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PROFESSOR: All right, so we
started talking about

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00:00:25,530 --> 00:00:29,450
transition metals, and at the
end of last time we'd given an

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00:00:29,450 --> 00:00:33,010
introduction to all the sort of
nomenclature and things you

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00:00:33,010 --> 00:00:36,660
need to know, and we had just
gotten up to d orbitals, and

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00:00:36,660 --> 00:00:38,200
when you're talking about
transition metals you're

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00:00:38,200 --> 00:00:38,960
talking about d orbitals.

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00:00:38,960 --> 00:00:44,060
So, we're going to start with a
little review of d orbitals,

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00:00:44,060 --> 00:00:45,430
some of you have seen
this before, maybe

16
00:00:45,430 --> 00:00:47,150
some of you have not.

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00:00:47,150 --> 00:00:50,380
But here is what you're
going to need to

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00:00:50,380 --> 00:00:51,990
know about the d orbitals.

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00:00:51,990 --> 00:00:54,450
You need to know the names of
all the d orbitals, you should

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00:00:54,450 --> 00:00:59,280
be able to draw the shapes of
the d orbitals, and so the bar

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00:00:59,280 --> 00:01:00,900
is not too high for this.

22
00:01:00,900 --> 00:01:04,660
You see the drawings that are
in your handouts, you should

23
00:01:04,660 --> 00:01:06,540
be able to do about that
well, it doesn't

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00:01:06,540 --> 00:01:08,360
have to be super fancy.

25
00:01:08,360 --> 00:01:10,690
But you should be able to draw
their shapes, and you should

26
00:01:10,690 --> 00:01:14,610
also be able to recognize which
d orbital it is -- if

27
00:01:14,610 --> 00:01:16,450
you have a picture of different
d orbitals, you

28
00:01:16,450 --> 00:01:19,890
should be able to name
that d orbital.

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00:01:19,890 --> 00:01:23,790
So let's just review what the
d orbitals look like.

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00:01:23,790 --> 00:01:26,210
And in this class, we're always
going to have the same

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00:01:26,210 --> 00:01:28,670
reference frame, so we're
always going to have the

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00:01:28,670 --> 00:01:34,480
z-axis up and down, the y-axis
is horizontal, and the x-axis

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00:01:34,480 --> 00:01:38,260
is coming out of the board
and going into the board.

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00:01:38,260 --> 00:01:42,820
So, we'll always use that
same description.

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00:01:42,820 --> 00:01:45,260
It'll often be given, but if
it's not, you can assume

36
00:01:45,260 --> 00:01:47,980
that's what we're
talking about.

37
00:01:47,980 --> 00:01:51,730
So, the first d orbital we'll
consider is d z squared.

38
00:01:51,730 --> 00:01:56,100
It has its maximum amplitude
along the z-axis, and it also

39
00:01:56,100 --> 00:02:01,060
has a little donut
in the x y plane.

40
00:02:01,060 --> 00:02:04,680
So, d x squared minus y squared
has its maximum

41
00:02:04,680 --> 00:02:11,370
amplitude along the x and the
y axis, so directly on-axis

42
00:02:11,370 --> 00:02:14,870
for this particular d orbital.

43
00:02:14,870 --> 00:02:18,830
The next sets of d orbitals have
their maximum amplitudes

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00:02:18,830 --> 00:02:22,490
off-axis, so they don't
correspond directly to the

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00:02:22,490 --> 00:02:24,600
axes that I just mentioned,
they're, in

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00:02:24,600 --> 00:02:27,880
fact, 45 degrees off-axis.

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00:02:27,880 --> 00:02:35,450
So we have the d y z shown here,
d x z shown here, so

48
00:02:35,450 --> 00:02:43,680
maximum amplitude 45 degrees off
z and x axes, and then z

49
00:02:43,680 --> 00:02:52,580
-- these pictures are a little
bit complicated to see -- d x

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00:02:52,580 --> 00:02:56,250
y, so it's 45 degrees off
of the x and the y.

51
00:02:56,250 --> 00:02:59,850
And so, here I tried to draw
them all in the same

52
00:02:59,850 --> 00:03:03,300
orientation of axes, which is
a little bit difficult.

53
00:03:03,300 --> 00:03:09,450
So now let's look at them in
terms of where they're drawn

54
00:03:09,450 --> 00:03:14,340
so you can kind of see them a
little bit better, and so why

55
00:03:14,340 --> 00:03:18,520
don't you try to learn to
recognize all of these.

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00:03:18,520 --> 00:03:24,600
So, what is this one called?
d z squared.

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00:03:24,600 --> 00:03:28,420
What is this one, so its maximum
amplitude is along x

58
00:03:28,420 --> 00:03:33,350
and y? d x squared
minus y squared.

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00:03:33,350 --> 00:03:35,580
I think this picture might be
a little -- you might have

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00:03:35,580 --> 00:03:38,580
somewhat aversion later on, but
this is just good practice

61
00:03:38,580 --> 00:03:41,330
for you in recognizing them.

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00:03:41,330 --> 00:03:47,900
So here we have one 45 degrees
off-axis, which one is this?

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00:03:47,900 --> 00:03:48,560
Yup.

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00:03:48,560 --> 00:03:52,750
And this one over here?

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00:03:52,750 --> 00:03:53,500
Yup.

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00:03:53,500 --> 00:03:55,310
So, y z.

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00:03:55,310 --> 00:03:58,320
And this last one here?

68
00:03:58,320 --> 00:04:01,630
Yup, we have the x z,
so it's going up and

69
00:04:01,630 --> 00:04:05,970
down for the for z-axis.

70
00:04:05,970 --> 00:04:09,410
So, a little more
practice now.

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00:04:09,410 --> 00:04:12,330
To show what these look like
again, you want to think in

72
00:04:12,330 --> 00:04:15,840
three dimensions, and on paper
and in most the time in

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00:04:15,840 --> 00:04:18,660
Powerpoint you're not in three
dimension, so here's a little

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00:04:18,660 --> 00:04:20,050
movie in three dimensions.

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00:04:20,050 --> 00:04:25,830
Here you can really see that
donut, so this is d x squared

76
00:04:25,830 --> 00:04:29,830
-- see the maximum amplitude
along z-axis here, and down

77
00:04:29,830 --> 00:04:35,680
here, and the little donut
in the x y plane.

78
00:04:35,680 --> 00:04:39,960
So this one is d x squared
minus y squared.

79
00:04:39,960 --> 00:04:43,840
The maximum amplitudes are right
directly along axis, so

80
00:04:43,840 --> 00:04:48,500
that allows you to distinguish
it from d x y.

81
00:04:48,500 --> 00:04:51,780
So when it's on-axis
here, it's the x

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00:04:51,780 --> 00:04:58,210
squared minus y squared.

83
00:04:58,210 --> 00:05:04,765
So moving along here, so this is
d x y, so you see that it's

84
00:05:04,765 --> 00:05:08,020
in that axis but it's not
directly on-axis -- the

85
00:05:08,020 --> 00:05:11,750
maximum amplitude is 45 degrees
off, so the orbitals

86
00:05:11,750 --> 00:05:19,860
are in between the axes there.

87
00:05:19,860 --> 00:05:24,250
Now we're looking at one that
has a z in it, and it looks

88
00:05:24,250 --> 00:05:28,540
like it's x z, so that's where
our maximum amplitude is

89
00:05:28,540 --> 00:05:41,150
between the x and the z-axes,
45 degrees off.

90
00:05:41,150 --> 00:05:45,580
And our last one, we
have y and z here.

91
00:05:45,580 --> 00:05:54,650
Again, 45 degrees off-axis
between the y-axis and z-axis.

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00:05:54,650 --> 00:05:57,760
So, hopefully these little
movies will help cement in

93
00:05:57,760 --> 00:06:05,060
your brain, what the shapes
of these d orbitals are.

94
00:06:05,060 --> 00:06:07,460
All right, so that's d orbitals,
and we're going to

95
00:06:07,460 --> 00:06:10,810
be mentioning d orbitals in
every lecture in this, and you

96
00:06:10,810 --> 00:06:13,460
have to be thinking about what
the shapes of the d orbitals

97
00:06:13,460 --> 00:06:17,360
are to talk about today's
topic, which is

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00:06:17,360 --> 00:06:23,860
crystal field theory.

99
00:06:23,860 --> 00:06:26,465
So, there are two types of
theories that you may hear of

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00:06:26,465 --> 00:06:29,490
and that your book mentions --
crystal field theory, and

101
00:06:29,490 --> 00:06:33,390
ligand field theory, and like
most things that you learn

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00:06:33,390 --> 00:06:36,830
about in freshman chemistry, the
theories were developed to

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00:06:36,830 --> 00:06:40,340
explain experimental
information.

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00:06:40,340 --> 00:06:42,800
So there are special properties
of coordination

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00:06:42,800 --> 00:06:45,690
complexes, so that's where you
have a transition metal in the

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00:06:45,690 --> 00:06:48,710
middle and you have ligands
all around it, so you have

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00:06:48,710 --> 00:06:51,890
these coordination complexes
and they have special

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00:06:51,890 --> 00:06:52,450
properties.

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00:06:52,450 --> 00:06:56,120
And so people wanted to try to
rationalize these special

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00:06:56,120 --> 00:07:01,720
properties and they came up
with these two theories.

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00:07:01,720 --> 00:07:06,920
So, the basic idea behind these
theories is that when

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00:07:06,920 --> 00:07:10,870
you place a metal ion with the
particular oxidation number in

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00:07:10,870 --> 00:07:13,890
the center of a coordination
sphere, and you have all these

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00:07:13,890 --> 00:07:17,520
ligands, these donor ligands,
all surrounding them, that the

115
00:07:17,520 --> 00:07:21,380
energy of the d orbitals is
going to be altered by the

116
00:07:21,380 --> 00:07:24,300
position of those ligands.

117
00:07:24,300 --> 00:07:28,150
So it's all about the d
orbitals, and the d orbitals

118
00:07:28,150 --> 00:07:32,550
are going to experience some
influence from these ligands,

119
00:07:32,550 --> 00:07:37,490
these donor ligands that are
surrounding the metal.

120
00:07:37,490 --> 00:07:40,950
So then, between these two
theories that are used to

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00:07:40,950 --> 00:07:44,670
explain how these d orbitals
are being affected.

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00:07:44,670 --> 00:07:48,580
The crystal field theory is
based on an ionic description,

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00:07:48,580 --> 00:07:52,080
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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00:07:57,980 --> 00:08:03,150
theory considers covalent, as
well as ionic aspects of

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00:08:03,150 --> 00:08:04,290
coordination.

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00:08:04,290 --> 00:08:08,090
It's more powerful it's more
useful, but it's also a bit

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00:08:08,090 --> 00:08:11,780
more complex, and so we don't
cover it in this of course,

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00:08:11,780 --> 00:08:14,550
and if you go on and take the
first level of inorganic

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00:08:14,550 --> 00:08:18,510
chemistry, which is 503, then
you'll hear about this.

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00:08:18,510 --> 00:08:20,570
But for this course, we're
just going to talk about

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00:08:20,570 --> 00:08:22,240
crystal field theory.

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00:08:22,240 --> 00:08:25,580
Even though it's very much
of a simplified model, it

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00:08:25,580 --> 00:08:26,900
actually works very well.

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00:08:26,900 --> 00:08:30,040
You can explain quite a few
properties of coordination

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00:08:30,040 --> 00:08:37,070
complexes just using this
simplified method.

137
00:08:37,070 --> 00:08:40,000
So, crystal field theory,
again, very simple.

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00:08:40,000 --> 00:08:44,860
It's just considering the
ionic interactions, it

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00:08:44,860 --> 00:08:48,210
considers the ligands as
negative point charges.

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00:08:48,210 --> 00:08:52,490
And so, the basic idea is that
ligands, as negative point

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00:08:52,490 --> 00:08:56,690
charges, are going to have
repulsive effects if they get

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00:08:56,690 --> 00:08:58,820
close to the d orbitals.

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00:08:58,820 --> 00:09:02,500
So here is a drawing of a metal,
and so this is metal

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00:09:02,500 --> 00:09:07,880
abbreviated m, its oxidation
number is m plus here, and it

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00:09:07,880 --> 00:09:09,840
has ligands all around it.

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00:09:09,840 --> 00:09:13,440
What is the geometry here?

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00:09:13,440 --> 00:09:15,550
It's octahedral geometry.

148
00:09:15,550 --> 00:09:20,390
And so we have ligands up and
down along z, ligands along y,

149
00:09:20,390 --> 00:09:22,980
and a ligand going back
along x, and a ligand

150
00:09:22,980 --> 00:09:25,280
coming out along x.

151
00:09:25,280 --> 00:09:28,120
And so here's another picture
of the same thing, the metal

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00:09:28,120 --> 00:09:31,580
is in the middle, and the
ligands -- in this case, you

153
00:09:31,580 --> 00:09:34,810
have these ammonia ligands or
these little negative point

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00:09:34,810 --> 00:09:38,040
charges, which are all
along the axes.

155
00:09:38,040 --> 00:09:43,250
You have four along the
equatorial, and one up and one

156
00:09:43,250 --> 00:09:47,960
down, so this is the octahedral
geometry.

157
00:09:47,960 --> 00:09:50,480
And so you can just think about
each of these ligands as

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00:09:50,480 --> 00:09:52,860
negative point charges.

159
00:09:52,860 --> 00:09:55,510
And so, if the negative point
charge is pointing right

160
00:09:55,510 --> 00:09:58,170
toward a d orbital, that'll
be very repulsive.

161
00:09:58,170 --> 00:10:00,580
If it's not it's
less repulsive.

162
00:10:00,580 --> 00:10:04,570
That's the whole idea behind
this crystal field theory.

163
00:10:04,570 --> 00:10:09,170
So, here again, is just another
little picture, so you

164
00:10:09,170 --> 00:10:11,550
can kind of get the idea that
we're going to be thinking

165
00:10:11,550 --> 00:10:14,290
about the all the shapes of
the d orbitals, and we're

166
00:10:14,290 --> 00:10:16,600
going to think about where
the ligands are.

167
00:10:16,600 --> 00:10:19,220
Today we're going to talk about
octahedral geometry, but

168
00:10:19,220 --> 00:10:21,960
we're also going to go on and
talk about tetrahedral

169
00:10:21,960 --> 00:10:23,240
geometry later.

170
00:10:23,240 --> 00:10:26,160
So here in octahedral geometry,
you can think about

171
00:10:26,160 --> 00:10:29,090
the positions of all of these
negative point charges

172
00:10:29,090 --> 00:10:31,810
surrounding your d orbitals.

173
00:10:31,810 --> 00:10:36,060
And when the d orbitals are
on axis, like the ligands,

174
00:10:36,060 --> 00:10:38,650
there's going to be more
repulsion, so you can see here

175
00:10:38,650 --> 00:10:40,740
that would be quite repulsive
-- you have a negative point

176
00:10:40,740 --> 00:10:42,420
charge by that d orbital.

177
00:10:42,420 --> 00:10:45,340
When the d orbitals are off-axis
and the ligands are

178
00:10:45,340 --> 00:10:48,190
on-axis, that's less
repulsive.

179
00:10:48,190 --> 00:10:51,570
And that's the basic idea.

180
00:10:51,570 --> 00:10:55,110
So, let's look at each one of
these orbitals now in detail

181
00:10:55,110 --> 00:10:58,960
and think about how a ligands
that's pointing directly

182
00:10:58,960 --> 00:11:03,750
toward it is going
to be affected.

183
00:11:03,750 --> 00:11:08,780
So we have the ligands, l, as
these point charges directed

184
00:11:08,780 --> 00:11:12,960
toward the d z squared, and
the d x squared minus y

185
00:11:12,960 --> 00:11:15,580
squared orbitals, and these
would result in

186
00:11:15,580 --> 00:11:17,140
quite a bit of repulsion.

187
00:11:17,140 --> 00:11:21,500
So if you had a ligand right up
here along z, and so that

188
00:11:21,500 --> 00:11:23,610
would be a very close
interaction.

189
00:11:23,610 --> 00:11:26,670
In this case, you're going to
have ligands along x and y,

190
00:11:26,670 --> 00:11:31,110
again pointing directly toward
the orbitals, that would be

191
00:11:31,110 --> 00:11:33,830
quite repulsive.

192
00:11:33,830 --> 00:11:37,530
And I'll just mention, we'll
come back to this later, that

193
00:11:37,530 --> 00:11:42,220
one can think about the case
where you have the octahedral

194
00:11:42,220 --> 00:11:45,490
geometry where the ligands are
in a definite position, and

195
00:11:45,490 --> 00:11:49,550
you can also think about this
sort of hypothetical case

196
00:11:49,550 --> 00:11:52,430
where you have a metal in the
middle and you have the

197
00:11:52,430 --> 00:11:55,470
ligands, here are the little
ligands, and they're

198
00:11:55,470 --> 00:11:58,950
everywhere, there's ligands
everywhere all around.

199
00:11:58,950 --> 00:12:03,210
And so, in this case where you
have ligands everywhere all

200
00:12:03,210 --> 00:12:05,860
around your metal, then all your
d orbitals would have the

201
00:12:05,860 --> 00:12:09,300
same energy, but if you take
the ligands and you isolate

202
00:12:09,300 --> 00:12:13,280
them in particular positions,
then you can consider how the

203
00:12:13,280 --> 00:12:16,400
different shapes of the d
orbitals will be affected.

204
00:12:16,400 --> 00:12:19,180
We'll come back to
that in a minute.

205
00:12:19,180 --> 00:12:21,650
All right, so here we have a
case where our ligands are

206
00:12:21,650 --> 00:12:27,250
on-axis, our orbitals on-axis,
this is a large repulsion.

207
00:12:27,250 --> 00:12:31,930
So, I will tell you that d x
squared and d z squared and d

208
00:12:31,930 --> 00:12:37,040
x squared minus y squared
orbitals are destabilized, and

209
00:12:37,040 --> 00:12:40,160
they are destabilized
by the same amount.

210
00:12:40,160 --> 00:12:44,830
So there's repulsion now, and
so they're destabilized, and

211
00:12:44,830 --> 00:12:47,750
they're destabilized by the
same amount of energy.

212
00:12:47,750 --> 00:12:49,830
So what's it called
when orbitals

213
00:12:49,830 --> 00:12:53,720
are of the same energy?

214
00:12:53,720 --> 00:12:54,570
Yup.

215
00:12:54,570 --> 00:12:59,510
So, d z squared and d x squared
minus y squared are

216
00:12:59,510 --> 00:13:02,640
degenerate.

217
00:13:02,640 --> 00:13:06,570
So, d z squared and d x squared
minus y squared

218
00:13:06,570 --> 00:13:10,850
orbitals are destabilized more
than the other three orbitals,

219
00:13:10,850 --> 00:13:15,400
and let's consider now
why that is true.

220
00:13:15,400 --> 00:13:18,790
So here are our other sets of
orbitals, and remember, here

221
00:13:18,790 --> 00:13:22,720
the maximum amplitude of these
orbitals are 45 degrees

222
00:13:22,720 --> 00:13:27,070
off-axis, whereas our ligands
are all on-axis.

223
00:13:27,070 --> 00:13:30,410
So, the ligand negative charges
are directed in

224
00:13:30,410 --> 00:13:34,990
between these orbitals, not
directly toward them.

225
00:13:34,990 --> 00:13:40,430
So that is stabilized compared
to this hypothetical case

226
00:13:40,430 --> 00:13:42,620
where the ligands are
everywhere, so some of them

227
00:13:42,620 --> 00:13:46,870
will be pointing toward them,
and also stabilized compared

228
00:13:46,870 --> 00:13:49,300
to the other sets of orbitals
where the ligands are now

229
00:13:49,300 --> 00:13:54,020
pointing directly at them.

230
00:13:54,020 --> 00:13:56,520
So these three sets of orbitals
are stabilized

231
00:13:56,520 --> 00:14:00,430
relative to the d z squared and
the d x squared minus y

232
00:14:00,430 --> 00:14:04,720
squared orbitals, and they're
stabilized by the same amount.

233
00:14:04,720 --> 00:14:09,450
So these three orbitals are also
degenerate with respect

234
00:14:09,450 --> 00:14:12,910
to each other.

235
00:14:12,910 --> 00:14:19,200
So then to sort of summarize
this set of orbitals, we have

236
00:14:19,200 --> 00:14:24,280
for d z squared and d x squared
minus y squared, we

237
00:14:24,280 --> 00:14:27,270
have large repulsions by those
negative point charges,

238
00:14:27,270 --> 00:14:30,290
they're pointing directly at the
orbitals, and so they're

239
00:14:30,290 --> 00:14:35,710
destabilized, higher in energy
than the other -- the d x y, d

240
00:14:35,710 --> 00:14:38,370
y z and d x z.

241
00:14:38,370 --> 00:14:46,180
For the d y z, d x z and d x y,
they're smaller repulsion,

242
00:14:46,180 --> 00:14:49,310
because these orbitals are
off-axis, and so the negative

243
00:14:49,310 --> 00:14:51,700
point charges aren't pointing
directly at them.

244
00:14:51,700 --> 00:14:56,580
So they're stabilized relative
to these guys up here.

245
00:14:56,580 --> 00:15:01,260
So that's the whole idea behind
an octahedral case of

246
00:15:01,260 --> 00:15:04,720
crystal field theory.

247
00:15:04,720 --> 00:15:07,460
And we can look at this
just one other way, if

248
00:15:07,460 --> 00:15:08,690
pictures help you.

249
00:15:08,690 --> 00:15:11,410
Here it's a little clearer
that those negative point

250
00:15:11,410 --> 00:15:14,580
charges are pointing directly
toward the orbitals, here I

251
00:15:14,580 --> 00:15:17,910
think you can see that the
negative point charges are not

252
00:15:17,910 --> 00:15:21,630
directly pointing toward
any of the orbitals.

253
00:15:21,630 --> 00:15:23,610
So I'll show you a bunch of
different figures, this all

254
00:15:23,610 --> 00:15:27,150
shows you the same thing, but
some might help you see this

255
00:15:27,150 --> 00:15:30,380
relationship better.

256
00:15:30,380 --> 00:15:34,910
OK, so now we're going to draw
some diagrams. I'm going to

257
00:15:34,910 --> 00:15:37,750
start over here.

258
00:15:37,750 --> 00:15:46,890
So we're going to draw what's
called a crystal field

259
00:15:46,890 --> 00:16:00,630
splitting diagram, and this
is for an octahedral case.

260
00:16:00,630 --> 00:16:03,380
And the diagrams are going to
look different depending on

261
00:16:03,380 --> 00:16:07,760
what the geometry is.

262
00:16:07,760 --> 00:16:12,120
So when we draw this diagram,
energy is going up, and we're

263
00:16:12,120 --> 00:16:19,770
going to start with our 5 d
orbitals, and so this is going

264
00:16:19,770 --> 00:16:25,970
to be the average energy,
the average

265
00:16:25,970 --> 00:16:32,500
energy of our d orbitals.

266
00:16:32,500 --> 00:16:41,100
And so, this is then with a
spherical crystal field.

267
00:16:41,100 --> 00:16:43,470
So that's where the ligands are

268
00:16:43,470 --> 00:16:46,390
distributed around uniformly.

269
00:16:46,390 --> 00:16:49,540
So it's all spherical, they
aren't set up in the

270
00:16:49,540 --> 00:16:53,250
octahedral case yet, our
octahedral diagram's going to

271
00:16:53,250 --> 00:16:58,560
be over here, but this is the
case that this represents.

272
00:16:58,560 --> 00:17:03,120
If you have all your ligands
spherically distributed around

273
00:17:03,120 --> 00:17:05,940
your metal, then the energy
of all the d orbitals are

274
00:17:05,940 --> 00:17:08,970
identical, because every d
orbital has the same amount of

275
00:17:08,970 --> 00:17:11,420
ligands, it's uniform,
it's symmetrical

276
00:17:11,420 --> 00:17:12,790
all around the metal.

277
00:17:12,790 --> 00:17:15,960
And I just want to tell you that
this is was very exciting

278
00:17:15,960 --> 00:17:17,280
to me when I saw this.

279
00:17:17,280 --> 00:17:20,810
I've been teaching this class
for a while, and I never had a

280
00:17:20,810 --> 00:17:24,170
real spherical crystal field
around my metal before.

281
00:17:24,170 --> 00:17:28,360
And then I walked into Walgreens
one day, and I was

282
00:17:28,360 --> 00:17:32,530
very excited to see that
Walgreens sold spherical

283
00:17:32,530 --> 00:17:33,660
crystal fields.

284
00:17:33,660 --> 00:17:35,440
I mean you never know what
you're going to get.

285
00:17:35,440 --> 00:17:37,590
I'm a big fan of Walgreens,
I've found a lot of good

286
00:17:37,590 --> 00:17:41,840
stuff, toys for my dog,
etcetera, but

287
00:17:41,840 --> 00:17:42,930
this was really amazing.

288
00:17:42,930 --> 00:17:46,370
So I asked the cashier on the
way out whether they knew they

289
00:17:46,370 --> 00:17:50,480
were selling spherical
crystal fields, and

290
00:17:50,480 --> 00:17:53,110
they did not actually.

291
00:17:53,110 --> 00:17:56,600
So, you just never know what
you're going to get.

292
00:17:56,600 --> 00:18:01,690
OK, so in that case, where the
ligands are uniform all

293
00:18:01,690 --> 00:18:07,220
around, the energy
is the same.

294
00:18:07,220 --> 00:18:10,670
But now, if we have an
octahedral crystal field over

295
00:18:10,670 --> 00:18:23,720
here, so we have our octahedral
crystal field, then

296
00:18:23,720 --> 00:18:26,090
we get some splitting.

297
00:18:26,090 --> 00:18:30,600
So some of our orbitals are
going to be destabilized, and

298
00:18:30,600 --> 00:18:32,890
they'll be higher
in energy here.

299
00:18:32,890 --> 00:18:37,010
So we have the d x squared
minus y squared, and d z

300
00:18:37,010 --> 00:18:40,540
squared over here are going
to be higher in energy.

301
00:18:40,540 --> 00:18:47,830
And we're going to have three
that lower in energy, so we'll

302
00:18:47,830 --> 00:18:55,230
have our d x y, our d y z, and
our d x z over here, will be

303
00:18:55,230 --> 00:18:58,390
lower in energy.

304
00:18:58,390 --> 00:19:05,050
This difference is called the
octahedral field splitting

305
00:19:05,050 --> 00:19:09,180
energy, because it's the amount
of energy that the

306
00:19:09,180 --> 00:19:11,750
octahedral field is split.

307
00:19:11,750 --> 00:19:20,170
So over here, we can put this
is for the octahedral case,

308
00:19:20,170 --> 00:19:34,380
crystal field splitting
energy.

309
00:19:34,380 --> 00:19:38,420
And again, some of the orbitals
go up in energy, some

310
00:19:38,420 --> 00:19:42,280
of the orbitals go down in
energy, and the overall energy

311
00:19:42,280 --> 00:19:44,170
needs to be conserved.

312
00:19:44,170 --> 00:19:55,930
So, if two orbitals go up in
energy, and three go down in

313
00:19:55,930 --> 00:20:01,660
energy, then to have everything
add up, you can say

314
00:20:01,660 --> 00:20:06,640
that three go up in energy by
3/5, and two, these three

315
00:20:06,640 --> 00:20:09,040
orbitals are going to
go down by 2/5.

316
00:20:09,040 --> 00:20:16,100
So overall, the energy of the
system is maintained.

317
00:20:16,100 --> 00:20:19,460
OK, so that's a crystal field
splitting diagram for an

318
00:20:19,460 --> 00:20:23,920
octahedral case, and now let's
look at some examples of this.

319
00:20:23,920 --> 00:20:29,450
So let's look at an example,
and we're going to have a

320
00:20:29,450 --> 00:20:34,490
chromium system that has
three n h 3 ligands

321
00:20:34,490 --> 00:20:38,090
and three b r ligands.

322
00:20:38,090 --> 00:21:34,520
Now, you tell me what the
d count of that is.

323
00:21:34,520 --> 00:21:52,410
Let's just take 10
more seconds.

324
00:21:52,410 --> 00:21:55,440
They're not as high overall, but
still more people got the

325
00:21:55,440 --> 00:21:56,740
right answer.

326
00:21:56,740 --> 00:22:00,530
So, let's take a look at this.

327
00:22:00,530 --> 00:22:04,642
What's the oxidation
number of bromium?

328
00:22:04,642 --> 00:22:11,638
What is it?

329
00:22:11,638 --> 00:22:13,970
Bromium?

330
00:22:13,970 --> 00:22:17,300
What's 1 b r minus?

331
00:22:17,300 --> 00:22:19,850
What's its oxidation number.

332
00:22:19,850 --> 00:22:21,260
Minus 1.

333
00:22:21,260 --> 00:22:22,600
There are three of them.

334
00:22:22,600 --> 00:22:25,200
What about ammonia?

335
00:22:25,200 --> 00:22:25,490
0.

336
00:22:25,490 --> 00:22:27,980
So, 3 times 0.

337
00:22:27,980 --> 00:22:31,060
And the overall charge
of this is 0, so

338
00:22:31,060 --> 00:22:32,470
there's nothing up there.

339
00:22:32,470 --> 00:22:35,570
So what does that mean
about chromium?

340
00:22:35,570 --> 00:22:38,070
Plus 3.

341
00:22:38,070 --> 00:22:41,540
All right, so now we have to
figure out the d count.

342
00:22:41,540 --> 00:22:47,940
So the d count is going to equal
the -- and the periodic

343
00:22:47,940 --> 00:22:50,890
table, the group number, so if
you switch to my slides, we

344
00:22:50,890 --> 00:22:52,170
can see what that is.

345
00:22:52,170 --> 00:22:55,370
So what is that for chromium?

346
00:22:55,370 --> 00:22:56,640
6.

347
00:22:56,640 --> 00:23:00,495
And then we have 6 minus 3,
because our oxidation number

348
00:23:00,495 --> 00:23:08,910
is 3, and so we have
a d 3 system.

349
00:23:08,910 --> 00:23:10,490
So, did some of you get
this wrong because

350
00:23:10,490 --> 00:23:13,690
you stopped too early?

351
00:23:13,690 --> 00:23:18,120
Here, the answer, if you had 3,
you could have stopped with

352
00:23:18,120 --> 00:23:20,760
oxidation number and still
gotten it correct.

353
00:23:20,760 --> 00:23:26,270
So that's a d 3 system.

354
00:23:26,270 --> 00:23:29,960
So, we're going to worry about
three d electrons, and we're

355
00:23:29,960 --> 00:23:35,450
going to put three d electrons
into our splitting diagram.

356
00:23:35,450 --> 00:23:38,920
OK, so if you had a hypothetical
spherical crystal

357
00:23:38,920 --> 00:23:43,170
field, you would have your one's
in here, but now let's

358
00:23:43,170 --> 00:23:46,760
consider what happens in
the octahedral case.

359
00:23:46,760 --> 00:23:48,900
So we can come down here.

360
00:23:48,900 --> 00:23:53,520
Am I going to put my first
electron down here or up here?

361
00:23:53,520 --> 00:23:54,320
Down.

362
00:23:54,320 --> 00:23:56,820
Oh, I just realized that I
didn't put two things on this

363
00:23:56,820 --> 00:24:01,390
diagram, so these are in your
notes, but these diagrams have

364
00:24:01,390 --> 00:24:06,380
little abbreviations in them
for the orbital levels.

365
00:24:06,380 --> 00:24:10,640
So we have an e g and t 2 g, and
that's an abbreviation for

366
00:24:10,640 --> 00:24:12,810
the names of the ts of orbitals,
which you'll see

367
00:24:12,810 --> 00:24:16,630
later is very convenient in
terms of writing things out.

368
00:24:16,630 --> 00:24:18,660
All right, so we're going
to put them down here.

369
00:24:18,660 --> 00:24:22,240
Am I going to put two of them
together with the spins up in

370
00:24:22,240 --> 00:24:23,710
the first orbital?

371
00:24:23,710 --> 00:24:24,800
No.

372
00:24:24,800 --> 00:24:27,560
So you know that that is not
good, give you the same four

373
00:24:27,560 --> 00:24:30,260
quantum numbers, you don't
want to do that.

374
00:24:30,260 --> 00:24:32,680
So, we can put them in.

375
00:24:32,680 --> 00:24:37,230
What about just putting in a
paired set over here yet?

376
00:24:37,230 --> 00:24:37,950
No.

377
00:24:37,950 --> 00:24:41,650
They have the same energies
here, so we're going to put

378
00:24:41,650 --> 00:24:45,130
them in all singly, and
then we're done.

379
00:24:45,130 --> 00:24:49,010
So we put three electrons
in these three orbitals.

380
00:24:49,010 --> 00:24:54,290
Now we can introduce a couple
other terms, which is where I

381
00:24:54,290 --> 00:24:58,560
realized I forgot to
put the labels on.

382
00:24:58,560 --> 00:25:07,650
So, you'll often
be asked for --

383
00:25:07,650 --> 00:25:12,150
OK, you'll often be asked for
something called the d n

384
00:25:12,150 --> 00:25:21,670
electron configuration.

385
00:25:21,670 --> 00:25:25,020
And so here you can use the
abbreviations for the

386
00:25:25,020 --> 00:25:30,040
orbitals, so we point three
electrons in to the t 2 g

387
00:25:30,040 --> 00:25:33,620
orbitals, so we can just
say that's t 2 g

388
00:25:33,620 --> 00:25:35,450
raised to the three.

389
00:25:35,450 --> 00:25:39,670
So that let's someone know that
you have three electron

390
00:25:39,670 --> 00:25:44,360
in the set of orbitals that
are stabilized in an

391
00:25:44,360 --> 00:25:48,580
octahedral crystal field.

392
00:25:48,580 --> 00:25:56,840
Then we can consider something
else that's called c f s e,

393
00:25:56,840 --> 00:26:03,120
and I think I should have --

394
00:26:03,120 --> 00:26:05,340
OK, so I'll write that out.

395
00:26:05,340 --> 00:26:19,640
So, this is the crystal field
stabilization energy.

396
00:26:19,640 --> 00:26:22,870
So it's not the crystal field
splitting energy, it's the

397
00:26:22,870 --> 00:26:26,870
stabilization energy, which
indicates how much those

398
00:26:26,870 --> 00:26:30,360
electrons are stabilized by
being in an octahedral field,

399
00:26:30,360 --> 00:26:35,490
rather than this hypothetical
spherical crystal field.

400
00:26:35,490 --> 00:26:39,510
And so what we can do there is
you see that you have three

401
00:26:39,510 --> 00:26:43,920
electrons in those lower sets
of orbitals, and those

402
00:26:43,920 --> 00:26:48,680
orbitals are stabilized by 2/5
times the octahedral crystal

403
00:26:48,680 --> 00:26:51,400
field splitting energy.

404
00:26:51,400 --> 00:26:58,030
And so that gives an answer of
minus 6/5 times the octahedral

405
00:26:58,030 --> 00:27:00,180
crystal field splitting
energy.

406
00:27:00,180 --> 00:27:03,720
So that's how much those
electrons are stabilized.

407
00:27:03,720 --> 00:27:07,020
So they are lower in energy --
see, the average energy is

408
00:27:07,020 --> 00:27:11,410
much, much higher in this
hypothetical case, but because

409
00:27:11,410 --> 00:27:15,810
of having this octahedral
geometry, and there are only

410
00:27:15,810 --> 00:27:19,990
three electrons to consider,
they all go into the

411
00:27:19,990 --> 00:27:23,770
stabilized energy, and so
they're stabilized by minus

412
00:27:23,770 --> 00:27:27,210
6/5 times whatever the
octahedral crystal field

413
00:27:27,210 --> 00:27:34,210
splitting energy is for
this particular case.

414
00:27:34,210 --> 00:27:40,570
So, now let's look at
another example.

415
00:27:40,570 --> 00:27:45,410
So let's look at an example of
a coordination complex -- you

416
00:27:45,410 --> 00:27:52,720
have manganese and you have
six water ligands and some

417
00:27:52,720 --> 00:27:55,020
chlorides hanging around.

418
00:27:55,020 --> 00:27:59,140
So why don't you tell me what
the oxidation number is for

419
00:27:59,140 --> 00:28:27,890
this now -- not the d count,
but the oxidation number?

420
00:28:27,890 --> 00:28:46,530
OK, so let's just take
10 more seconds.

421
00:28:46,530 --> 00:28:50,000
OK, so let's just look at that
one for a minute, people did

422
00:28:50,000 --> 00:28:51,510
very well on that.

423
00:28:51,510 --> 00:28:57,460
So, what's the overall charge in
this coordination complex?

424
00:28:57,460 --> 00:29:03,570
So we can write this out here.

425
00:29:03,570 --> 00:29:08,220
Our six ligands and we say that
here it's plus 3 overall,

426
00:29:08,220 --> 00:29:11,580
because we have three chloride
ions hanging around with a

427
00:29:11,580 --> 00:29:12,820
negative charge.

428
00:29:12,820 --> 00:29:16,310
So this tells us that the
overall charge on the

429
00:29:16,310 --> 00:29:19,360
coordination complex
had to be plus 3.

430
00:29:19,360 --> 00:29:24,120
And this again is 0, so that
means that is plus 3.

431
00:29:24,120 --> 00:29:26,260
So, people did very
well on that.

432
00:29:26,260 --> 00:29:31,440
All right, so then what
is the d count?

433
00:29:31,440 --> 00:29:32,980
What is it?

434
00:29:32,980 --> 00:29:34,160
4, right.

435
00:29:34,160 --> 00:29:41,550
So we have 7 minus 3 is 4,
so we have a d 4 system.

436
00:29:41,550 --> 00:29:46,960
All right, so now, if you look
up there, we have to make a

437
00:29:46,960 --> 00:29:50,440
decision about that fourth
electron. three electrons were

438
00:29:50,440 --> 00:29:52,790
easy, four makes
it complicated.

439
00:29:52,790 --> 00:29:55,220
Do we put the fourth one
down in the lower

440
00:29:55,220 --> 00:29:57,360
set or do we go up?

441
00:29:57,360 --> 00:30:00,130
So there are two possibilities
here.

442
00:30:00,130 --> 00:30:03,490
So I have two diagrams
drawn over here.

443
00:30:03,490 --> 00:30:07,580
And you might be in a case where
you have a small crystal

444
00:30:07,580 --> 00:30:11,100
field splitting energy, or you
might be in a case where you

445
00:30:11,100 --> 00:30:15,380
have a large crystal field
splitting energy.

446
00:30:15,380 --> 00:30:17,690
And so, there are two
different ways the

447
00:30:17,690 --> 00:30:21,430
electrons can go.

448
00:30:21,430 --> 00:30:26,650
So over here where you have a
small crystal field splitting

449
00:30:26,650 --> 00:30:31,040
energy, that's called
a weak field.

450
00:30:31,040 --> 00:30:34,420
And when you have a big
splitting energy, that's a

451
00:30:34,420 --> 00:30:40,160
strong field.

452
00:30:40,160 --> 00:30:44,760
So, with the weak field there's
not that much of an

453
00:30:44,760 --> 00:30:47,240
energy difference
between them.

454
00:30:47,240 --> 00:30:51,100
And so, when you're putting in,
you do your first three

455
00:30:51,100 --> 00:30:54,060
electrons, that's always
going to be the same.

456
00:30:54,060 --> 00:30:58,495
But then the fourth electron, in
this case, if there's not a

457
00:30:58,495 --> 00:31:01,920
big difference in the energy, if
it's pretty small, if it's

458
00:31:01,920 --> 00:31:05,690
a weak field, you can put that
fourth one up there.

459
00:31:05,690 --> 00:31:10,200
Because it takes energy to pair
the electrons up, and so

460
00:31:10,200 --> 00:31:13,060
you're asking the question, does
it take more energy to

461
00:31:13,060 --> 00:31:16,160
pair them, or does it take
more energy to put one

462
00:31:16,160 --> 00:31:17,420
in the upper set?

463
00:31:17,420 --> 00:31:20,730
And for a weak field you say
that the crystal field

464
00:31:20,730 --> 00:31:24,930
splitting energy is smaller than
the pairing energy or p

465
00:31:24,930 --> 00:31:27,560
e, so p e is the
pairing energy.

466
00:31:27,560 --> 00:31:31,870
And so it takes more energy to
pair than it does to bump one

467
00:31:31,870 --> 00:31:34,280
electron up to the
higher level.

468
00:31:34,280 --> 00:31:38,840
So that's what a weak field
situation would look like.

469
00:31:38,840 --> 00:31:43,360
Now in a strong field situation,
boy, there's a big

470
00:31:43,360 --> 00:31:46,500
splitting difference, a big
energy difference here.

471
00:31:46,500 --> 00:31:52,870
So in this case, the crystal
field splitting is much larger

472
00:31:52,870 --> 00:31:56,340
than p e, that pairing energy
for the electron.

473
00:31:56,340 --> 00:31:59,010
So it's better to pair,
then to put one up.

474
00:31:59,010 --> 00:32:03,510
I can't even reach those,
that's really far up.

475
00:32:03,510 --> 00:32:07,035
So I'm not going to do
that, I'm just going

476
00:32:07,035 --> 00:32:07,890
to put them in here.

477
00:32:07,890 --> 00:32:11,350
I'll put the first three in,
and then the fourth one is

478
00:32:11,350 --> 00:32:13,480
going to go down where
I can reach it.

479
00:32:13,480 --> 00:32:15,960
I don't have the energy
to put it up there.

480
00:32:15,960 --> 00:32:18,920
So that's a strong field.

481
00:32:18,920 --> 00:32:22,250
Weak field I can handle, strong
field I'm going to try

482
00:32:22,250 --> 00:32:26,250
pair them all up.

483
00:32:26,250 --> 00:32:31,740
So, now we can write the
different d n electron

484
00:32:31,740 --> 00:32:34,790
configurations for these two.

485
00:32:34,790 --> 00:32:45,410
So, in this case, if we
have our d n electron

486
00:32:45,410 --> 00:32:55,400
configuration, so we
have three in the t

487
00:32:55,400 --> 00:32:57,750
2 g, we have three.

488
00:32:57,750 --> 00:33:03,000
And in the e g set we have one,
so that is our electron

489
00:33:03,000 --> 00:33:06,320
configuration for this
weak field case.

490
00:33:06,320 --> 00:33:09,680
And for the strong field case,
we didn't put any up in the e

491
00:33:09,680 --> 00:33:15,710
g, so we just have t
2 g, four electrons

492
00:33:15,710 --> 00:33:20,390
in that set of orbitals.

493
00:33:20,390 --> 00:33:28,110
OK, so let's just put up what
we've done here, and introduce

494
00:33:28,110 --> 00:33:32,920
another term, which are high
spin and low spin.

495
00:33:32,920 --> 00:33:35,850
So we have these two cases
here, and again, we're

496
00:33:35,850 --> 00:33:40,320
considering how big is this
octahedral crystal field

497
00:33:40,320 --> 00:33:43,080
splitting energy compared
to a pairing energy.

498
00:33:43,080 --> 00:33:46,330
The energy involved in pairing
electrons together.

499
00:33:46,330 --> 00:33:49,970
In a weak field, the splitting
energy is small, so electrons

500
00:33:49,970 --> 00:33:54,750
are placed singly with spins
parallel to the fullest extent

501
00:33:54,750 --> 00:33:57,480
in all the sets of orbitals.

502
00:33:57,480 --> 00:34:00,850
In this other case with the
strong field, the pairing

503
00:34:00,850 --> 00:34:04,900
energy is smaller than the
splitting energy -- strong

504
00:34:04,900 --> 00:34:07,800
field you have a big
splitting energy.

505
00:34:07,800 --> 00:34:11,680
And so, in that case, with the
splitting energy is large,

506
00:34:11,680 --> 00:34:14,630
you're going to put all your
electrons in and pair them up

507
00:34:14,630 --> 00:34:18,310
in t 2 g and don't put any
electrons in the e g sets of

508
00:34:18,310 --> 00:34:22,880
orbitals until you completely
filled your t 2 g set.

509
00:34:22,880 --> 00:34:27,210
So, the net result of this is
for a weak field, you have the

510
00:34:27,210 --> 00:34:31,410
maximum number of unpaired
electrons, so see, you have a

511
00:34:31,410 --> 00:34:33,350
maximum number, you have
four electrons,

512
00:34:33,350 --> 00:34:35,030
all four are unpaired.

513
00:34:35,030 --> 00:34:38,030
So that's the maximum number
of unpaired electrons, and

514
00:34:38,030 --> 00:34:40,680
this is referred to
as high spin.

515
00:34:40,680 --> 00:34:43,720
And in the other case, you have
the minimum number of

516
00:34:43,720 --> 00:34:47,340
unpaired electrons that you can
have, and so you have this

517
00:34:47,340 --> 00:34:50,180
one set that's paired here,
so that would be

518
00:34:50,180 --> 00:34:54,710
considered a low spin case.

519
00:34:54,710 --> 00:35:01,060
We can also talk about the
stabilization energy of these

520
00:35:01,060 --> 00:35:05,870
two cases, and so we have
the crystal field

521
00:35:05,870 --> 00:35:08,110
stabilization energy.

522
00:35:08,110 --> 00:35:11,650
So why don't you go ahead and
tell me for a weak field case,

523
00:35:11,650 --> 00:36:42,750
what is our stabilization
energy?

524
00:36:42,750 --> 00:36:57,730
Let's just take 10
more seconds.

525
00:36:57,730 --> 00:36:59,760
OK, pretty good.

526
00:36:59,760 --> 00:37:01,960
So let's work this out.

527
00:37:01,960 --> 00:37:07,420
So, first we consider how many
electrons we have in the lower

528
00:37:07,420 --> 00:37:09,910
set of orbitals, so
we have three.

529
00:37:09,910 --> 00:37:14,530
Those three are stabilized
by 2/5.

530
00:37:14,530 --> 00:37:22,060
And then we have one in the
upper set, so we have one at

531
00:37:22,060 --> 00:37:25,020
3/5 times the octahedral
crystal

532
00:37:25,020 --> 00:37:26,630
field splitting energy.

533
00:37:26,630 --> 00:37:32,740
So this ends up with minus 3/5
times the octahedral crystal

534
00:37:32,740 --> 00:37:34,900
field splitting energy.

535
00:37:34,900 --> 00:37:39,440
And notice why a is not correct
-- you don't have the

536
00:37:39,440 --> 00:37:41,370
symbol for the octahedral
crystal

537
00:37:41,370 --> 00:37:43,810
field splitting energy.

538
00:37:43,810 --> 00:37:47,090
On a test, you need to make
sure that you remember to

539
00:37:47,090 --> 00:37:52,380
write this term, so this was
a little test so that you

540
00:37:52,380 --> 00:37:57,210
hopefully emphasize that you
want to have that there.

541
00:37:57,210 --> 00:37:59,330
All right, so that's
for this one.

542
00:37:59,330 --> 00:38:06,540
Let's look at the low spin case,
the strong field case,

543
00:38:06,540 --> 00:38:11,040
and do our crystal field
splitting energy for that.

544
00:38:11,040 --> 00:38:19,130
So in this case we're going to
have four electrons times

545
00:38:19,130 --> 00:38:23,500
minus 2/5 times the octahedral
crystal field splitting

546
00:38:23,500 --> 00:38:30,530
energy, so that's equal to minus
8/5 times the octahedral

547
00:38:30,530 --> 00:38:35,060
crystal field splitting energy,
and some books will

548
00:38:35,060 --> 00:38:41,590
also indicate, and they'll say
plus p e to indicate that

549
00:38:41,590 --> 00:38:44,380
there's pairing energy that's
associated there.

550
00:38:44,380 --> 00:38:49,570
So it's not quite as beneficial
as one might think.

551
00:38:49,570 --> 00:38:55,130
You do have a lot of electrons
in these in lower energy

552
00:38:55,130 --> 00:38:59,080
orbitals, but you did have to
pair some of them, so you had

553
00:38:59,080 --> 00:39:01,160
one, and if two of them are
paired, you can see

554
00:39:01,160 --> 00:39:02,920
sometimes 2 p e.

555
00:39:02,920 --> 00:39:05,480
So, some books will do that,
some books will not.

556
00:39:05,480 --> 00:39:09,950
So I just wanted to mention
that both are OK.

557
00:39:09,950 --> 00:39:13,270
And whether you're asked to
write that or not, and the

558
00:39:13,270 --> 00:39:16,220
question will say include the
pairing energy, so you know

559
00:39:16,220 --> 00:39:19,830
whether you're supposed to do
that or not, that there is

560
00:39:19,830 --> 00:39:22,820
that energy associated
with pairing in this

561
00:39:22,820 --> 00:39:29,370
strong field case.

562
00:39:29,370 --> 00:39:33,610
OK, so let's look at another
example, and then you should

563
00:39:33,610 --> 00:39:36,400
be all set to do these
problems for

564
00:39:36,400 --> 00:39:41,020
an octahedral field.

565
00:39:41,020 --> 00:39:44,650
So we'll take our
electrons down.

566
00:39:44,650 --> 00:39:53,690
All right, so let's at a
case of cobalt plus 2.

567
00:39:53,690 --> 00:39:59,200
So let's consider how many we're
going to put in, the

568
00:39:59,200 --> 00:40:02,880
oxidation number is?

569
00:40:02,880 --> 00:40:03,920
Plus 2.

570
00:40:03,920 --> 00:40:07,990
And what is the d count then?

571
00:40:07,990 --> 00:40:14,340
What group number?

572
00:40:14,340 --> 00:40:20,650
9 minus 2 is 7, so we're
doing a d 7 system.

573
00:40:20,650 --> 00:40:24,670
All right, so now for the weak
field case here, why don't you

574
00:40:24,670 --> 00:41:12,610
tell me what is the correct
electron distribution.

575
00:41:12,610 --> 00:41:28,280
OK, let's just take
10 more seconds.

576
00:41:28,280 --> 00:41:30,960
OK, very good.

577
00:41:30,960 --> 00:41:35,530
This is the weak field case, so
in this case, we are going

578
00:41:35,530 --> 00:41:40,240
to fill up singly all of the
orbitals, because the

579
00:41:40,240 --> 00:41:43,080
splitting energy is less than
the pairing energy, so we're

580
00:41:43,080 --> 00:41:45,870
going to put them to the fullest
extent possible before

581
00:41:45,870 --> 00:41:47,120
we have to pair.

582
00:41:47,120 --> 00:41:55,000
So we have 7, so we're going to
do 1, 2, 3, 4, 5, and now

583
00:41:55,000 --> 00:41:55,800
we have to pair.

584
00:41:55,800 --> 00:41:58,860
We have no -- we've used up
all our orbitals, so we're

585
00:41:58,860 --> 00:42:03,090
going to start pairing down here
in the lower energy, so

586
00:42:03,090 --> 00:42:06,620
that would be 6, 7.

587
00:42:06,620 --> 00:42:10,090
So we had no choice, we had to
pair them, but because it was

588
00:42:10,090 --> 00:42:12,940
a weak field, we filled
them all up singly

589
00:42:12,940 --> 00:42:15,330
first before we paired.

590
00:42:15,330 --> 00:42:18,370
So now let's consider what we're
going to do down here.

591
00:42:18,370 --> 00:42:21,330
Now remember, this is a strong
field, so there's a big

592
00:42:21,330 --> 00:42:26,350
splitting energy, so it takes
less energy to pair them than

593
00:42:26,350 --> 00:42:29,060
to reach this higher level.

594
00:42:29,060 --> 00:42:31,370
So first we put them
in the same way --

595
00:42:31,370 --> 00:42:36,640
1, 2, 3, but now that we have
the 3 in, it's better to pair

596
00:42:36,640 --> 00:42:38,280
than to bring them up here.

597
00:42:38,280 --> 00:42:42,400
So we'll do 1, 2, 3, we'll
pair them all up.

598
00:42:42,400 --> 00:42:46,290
Now it's all filled, we
have no other choice

599
00:42:46,290 --> 00:42:50,330
but to go up here.

600
00:42:50,330 --> 00:42:53,830
So, we have these very different
cases depending on

601
00:42:53,830 --> 00:42:55,250
the splitting energy.

602
00:42:55,250 --> 00:42:57,820
So what controls the
splitting energy?

603
00:42:57,820 --> 00:43:00,170
Well, what controls the
splitting energy is nature of

604
00:43:00,170 --> 00:43:02,880
the ligands, so we're going to
be talking about that next

605
00:43:02,880 --> 00:43:06,140
time, and you'll recognize for
certain kinds of ligands

606
00:43:06,140 --> 00:43:08,770
you're going to have a strong
field, and other kinds you'll

607
00:43:08,770 --> 00:43:10,070
have a weak field.

608
00:43:10,070 --> 00:43:12,350
But right now we're not talking
about that, we're just

609
00:43:12,350 --> 00:43:15,220
showing those two
possibilities.

610
00:43:15,220 --> 00:43:18,765
So, for this system, is this
going to be a high spin or a

611
00:43:18,765 --> 00:43:21,180
low spin system?

612
00:43:21,180 --> 00:43:24,870
So, this will be high spin,
because we have the maximum

613
00:43:24,870 --> 00:43:27,570
amount of unpaired electrons.

614
00:43:27,570 --> 00:43:30,810
And over here we're going to
have a low spin system.

615
00:43:30,810 --> 00:43:34,210
We have the minimum
number possible of

616
00:43:34,210 --> 00:43:36,750
the unpaired electrons.

617
00:43:36,750 --> 00:43:42,790
All right, so let's finish this
up now, and do our d n

618
00:43:42,790 --> 00:43:45,440
electron configurations
and our crystal

619
00:43:45,440 --> 00:43:47,980
field splitting energies.

620
00:43:47,980 --> 00:43:52,130
So, for this case, we're going
to have in our t 2

621
00:43:52,130 --> 00:43:55,010
g system, how many?

622
00:43:55,010 --> 00:43:56,220
5.

623
00:43:56,220 --> 00:43:58,520
And in e g?

624
00:43:58,520 --> 00:44:00,140
2.

625
00:44:00,140 --> 00:44:05,680
And for our splitting energy,
we have 5 times minus 2/5

626
00:44:05,680 --> 00:44:10,290
times the octahedral crystal
field splitting energy plus 2

627
00:44:10,290 --> 00:44:16,030
times plus 3/5, and what does
that end up equaling?

628
00:44:16,030 --> 00:44:20,810
Minus 4/5 times the
octahedral crystal

629
00:44:20,810 --> 00:44:22,320
field splitting energy.

630
00:44:22,320 --> 00:44:26,760
And we could also optionally put
2 p e because we have two

631
00:44:26,760 --> 00:44:28,230
sets paired.

632
00:44:28,230 --> 00:44:31,360
All right, so let's look at
our strong field system.

633
00:44:31,360 --> 00:44:35,050
How many do we have
in our e 2 g set?

634
00:44:35,050 --> 00:44:36,080
6.

635
00:44:36,080 --> 00:44:39,180
What about e g?

636
00:44:39,180 --> 00:44:40,360
1.

637
00:44:40,360 --> 00:44:44,270
And for our splitting energy
then, we have 6 times minus

638
00:44:44,270 --> 00:44:48,650
2/5 times the octahedral crystal
field splitting energy

639
00:44:48,650 --> 00:44:55,900
plus 1 times 3/5, and what
is that going to equal?

640
00:44:55,900 --> 00:44:57,890
Minus what?

641
00:44:57,890 --> 00:44:59,500
9/5.

642
00:44:59,500 --> 00:45:05,740
And how many pairing energies?
three pairing energies, great.

643
00:45:05,740 --> 00:45:07,470
I think you have
that part down.

644
00:45:07,470 --> 00:45:09,630
Next time we get more
complicated, we're going to

645
00:45:09,630 --> 00:45:12,010
talk about types of ligands,
we're going to talk about

646
00:45:12,010 --> 00:45:16,110
tetrahedral, we're going to talk
about square planar, and

647
00:45:16,110 --> 00:45:20,300
that's, of course, after
the exam on Wednesday.

648
00:45:20,300 --> 00:45:23,470
So, good luck, everyone, with
the exam on Wednesday.