.
And then, with the

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00:14:31 --> 00:14:35
hexachloride,
we are down to about a delta O

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00:14:35 --> 00:14:37
of 12,000 reciprocal
centimeters.

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00:14:37 --> 00:14:42
And then we put cyanides on,
and delta O pops up to about

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00:14:42 --> 00:14:46
23,000 wave numbers.
So this is the same metal ion

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00:14:46 --> 00:14:50
but in five different ligand
environments.

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00:14:50 --> 00:14:54
It has five very different
values of delta O.

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00:14:54 --> 00:14:57
And from this,
we can derive a spectrochemical

191
00:14:57 --> 00:15:00
series --

192
00:15:00 --> 00:15:05


193
00:15:05 --> 00:15:08
-- for organizing ligands with
respect to the magnitude of

194
00:15:08 --> 00:15:11
delta O that they exert for a
given metal ion.

195
00:15:11 --> 00:15:14
And this one just gives us a
series that contains five

196
00:15:14 --> 00:15:16
ligands.
But, as you can imagine,

197
00:15:16 --> 00:15:20
many more ligands than just
these five simple ligands have

198
00:15:20 --> 00:15:23
been looked at with a variety of
different metal ions to make a

199
00:15:23 --> 00:15:27
pretty big overall comprehensive
spectrochemical series that sort

200
00:15:27 --> 00:15:31
of allows you to pick out which
ligand you want when you are

201
00:15:31 --> 00:15:36
interested in generating a
particular value of delta O.

202
00:15:36 --> 00:15:45
And here what you see is that
the weakest one is chloride.

203
00:15:45 --> 00:15:52
We have chloride.
And then next was fluoride.

204
00:15:52 --> 00:16:00
And then next was urea followed
by water.

205
00:16:00 --> 00:16:05
And then the strongest in this
small series of five was

206
00:16:05 --> 00:16:09
cyanide.
And when we try to understand

207
00:16:09 --> 00:16:13
the order that these different
ligands appear in,

208
00:16:13 --> 00:16:19
in the spectrochemical series,
we are going to find out,

209
00:16:19 --> 00:16:25
as we study the properties of
the molecular orbitals of these

210
00:16:25 --> 00:16:30
systems, that cyanide is a pi
acid.

211
00:16:30 --> 00:16:33
And that down here,
chloride is a pi donor.

212
00:16:33 --> 00:16:37
And in the middle,
you have systems like water

213
00:16:37 --> 00:16:40
which is more or less sigma
only.

214
00:16:40 --> 00:16:45
So we can understand where
specific ligands appear in the

215
00:16:45 --> 00:16:50
spectrochemical series on the
basis of their orbital

216
00:16:50 --> 00:16:54
considerations.
And that will be the focus of

217
00:16:54 --> 00:16:58
the next part of the lecture.

218
00:16:58 --> 00:17:15


219
00:17:15 --> 00:17:18
I would like to talk a little
bit about sigma-only ligands.

220
00:17:18 --> 00:17:23
The process in which we are now
about to engage is very similar

221
00:17:23 --> 00:17:27
to that which we used in class
for generating the molecular

222
00:17:27 --> 00:17:32
orbital energy level diagram for
the BH three molecule.

223
00:17:32 --> 00:17:36
In that case we had a central
boron and three hydrogens around

224
00:17:36 --> 00:17:40
it, and we made some hydrogen
linear combinations.

225
00:17:40 --> 00:17:43
And we saw how they would
interact with the atomic

226
00:17:43 --> 00:17:47
orbitals of the boron.
And now we are going to do the

227
00:17:47 --> 00:17:52
same thing, except we have a lot
more orbitals in the system as a

228
00:17:52 --> 00:17:55
whole, so we are approximating
some of them.

229
00:17:55 --> 00:18:00
Here is a typical sigma-only
ligand, NH three.

230
00:18:00 --> 00:18:05
And for NH three,
we have a lone pair on the

231
00:18:05 --> 00:18:09
nitrogen here.
And I am drawing it in very

232
00:18:09 --> 00:18:13
simplified fashion,
as you will no doubt

233
00:18:13 --> 00:18:16
appreciate.
There is our lone pair.

234
00:18:16 --> 00:18:21
And, when this points directly
at the metal,

235
00:18:21 --> 00:18:27
the lone pair can make a sigma
bond to the metal.

236
00:18:27 --> 00:18:39


237
00:18:39 --> 00:18:43
I think you will appreciate
that if we have a metal out here

238
00:18:43 --> 00:18:47
such that this lone pair of
electrons is directed right at

239
00:18:47 --> 00:18:51
the metal, then that results in
a cylindrically symmetric lone

240
00:18:51 --> 00:18:55
pair about that metal-nitrogen
internuclear axis.

241
00:18:55 --> 00:18:58
And so that would be a
sigma-type of interaction.

242
00:18:58 --> 00:19:02
So this is called a sigma-only
ligand.

243
00:19:02 --> 00:19:08
And other ligands,
like cyanide or like chloride,

244
00:19:08 --> 00:19:16
we are going to have to add in
pi effects, but this is the

245
00:19:16 --> 00:19:23
simple sigma-only case.
And so if you take a molecule

246
00:19:23 --> 00:19:30
such as this cobalt hexamine two
plus, --

247
00:19:30 --> 00:19:34
-- or, actually,
let's say three plus for

248
00:19:34 --> 00:19:38
simplicity here.
Cobalt three plus.

249
00:19:38 --> 00:19:44
And we have these NH three
ligands at each of the

250
00:19:44 --> 00:19:47
six positions.
And, in each case,

251
00:19:47 --> 00:19:52
the orientation of the
hydrogens on these nitrogens is

252
00:19:52 --> 00:19:58
such as to promote a sigma
directing effect of that lone

253
00:19:58 --> 00:20:04
pair toward the metal.
And so that lone pair of

254
00:20:04 --> 00:20:09
electrons on the nitrogen for
each of these ammonia ligands

255
00:20:09 --> 00:20:15
directed right at the metal is
providing this repulsion that

256
00:20:15 --> 00:20:19
pumps e(g) up in energy.
And you will see that,

257
00:20:19 --> 00:20:25
hopefully, very clearly now.
And let me point out that this

258
00:20:25 --> 00:20:29
orbital, here,
that I am focusing on is the

259
00:20:29 --> 00:20:34
HOMO of NH three.
What we are doing is saying you

260
00:20:34 --> 00:20:37
have a central metal ion and
then you have six ammonia

261
00:20:37 --> 00:20:40
ligands pointing at it,
each of them pointing their

262
00:20:40 --> 00:20:43
HOMO at the metal,
their highest occupied

263
00:20:43 --> 00:20:45
molecular orbital.
What does that do?

264
00:20:45 --> 00:20:48
What kinds of bonds arise as a
consequence of that between the

265
00:20:48 --> 00:20:52
metal ion and these six ammonia
molecules?

266
00:20:52 --> 00:20:56
And so we will now see what
that is on the basis of some of

267
00:20:56 --> 00:21:01
the linear combinations that we
can generate between the six

268
00:21:01 --> 00:21:06
HOMOs of the NH three's in this
kind of a geometry.

269
00:21:06 --> 00:21:22


270
00:21:22 --> 00:21:24
I will do the first one over
here.

271
00:21:24 --> 00:21:32


272
00:21:32 --> 00:21:36
I would like to use a different
color for that.

273
00:21:36 --> 00:21:40
I am going to use my blue.
All right.

274
00:21:40 --> 00:21:46
I am going to draw for you some
linear combinations of ammonia

275
00:21:46 --> 00:21:49
lone pairs.
These are simplistically

276
00:21:49 --> 00:21:55
representing the homo of each NH
three directed at the

277
00:21:55 --> 00:21:59
metal.
That one has the symmetry of a

278
00:21:59 --> 00:22:03
cobalt s orbital.
It has the same sign

279
00:22:03 --> 00:22:06
everywhere.
And then, we are going to see

280
00:22:06 --> 00:22:10
that you can draw three of
these.

281
00:22:10 --> 00:22:15


282
00:22:15 --> 00:22:17
And I will draw them all right
here --

283
00:22:17 --> 00:22:24


284
00:22:24 --> 00:22:30
-- in pairs.
And this one has the symmetry

285
00:22:30 --> 00:22:37
of a cobalt pz atomic orbital.
You see it has positive up

286
00:22:37 --> 00:22:39
there.
And down here,

287
00:22:39 --> 00:22:42
we are taking this to be x,
this to be y,

288
00:22:42 --> 00:22:46
and this to be z for each of
our diagrams,

289
00:22:46 --> 00:22:52
so that the phase properties of
this combination is that of pz.

290
00:22:52 --> 00:22:57
This one is like px.
This one is like py.

291
00:22:57 --> 00:23:01
And the only reason we have to
take these linear combinations

292
00:23:01 --> 00:23:06
is because we have multiple
equivalent ammonia molecules in

293
00:23:06 --> 00:23:09
this problem.
And then, we have two more that

294
00:23:09 --> 00:23:14
are of interest to us.
One of these will have a couple

295
00:23:14 --> 00:23:18
of big lobes located on z,
pointed at the metal and then

296
00:23:18 --> 00:23:21
four small lobes,
each with negative phase.

297
00:23:21 --> 00:23:25
I will shade them to indicate
that negative phase.

298
00:23:25 --> 00:23:30
And that one will have the same
phase properties as a cobalt d z

299
00:23:30 --> 00:23:35
squared orbital.
Plus above, plus below.

300
00:23:35 --> 00:23:40
And then, to match up with the
torus in the center of d z

301
00:23:40 --> 00:23:45
squared in the
x,y-plane, the negative phase

302
00:23:45 --> 00:23:47
shown there.
And then, finally,

303
00:23:47 --> 00:23:52
over here we have one where all
four contributions to this one

304
00:23:52 --> 00:23:57
are in the x,y-plane,
along the x and y axes and with

305
00:23:57 --> 00:24:01
shading as shown there.
And that is of the same

306
00:24:01 --> 00:24:07
symmetry as our d x squared
minus y squared

307
00:24:07 --> 00:24:10
orbital.
Having written down this set of

308
00:24:10 --> 00:24:15
six linear combinations that we
can generate from our six

309
00:24:15 --> 00:24:18
ammonia HOMOs,
we are done because the cobalt

310
00:24:18 --> 00:24:22
has atomic orbitals of these
symmetries.

311
00:24:22 --> 00:24:26
We can now use these to make
bonds between the ammonia

312
00:24:26 --> 00:24:32
molecules and the cobalt.
And we can use them to make

313
00:24:32 --> 00:24:34
corresponding antibonds.

314
00:24:34 --> 00:24:39


315
00:24:39 --> 00:24:43
Here is the MO diagram for the
sigma-only case.

316
00:24:43 --> 00:25:00


317
00:25:00 --> 00:25:07
What we have is an energy level
diagram that will represent the

318
00:25:07 --> 00:25:13
interaction of these linear
combinations with the metal

319
00:25:13 --> 00:25:18
valance orbitals.
And so I am going to draw the

320
00:25:18 --> 00:25:23
metal valance orbitals over here
as follows.

321
00:25:23 --> 00:25:27
We have, on the metal,
the 3d, the 4s,

322
00:25:27 --> 00:25:32
and the 4p.
And some of you will notice

323
00:25:32 --> 00:25:37
that this ordering of energies
is a little different than what

324
00:25:37 --> 00:25:41
you saw when you just built up
atomic configurations,

325
00:25:41 --> 00:25:45
because what I have drawn here
is the set of five 3d atomic

326
00:25:45 --> 00:25:51
orbitals is down lower in energy
than the cobalt 4s and lower in

327
00:25:51 --> 00:25:54
energy, that is,
even still, than the cobalt 4p.

328
00:25:54 --> 00:25:59
This is our cobalt atom here.
And the reason this energy

329
00:25:59 --> 00:26:03
ordering for the valance
orbitals is difference is

330
00:26:03 --> 00:26:06
because we have an ionized
cobalt.

331
00:26:06 --> 00:26:10
And the energies change around
when you remove an electron from

332
00:26:10 --> 00:26:14
the system as compared to the
neutral atom.

333
00:26:14 --> 00:26:18
But one thing that will help
you remember this ordering of

334
00:26:18 --> 00:26:22
energy levels is that it goes in
the order of the principle

335
00:26:22 --> 00:26:25
quantum number,
which kind of does make a

336
00:26:25 --> 00:26:29
little sense.
In fact, these energies switch

337
00:26:29 --> 00:26:33
around, depending on which of
the metals you are talking

338
00:26:33 --> 00:26:35
about.
But generally 3d and 4s,

339
00:26:35 --> 00:26:39
or alternatively 4d and 5s,
are pretty close in energy to

340
00:26:39 --> 00:26:43
each other, depending on the ion
that you are talking about.

341
00:26:43 --> 00:26:46
And then 4p is usually
energetically a bit separated

342
00:26:46 --> 00:26:49
from that.
And then the thing that makes

343
00:26:49 --> 00:26:52
us focus our attention so
strongly on the d orbitals is

344
00:26:52 --> 00:26:57
that those are the ones closest
in energy to the ligand orbitals

345
00:26:57 --> 00:27:03
that can interact with them.
And so let me draw over here a

346
00:27:03 --> 00:27:10
bar that represents the six LCs
of NH three HOMOs.

347
00:27:10 --> 00:27:16
In essence, this represents
these six drawings that I drew

348
00:27:16 --> 00:27:23
over here, linear combinations
that have the right symmetry to

349
00:27:23 --> 00:27:30
interact with certain of valance
orbitals on the cobalt,

350
00:27:30 --> 00:27:36
here on the left.
And what we will find is that--

351
00:27:36 --> 00:27:42
And we will start with the 3d,
since that is what we are going

352
00:27:42 --> 00:27:45
to be principally interested in
here.

353
00:27:45 --> 00:27:51
We come over and find that
three of the d orbitals do not

354
00:27:51 --> 00:27:57
match any of these because these
NH three HOMOs all lie

355
00:27:57 --> 00:28:02
in nodal surfaces of them.
And that will be,

356
00:28:02 --> 00:28:06
of course, our t(2g) set.

357
00:28:06 --> 00:28:12


358
00:28:12 --> 00:28:15
Those have the same energy as
in the ion itself.

359
00:28:15 --> 00:28:20
They come straight over and
don't get involved in bonding or

360
00:28:20 --> 00:28:24
antibonding interactions.
These are nonbonding.

361
00:28:24 --> 00:28:30


362
00:28:30 --> 00:28:33
That is t(2g).
And then, what we find is that

363
00:28:33 --> 00:28:35
of these six linear
combinations,

364
00:28:35 --> 00:28:38
two of them,
shown right here,

365
00:28:38 --> 00:28:42
have the correct phase
properties to make bonding and

366
00:28:42 --> 00:28:46
antibonding combinations by
interacting with d z squared

367
00:28:46 --> 00:28:51
and d x squared minus
y squared.

368
00:28:51 --> 00:28:54
We show that down here.

369
00:28:54 --> 00:29:00


370
00:29:00 --> 00:29:06
Here is a bonding combination.
This has e(g) symmetry,

371
00:29:06 --> 00:29:14
and it represents the formation
of two bonds between the metal

372
00:29:14 --> 00:29:18
and the ligands.
And, of course,

373
00:29:18 --> 00:29:24
we also make an antibonding
combination of the same

374
00:29:24 --> 00:29:29
symmetry.
This should just remind you of

375
00:29:29 --> 00:29:33
the hydrogen H two
molecule molecular orbital

376
00:29:33 --> 00:29:36
problem built into this much
larger structure.

377
00:29:36 --> 00:29:39
And this one,
this antibonding case is e g

378
00:29:39 --> 00:29:42
star.
And let's just quickly look at

379
00:29:42 --> 00:29:44
them.

380
00:29:44 --> 00:29:55


381
00:29:55 --> 00:30:00
Here, what we have is a d z
squared orbital with

382
00:30:00 --> 00:30:05
its torus interacting in an
out-of-phase manner with these

383
00:30:05 --> 00:30:09
ammonia lone pairs.
That creates antibonding

384
00:30:09 --> 00:30:14
character here and here,
making this a high-energy

385
00:30:14 --> 00:30:18
orbital.
And then, we have antibonding

386
00:30:18 --> 00:30:22
character, too,
in between each of the ammonias

387
00:30:22 --> 00:30:27
located on the x,y-plane and the
torus of the d z squared.

388
00:30:27 --> 00:30:33
So that is one of our two e g

389
00:30:33 --> 00:30:38
star orbitals.
And over here,

390
00:30:38 --> 00:30:46
we have our d x squared minus y
squared orbital

391
00:30:46 --> 00:30:52
making antibonding interactions
with this other linear

392
00:30:52 --> 00:30:59
combination, as shown here,
such that we get antibonding

393
00:30:59 --> 00:31:05
all the way around.
That is e g star.

394
00:31:05 --> 00:31:10
That is the reason why the e(g)
set, derived from our set of d

395
00:31:10 --> 00:31:12
orbitals, is marked with an
asterisk.

396
00:31:12 --> 00:31:16
It is antibonding with respect
to these bonds.

397
00:31:16 --> 00:31:20
If you start to populate e(g)*
with electrons,

398
00:31:20 --> 00:31:23
as you will do in certain cases
that are high-spin,

399
00:31:23 --> 00:31:27
for example,
those electrons that go into

400
00:31:27 --> 00:31:31
e(g)*, if you reflect back on
the way that we calculate bond

401
00:31:31 --> 00:31:36
order, they go in there and
weaken these two metal ligand

402
00:31:36 --> 00:31:40
bonds.
And these two bonds look just

403
00:31:40 --> 00:31:43
identical to the ones I drew
here for e(g)*,

404
00:31:43 --> 00:31:47
just reversing the phase and
making them bonding everywhere.

405
00:31:47 --> 00:31:50
Let's just look at those.

406
00:31:50 --> 00:31:58


407
00:31:58 --> 00:32:03
Here, we have d z squared
making a nice bonding

408
00:32:03 --> 00:32:05
combination.

409
00:32:05 --> 00:32:10


410
00:32:10 --> 00:32:14
It is interacting in an
in-phase manner with that linear

411
00:32:14 --> 00:32:19
combination, so we have bonding
both in the x,y-plane and

412
00:32:19 --> 00:32:25
strongly along the z-axis.
That is one of these two bonds.

413
00:32:25 --> 00:32:29
And then over here,
we will have x squared minus y

414
00:32:29 --> 00:32:34
squared,
making bonds also --

415
00:32:34 --> 00:32:39


416
00:32:39 --> 00:32:45
-- like that.
Down here, this is bonding,

417
00:32:45 --> 00:32:50
and this is antibonding.

418
00:32:50 --> 00:32:55


419
00:32:55 --> 00:33:00
Now, that is not the entire
diagram.

420
00:33:00 --> 00:33:04
One runs out of space pretty
quickly on these

421
00:33:04 --> 00:33:09
horizontally-oriented boards for
putting together tall MO

422
00:33:09 --> 00:33:12
diagrams, but there were six LCs
over here.

423
00:33:12 --> 00:33:18
And you will see that there
will be another one that makes a

424
00:33:18 --> 00:33:22
bond with the 4s orbital.
And so, accordingly,

425
00:33:22 --> 00:33:27
the 4s orbital comes up here.
There will be an antibond

426
00:33:27 --> 00:33:32
derived from 4s.
There will be also a set of

427
00:33:32 --> 00:33:39
three that are antibonding
derived from interaction of 4p

428
00:33:39 --> 00:33:41
with the other ones,
here.

429
00:33:41 --> 00:33:47
And there is a big energy
mismatch between 4p and these,

430
00:33:47 --> 00:33:55
so we will draw these as the
least stabilized of the set.

431
00:33:55 --> 00:34:00
But now, what you can see down
here is that we have found a way

432
00:34:00 --> 00:34:04
to form six bonds,
six pairs of electrons,

433
00:34:04 --> 00:34:09
each coming from the highest
occupied molecular orbital of

434
00:34:09 --> 00:34:14
the six ammonia molecules.
We have formed six bonds using

435
00:34:14 --> 00:34:17
these valance orbitals of the
metal.

436
00:34:17 --> 00:34:22
And how many more electrons do
we have to put into the diagram?

437
00:34:22 --> 00:34:27
We have six because this,
in the case of our cobalt (NH

438
00:34:27 --> 00:34:33
three) six three plus --

439
00:34:33 --> 00:34:37
This is Group 9.
Minus three for the 3+ charge.

440
00:34:37 --> 00:34:41
All the ammonia ligands are
neutral, equals six.

441
00:34:41 --> 00:34:43
So this is a d six case.

442
00:34:43 --> 00:34:48
The orbitals here that we
called t(2g) and e g star

443
00:34:48 --> 00:34:52
can now take up six
more electrons.

444
00:34:52 --> 00:34:57
And I am drawing them in here
with the assumption that this is

445
00:34:57 --> 00:35:02
a low-spin case.
And that is reasonable based on

446
00:35:02 --> 00:35:06
the 3+ charge of this ion.
We have already discussed the

447
00:35:06 --> 00:35:09
effective charge.
It draws the ligands in.

448
00:35:09 --> 00:35:14
It tends to increase the value
of delta O, as we have seen.

449
00:35:14 --> 00:35:17
And so this is how I would
populate that diagram,

450
00:35:17 --> 00:35:21
with the 6d electrons going
into the nonbonding t(2g)

451
00:35:21 --> 00:35:26
constituting the highest
occupied molecular orbital of

452
00:35:26 --> 00:35:30
this system.
And then, stabilize the lone

453
00:35:30 --> 00:35:32
pairs.
Down here what is really going

454
00:35:32 --> 00:35:37
on, you can think about these
six ammonia molecules acting

455
00:35:37 --> 00:35:42
simultaneously as six Lewis
bases to a metal that has enough

456
00:35:42 --> 00:35:46
empty orbitals to accept six
lone pair donations to that same

457
00:35:46 --> 00:35:49
metal.
So it is a Lewis acid times

458
00:35:49 --> 00:35:51
six.
And it is positively charged,

459
00:35:51 --> 00:35:57
which of course tends to draw
electron density to it.

460
00:35:57 --> 00:36:00
And that is our simplified
molecular orbital diagram for

461
00:36:00 --> 00:36:04
the sigma-only case.
Now, there are a lot of other

462
00:36:04 --> 00:36:07
interesting cases.
As you can see here from this

463
00:36:07 --> 00:36:11
spectrochemical series where the
ligands in the middle are

464
00:36:11 --> 00:36:13
basically sigma-only urea,
water.

465
00:36:13 --> 00:36:17
But then at either end of the
spectrochemical series,

466
00:36:17 --> 00:36:21
you get into systems where you
must take pi effects into

467
00:36:21 --> 00:36:23
account.

468
00:36:23 --> 00:36:39


469
00:36:39 --> 00:36:43
And we will treat,
first, the case of a pi donor.

470
00:36:43 --> 00:36:48
Remember that if we are talking
about a donor,

471
00:36:48 --> 00:36:53
that means we are effectively
talking about a Lewis base.

472
00:36:53 --> 00:36:59
And you have to ask yourself
the question in a system that

473
00:36:59 --> 00:37:05
has a ligand that can make pi
bonds, are the orbitals on the

474
00:37:05 --> 00:37:12
metal that have pi symmetry
filled, or are they empty?

475
00:37:12 --> 00:37:14
And, similarly,
are the pi symmetry orbitals on

476
00:37:14 --> 00:37:17
the ligand in question filled or
are they empty?

477
00:37:17 --> 00:37:20
And, if you can get all that
right, you will really

478
00:37:20 --> 00:37:24
understand what happens in terms
of attenuating t(2g) when you

479
00:37:24 --> 00:37:26
add in pi effects.
We have seen that the e(g)

480
00:37:26 --> 00:37:30
orbitals of a metal are the d z
squared and d x

481
00:37:30 --> 00:37:33
squared minus y squared
that point along the

482
00:37:33 --> 00:37:38
axes.
The xz, yz, and xy that point

483
00:37:38 --> 00:37:45
between the axes have the
potential to make pi bonds with

484
00:37:45 --> 00:37:49
ligands.
And so here is an example of a

485
00:37:49 --> 00:37:55
type of ligand that can make pi
bonds to a metal.

486
00:37:55 --> 00:38:01
This ligand is NH two minus.

487
00:38:01 --> 00:38:04
And it can make both sigma and
pi bonds to a metal.

488
00:38:04 --> 00:38:09
It is usually the case that if
a ligand is capable of making pi

489
00:38:09 --> 00:38:12
bonds to a metal,
it is also capable of making

490
00:38:12 --> 00:38:15
sigma bonds.
And so the pi effects are sort

491
00:38:15 --> 00:38:17
of mapped onto the sigma
framework.

492
00:38:17 --> 00:38:21
And so what we found over here
and here about the sigma only

493
00:38:21 --> 00:38:26
case, that will also be true for
pi systems.

494
00:38:26 --> 00:38:31
But then we are superposing on
that diagram the pi bonds that

495
00:38:31 --> 00:38:35
can form in the system.
And the way that NH two minus

496
00:38:35 --> 00:38:41
can make both sigma
and pi bonds with a metal is,

497
00:38:41 --> 00:38:44
first of all,
it has a lone pair that is

498
00:38:44 --> 00:38:48
directed at the metal,
like this.

499
00:38:48 --> 00:38:53


500
00:38:53 --> 00:38:57
For forming sigma contacts.
And, if you have six of these

501
00:38:57 --> 00:39:00
around a metal,
the situation would be just the

502
00:39:00 --> 00:39:05
same as what we derived over
here for the cobalt hexamine.

503
00:39:05 --> 00:39:10
But this is a planar system.
The sum of the bond angles

504
00:39:10 --> 00:39:15
around the nitrogen in systems
like this are 360 degrees

505
00:39:15 --> 00:39:18
meaning that,
unlike ammonia itself,

506
00:39:18 --> 00:39:23
which is a trigonal pyramid,
this is a planar system.

507
00:39:23 --> 00:39:29
And so it has a lone pair
perpendicular to that plane.

508
00:39:29 --> 00:39:34


509
00:39:34 --> 00:39:38
I will draw it that way.
It is just a pure p-orbital,

510
00:39:38 --> 00:39:42
perpendicular to the plane of
the substituents on that

511
00:39:42 --> 00:39:46
nitrogen.
And the way that could make a

512
00:39:46 --> 00:39:50
pi bond with the metal is
through simultaneous donation

513
00:39:50 --> 00:39:56
above and below the plane of its
substituents on that nitrogen,

514
00:39:56 --> 00:40:00
so that this ligand can
interact as a double Lewis base

515
00:40:00 --> 00:40:07
with a metal if the metal has
appropriate orbitals available.

516
00:40:07 --> 00:40:13
And so a situation in which you
might find this would be the

517
00:40:13 --> 00:40:15
following.

518
00:40:15 --> 00:40:30


519
00:40:30 --> 00:40:34
An example of such a molecule,
this would be a neutral one.

520
00:40:34 --> 00:41:00


521
00:41:00 --> 00:41:05
And what you see is that the
planes of these NH two

522
00:41:05 --> 00:41:10
units are lining up with the
coordinate xz,

523
00:41:10 --> 00:41:14
yz, and xy Cartesian planes in
the molecule.

524
00:41:14 --> 00:41:20
Since each of these ligands is
negatively charged and the

525
00:41:20 --> 00:41:25
molecule is neutral,
the chromium is therefore in

526
00:41:25 --> 00:41:31
the +6 oxidation state to
balance the six negative charges

527
00:41:31 --> 00:41:36
on the amido ligands,
we call them.

528
00:41:36 --> 00:41:38
This is amido.
And so this one,

529
00:41:38 --> 00:41:41
in fact, is a d zero case.

530
00:41:41 --> 00:41:45
And d zero is an
electron count that is pretty

531
00:41:45 --> 00:41:50
typical for the formation of pi
bonds from ligands that can

532
00:41:50 --> 00:41:55
donate into the metal center.
If you have d electrons present

533
00:41:55 --> 00:41:59
in a system like this,
then you won't have the empty

534
00:41:59 --> 00:42:04
d-orbitals on the metal that are
necessary to accept bonds formed

535
00:42:04 --> 00:42:09
by lone pair donation of this
sort.

536
00:42:09 --> 00:42:13
The system will become choked
up on itself with too many

537
00:42:13 --> 00:42:15
electrons.
Let's see what those

538
00:42:15 --> 00:42:20
perturbations will lead to for
our MO diagram.

539
00:42:20 --> 00:42:40


540
00:42:40 --> 00:42:44
I am going to focus in on
linear combinations of amide

541
00:42:44 --> 00:42:48
lone pair orbitals that,
in fact, have the correct

542
00:42:48 --> 00:42:52
symmetry to interact with our
t(2g) set, since that is our pi

543
00:42:52 --> 00:42:56
set of orbitals from the d
manifold on the metal.

544
00:42:56 --> 00:42:59
So let's look at this.

545
00:42:59 --> 00:43:09


546
00:43:09 --> 00:43:12
This would be d(yz).

547
00:43:12 --> 00:43:19


548
00:43:19 --> 00:43:23
And then, let me choose --

549
00:43:23 --> 00:43:41


550
00:43:41 --> 00:43:45
We can make a pi bond of this
sort using a linear combination

551
00:43:45 --> 00:43:50
that I am mating up together
with the d(yz) orbital.

552
00:43:50 --> 00:43:54
And while I have drawn here the
bonding counterpart there,

553
00:43:54 --> 00:43:58
of course, will be an
antibonding counterpart for

554
00:43:58 --> 00:44:03
that.
Let's draw the one that belongs

555
00:44:03 --> 00:44:04
to d(xz).

556
00:44:04 --> 00:44:10


557
00:44:10 --> 00:44:13
And that will be the one up
top, here.

558
00:44:13 --> 00:44:31


559
00:44:31 --> 00:44:34
So what we have is pi bonding
happening here,

560
00:44:34 --> 00:44:39
here, here, and here that
corresponds to pi lone paired

561
00:44:39 --> 00:44:42
donation into that metal
orbital.

562
00:44:42 --> 00:44:46
And then, finally,
we have one that involves the

563
00:44:46 --> 00:44:48
d(xy).

564
00:44:48 --> 00:44:55


565
00:44:55 --> 00:45:01
And this would be with our
hydrogens up and down,

566
00:45:01 --> 00:45:04
here and here.
Sorry.

567
00:45:04 --> 00:45:10
Up and down in front and in
back like that,

568
00:45:10 --> 00:45:18
so that we can make two pi
bonding interactions over here

569
00:45:18 --> 00:45:22
with this.
There is pi bonding,

570
00:45:22 --> 00:45:28
pi bonding, bonding,
bonding.

571
00:45:28 --> 00:45:31
At this point,
we have gotten to where we can

572
00:45:31 --> 00:45:35
recognize how there are three
linear combinations of the pi

573
00:45:35 --> 00:45:39
lone pairs from these amido
ligands that will have the

574
00:45:39 --> 00:45:43
correct symmetry to interact
with the t(2g) set from our

575
00:45:43 --> 00:45:46
metal.
There are three more where you

576
00:45:46 --> 00:45:51
would just flip one of the two
on each, and those would have

577
00:45:51 --> 00:45:54
the correct symmetry to interact
with the px, py,

578
00:45:54 --> 00:45:59
and pz orbitals on the metal.
I am not going to draw those

579
00:45:59 --> 00:46:03
out since we are focusing on the
d part of our diagram at the

580
00:46:03 --> 00:46:04
moment.

581
00:46:04 --> 00:46:10


582
00:46:10 --> 00:46:15
And what we will find then,
in the molecular orbital

583
00:46:15 --> 00:46:21
diagram for a system of this
sort, is that our d manifold,

584
00:46:21 --> 00:46:25
this is our 3d,
4s, 4p, is such that,

585
00:46:25 --> 00:46:33
you remember previously t two g
came straight over.

586
00:46:33 --> 00:46:36
And now, instead,
we are going to see that it

587
00:46:36 --> 00:46:40
goes up in energy because what
t(2g) now is,

588
00:46:40 --> 00:46:44
it still has a lot of d(xz),
d(yz) and d(xy).

589
00:46:44 --> 00:46:49
But now, t two g has
acquired a pi star

590
00:46:49 --> 00:46:54
character due to the fact that
we have these linear

591
00:46:54 --> 00:46:58
combinations over here.
These are our pi LCs that we

592
00:46:58 --> 00:47:04
drew over there that are of the
appropriate symmetry to interact

593
00:47:04 --> 00:47:09
with d(xz), d(yz) and d(xy).
And, therefore,

594
00:47:09 --> 00:47:14
these that are filled are
stabilized, come down here and

595
00:47:14 --> 00:47:19
form a t two g set
that is bonding because those,

596
00:47:19 --> 00:47:24
of course, are filled in,
NH two minus.

597
00:47:24 --> 00:47:28
And, if the metal has an empty
t two g set,

598
00:47:28 --> 00:47:33
you see that we do get three pi
bonds.

599
00:47:33 --> 00:47:36
t two g now gives us
pi antibonds.

600
00:47:36 --> 00:47:40
This is being mapped on the
sigma framework that is the same

601
00:47:40 --> 00:47:44
as what we have right here for
the cobalt hexamine,

602
00:47:44 --> 00:47:47
so that above t(2g) we will
have the e(g)*.

603
00:47:47 --> 00:47:51
And will now recognize that
e(g) is sigma star

604
00:47:51 --> 00:47:55
rather than pi star,
so it is more strongly

605
00:47:55 --> 00:47:59
destabilized due to the greater
overlap considerations of

606
00:47:59 --> 00:48:03
forming sigma bonds versus the
side to side overlap of pi

607
00:48:03 --> 00:48:10
bonds.
And the key observation here is

608
00:48:10 --> 00:48:14
that pi donors --

609
00:48:14 --> 00:48:20


610
00:48:20 --> 00:48:26
-- decrease the magnitude of
delta O by raising the energy of

611
00:48:26 --> 00:48:30
t(2g), by making t(2g) pi* in
character.

612
00:48:30 --> 00:48:34
Antibonding.
We can see, not only that t(2g)

613
00:48:34 --> 00:48:39
should be raised up,
but that mapping that onto our

614
00:48:39 --> 00:48:44
full sigma framework diagram,
delta O is shrinking.

615
00:48:44 --> 00:48:51
We still have our six sigma
bonds between the NH two

616
00:48:51 --> 00:48:55
ligands and the metal.
They are down here,

617
00:48:55 --> 00:49:01
just not drawn.
It is the same as up here.

618
00:49:01 --> 00:49:03
And now, we have three
additional pi bonds.

619
00:49:03 --> 00:49:07
There are another three
additional pi bonds that you can

620
00:49:07 --> 00:49:11
draw because we do have six of
these NH two minus

621
00:49:11 --> 00:49:13
ligands.
And then, the corresponding

622
00:49:13 --> 00:49:17
antibonding orbitals involve 4p.
And they are way up here

623
00:49:17 --> 00:49:19
somewhere in energy and very
empty.

624
00:49:19 --> 00:49:23
Since this was a d zero
case, what we have is that you

625
00:49:23 --> 00:49:27
have we pairs of electrons on
six NH two minus's

626
00:49:27 --> 00:49:30
that are down here in this
manifold of metal ligand sigma

627
00:49:30 --> 00:49:33
and pi bonding.

628
00:49:33 --> 00:49:38


629
00:49:38 --> 00:49:40
And so we have 12 pairs of
electrons down here that

630
00:49:40 --> 00:49:44
describe the sigma plus pi
bonding between the metal and

631
00:49:44 --> 00:49:46
the ligands.
And then you come here to your

632
00:49:46 --> 00:49:49
d manifold, these are empty
because this is a d zero

633
00:49:49 --> 00:49:53
case, because I happened to
choose chromium in the six plus

634
00:49:53 --> 00:49:56
oxidation here.
So it is a d zero case,

635
00:49:56 --> 00:50:00
and we wouldn't have any
electrons to put in here.

636
0:50:00 --> 00:50:04
But, under these circumstances,
in order to get color in a

637
0:50:04 --> 00:50:07
system like this,
you would have to be promoting

638
0:50:07 --> 00:50:12
an electron from down here from
these pi bonds probably into the

639
0:50:12 --> 00:50:16
d manifold, for example.
And what we have seen here,

640
0:50:16.13 --> 00:50:20
namely that pi donors decrease
delta O should give you a clue

641
0:50:20 --> 00:50:24
as to what is going on with
chloride and fluoride.

642
0:50:24 --> 00:50:28
Since those have small values
of delta O, they lie at a

643
0:50:28.19 --> 00:50:33
position of weakness in the
spectrochemical series.

644
0:50:33 --> 00:50:36
And in the converse,
that ligands like cyanide and

645
0:50:36 --> 00:50:41
especially carbon monoxide are
very high in the spectrochemical

646
0:50:41 --> 00:50:44
series because they are pi acid
ligands.

647
0:50:44 --> 00:50:48
And this is something you will
be getting more information

648
0:50:48.382 --> 50:51
about in recitation this week.
See you all on Wednesday.