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PROFESSOR: -- that this is not
a quick clicker question, so

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00:00:23,575 --> 00:00:26,090
you actually need to maybe write
something down to figure

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00:00:26,090 --> 00:00:26,740
out the answer.

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00:00:26,740 --> 00:00:30,520
So if you haven't clicked in
yet, or if you want to change

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00:00:30,520 --> 00:00:33,050
your answer, keep in mind that
you might need to jot down,

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00:00:33,050 --> 00:00:36,420
for example, a Lewis structure
before you can answer this

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00:00:36,420 --> 00:00:59,900
question.

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00:00:59,900 --> 00:01:01,480
-- and get in your final answer

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00:01:01,480 --> 00:01:03,030
to the clicker question.

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00:01:03,030 --> 00:01:05,970
For those of you just walking
in now, you might not have a

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00:01:05,970 --> 00:01:08,770
chance to get all of the thought
process that you need

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00:01:08,770 --> 00:01:11,260
in on this clicker question,
because it is based on a Lewis

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00:01:11,260 --> 00:01:13,700
structure, so we will
go over it.

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00:01:13,700 --> 00:01:16,880
But for those of you that have
been here for 30 seconds or

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00:01:16,880 --> 00:01:19,480
longer, see if you can get
the right answer in here.

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00:01:19,480 --> 00:01:24,450
All right, so OK, it looks
like we have a very mixed

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response in terms of
the answer to the

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00:01:26,380 --> 00:01:28,030
clicker question today.

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00:01:28,030 --> 00:01:30,240
Raise your hand if you didn't
have time to figure out the

27
00:01:30,240 --> 00:01:32,360
Lewis structure.

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00:01:32,360 --> 00:01:34,740
OK, so that accounts
for some of you.

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00:01:34,740 --> 00:01:37,160
Let's go over the correct
answer this question.

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00:01:37,160 --> 00:01:39,000
So, who got the right answer --

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00:01:39,000 --> 00:01:40,890
31% of us.

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This is not the kind of
percentages we're looking for,

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00:01:44,810 --> 00:01:46,260
so let's go over this.

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00:01:46,260 --> 00:01:52,150
In class on Monday, we did go
over the geometries, and the

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00:01:52,150 --> 00:01:55,530
geometries themselves are very
straightforward, once you know

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00:01:55,530 --> 00:01:58,400
what the Lewis structure is, but
remember, you can't just

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00:01:58,400 --> 00:02:00,300
always look at a molecule
and automatically

38
00:02:00,300 --> 00:02:01,060
know the Lewis structure.

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00:02:01,060 --> 00:02:02,960
We actually need to think about
those valence electrons.

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00:02:02,960 --> 00:02:08,500
So, here we're dealing with
selenium hydride, so s e h 2.

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00:02:08,500 --> 00:02:12,020
I told you that there's 6
valence electrons in selenium,

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00:02:12,020 --> 00:02:16,310
so we have 6 there, plus 1
for each of the hydrogen.

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00:02:16,310 --> 00:02:19,420
So what we should have is
8 valence electrons

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00:02:19,420 --> 00:02:20,980
in our Lewis structure.

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00:02:20,980 --> 00:02:25,050
How many electrons do we need
to have full valence shells?

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00:02:25,050 --> 00:02:26,470
STUDENT: [INAUDIBLE]

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00:02:26,470 --> 00:02:27,010
PROFESSOR: 12, that's right.

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00:02:27,010 --> 00:02:32,120
We need 8 plus 4 is 12
for full shells.

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00:02:32,120 --> 00:02:41,300
That means that we need 12
minus 8, or 4 bonding

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00:02:41,300 --> 00:02:44,870
electrons in our structure.

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00:02:44,870 --> 00:02:46,990
So I tried to give you one that
you could draw pretty

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00:02:46,990 --> 00:02:49,170
quickly, it just has
hydrogens in It.

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00:02:49,170 --> 00:02:52,550
So we have s e h 2.

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We can do our 4 bonding
electrons.

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00:02:55,600 --> 00:02:57,660
How many valence electrons
do we have left?

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00:02:57,660 --> 00:02:59,500
STUDENT: [INAUDIBLE]

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00:02:59,500 --> 00:03:00,220
PROFESSOR: 4, that's right.

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So, we need to fill our octet
for selenium, so 1, 2, 3, 4.

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00:03:04,740 --> 00:03:07,520
So, this is our Lewis structure
here, hopefully you

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00:03:07,520 --> 00:03:09,600
can see why it's not linear.

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If it were linear, which 32% of
you seem have thought, that

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would have meant that our Lewis
structure had no lone

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pairs in it, right, and
that's not the case.

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We have two lone pairs, so if
we thought about what the

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bonds were everywhere,
it would be 109 .

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5, but it's bent because we're
only looking at the bonds,

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we're not counting the Lewis
structures in naming our

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geometry, but they do
affect the angles.

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And it turns out that it's
actually less than 109 .

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00:03:37,600 --> 00:03:40,540
5, because those lone pairs
are pushing the bonds even

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00:03:40,540 --> 00:03:41,700
further away.

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00:03:41,700 --> 00:03:44,590
So, does this make sense to
everyone if you think

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about it this way?

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00:03:47,450 --> 00:03:48,310
Pretty much, okay.

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00:03:48,310 --> 00:03:52,570
So, we'll try another clicker
question like this later.

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Some of these questions that
look very straightforward just

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naming the geometry, you have
to remember to do the first

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step before you jump in and
go ahead with a naming.

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00:04:00,580 --> 00:04:02,770
So you'll got plenty of practice
with this on your

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problem-set if you
haven't already.

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00:04:04,340 --> 00:04:06,050
All right.

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00:04:06,050 --> 00:04:09,030
So before we start in with
today's notes, I do want to

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mention that this morning
the Nobel Prize in

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chemistry was announced.

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This is an exciting week in
science in general because we

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got to hear another
Nobel Prize every

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00:04:19,290 --> 00:04:21,300
morning pretty much.

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So, let's settle down for a
second and start listening.

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All right.

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00:04:26,230 --> 00:04:29,400
So, today we're going to be
talking about molecular

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orbital theory, but first I
wanted to just mention, in

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case some of you didn't hear
what the Nobel Prize was this

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morning, and this was in
chemistry, it went to three

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00:04:37,230 --> 00:04:38,430
different chemists.

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00:04:38,430 --> 00:04:47,600
Osamu Shimomura, who's a
Japanese chemist, and then

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00:04:47,600 --> 00:04:50,970
Martin Chalfi who's at Columbia,
and Robert Chen

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00:04:50,970 --> 00:04:52,880
who's at U. C. San Diego.

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00:04:52,880 --> 00:04:55,670
The three of these chemists
split the Nobel Prize this

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00:04:55,670 --> 00:04:59,490
morning for their discovery
and/or their application of

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using green fluorescent
protein, which

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is also called GFP.

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How many of you have heard
of GFP before?

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00:05:05,970 --> 00:05:06,460
Oh, that's so great.

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00:05:06,460 --> 00:05:07,070
OK.

105
00:05:07,070 --> 00:05:08,660
Many of you have heard of GFP.

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For some of you that haven't
I'll just say that it's a

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protein, it's 238 amino acids,
which means that it's about

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1,000, actually more than 1,000
atoms in size, and this

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protein is fluorescent.

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00:05:21,600 --> 00:05:24,960
The protein was first discovered
and first isolated

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from this jellyfish here.

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00:05:26,760 --> 00:05:30,890
This was done by Shimomura,
and he did this in

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00:05:30,890 --> 00:05:32,090
the 60's and 70's.

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00:05:32,090 --> 00:05:35,340
He actually recognized and, of
course, many people recognized

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that this jellyfish was
fluorescent, and he isolated

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00:05:38,080 --> 00:05:41,020
the actual protein, and
determined and proved that

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00:05:41,020 --> 00:05:43,620
this protein was sufficient to
cause this fluorescence.

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So, in terms of thinking about
applications of why it's so

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00:05:47,140 --> 00:05:49,360
exciting that you have this
fluorescent protein, other

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00:05:49,360 --> 00:05:51,670
than it's always really fun
to look at things that are

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00:05:51,670 --> 00:05:54,810
fluorescent, we can think about
in terms of biology why

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00:05:54,810 --> 00:05:58,080
it's so exciting, you can
actually tag this protein to

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00:05:58,080 --> 00:06:00,850
any other protein that you're
studying and now you have a

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00:06:00,850 --> 00:06:02,640
visual handle on what's
going on.

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So, for example, if you were
interested in some protein

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00:06:05,340 --> 00:06:08,150
involved in cancer, you
could tag it with GFP.

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00:06:08,150 --> 00:06:11,240
You could watch where it
localizes in the cell, there

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are fluorescent assays you could
use to determine what

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00:06:13,440 --> 00:06:15,400
other proteins it
interacts with.

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You could see, for example,
when it's expressed in a

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cancer cell, and where
it's expressed.

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There are all sorts of things
you can do once you can

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visualize something
with fluorescence.

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The reason it is so exciting
that it's a protein, and it's

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a protein, this is the structure
here, it's a ribbon

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structure so you can kind of see
what it looks like, it's

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made up of all natural
amino acids.

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00:06:35,150 --> 00:06:37,840
So this means we can code for
it in DNA, you don't have to

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00:06:37,840 --> 00:06:40,100
worry how am I going to
get into the cell.

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00:06:40,100 --> 00:06:43,370
All you have to do is mutate
the DNA, which is very

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00:06:43,370 --> 00:06:46,760
straightforward to do in
molecular biology, and now you

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00:06:46,760 --> 00:06:50,070
can tag absolutely any protein
that you're interested in.

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00:06:50,070 --> 00:06:53,150
So, as I said, this was first
discovered and isolated from

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00:06:53,150 --> 00:06:53,890
the jellyfish.

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00:06:53,890 --> 00:06:56,750
This was done by Shimomura --
that was kind of the first

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00:06:56,750 --> 00:07:00,550
step in this process of having
it become such a useful tool.

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And then, many years later,
not until 1994 did Martin

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00:07:04,530 --> 00:07:08,810
Chalfi, at Columbia, show that
yes, I can, in fact, take the

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DNA and put it into a different
organism, and he put

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it into e coli, a bacteria.

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00:07:13,390 --> 00:07:16,200
And what he could show was that
it could be expressed,

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00:07:16,200 --> 00:07:19,560
this is a picture from his 1994
science paper, in that e

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00:07:19,560 --> 00:07:22,160
coli, and it is going
to fluoresce green.

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Now, the first application
tends to not be quite as

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exciting as, for example, all
the other organisms people

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00:07:27,060 --> 00:07:29,820
have put it in since then --
you can have flies, you see

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00:07:29,820 --> 00:07:32,830
transgenic mice that are glowing
green with this GFP.

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Of course, that's not the useful
application for it,

159
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it's more of a proof of
principle, but it does show

160
00:07:38,610 --> 00:07:42,240
you that you can put it in for
studies in any organisms.

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And the field was really
pushed forward by the

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00:07:45,160 --> 00:07:49,550
discoveries of Robert Chen at UC
San Diego, and what he did

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00:07:49,550 --> 00:07:53,370
was he actually figured out how
it was that this protein

164
00:07:53,370 --> 00:07:56,030
fluoresced, what caused the
actual fluorescence.

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00:07:56,030 --> 00:08:00,050
And once he did that, both he
and many other scientists,

166
00:08:00,050 --> 00:08:02,250
could then, once they understood
what caused the

167
00:08:02,250 --> 00:08:05,450
fluorescence, make little
changes to the actual protein,

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00:08:05,450 --> 00:08:07,300
and tune what the properties
of that

169
00:08:07,300 --> 00:08:08,890
fluorescent protein were.

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00:08:08,890 --> 00:08:11,630
So now, for example, there are
a whole range, just a whole

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00:08:11,630 --> 00:08:14,050
rainbow of fluorescent proteins
that can be used.

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00:08:14,050 --> 00:08:17,500
And I'm sure you can imagine
that if you want to label onw

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00:08:17,500 --> 00:08:20,250
protein green and one red and
one yellow, now you can start

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00:08:20,250 --> 00:08:23,630
looking at really complex
biological processes.

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00:08:23,630 --> 00:08:25,910
So, it's pretty rare that
chemistry makes

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00:08:25,910 --> 00:08:26,630
the every day news.

177
00:08:26,630 --> 00:08:29,470
So hopefully you'll all look
in the normal papers today,

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00:08:29,470 --> 00:08:31,550
not just the scientific
journals, and get to read

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00:08:31,550 --> 00:08:32,570
something about chemistry.

180
00:08:32,570 --> 00:08:35,430
It's always fun to see how its
described in The New York

181
00:08:35,430 --> 00:08:37,540
Times or in The Boston Globe.

182
00:08:37,540 --> 00:08:39,520
The other thing I wanted to
mention and I'm not sure if

183
00:08:39,520 --> 00:08:41,020
the exhibit's still there.

184
00:08:41,020 --> 00:08:43,340
But there was an exhibit of
jellyfish, I know at least

185
00:08:43,340 --> 00:08:46,760
until last year, at the Boston
Museum of Science, and all of

186
00:08:46,760 --> 00:08:48,370
you guys can get
in there free.

187
00:08:48,370 --> 00:08:50,400
And it's neat to see the glowing
jellyfish and think

188
00:08:50,400 --> 00:08:53,020
about the fluorescent protein
that's in them.

189
00:08:53,020 --> 00:08:55,610
So, I encourage you to do that
the next time you have some

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00:08:55,610 --> 00:09:00,940
free time on your hands, maybe
at IAP or some time like that.

191
00:09:00,940 --> 00:09:03,680
All right, so let's move
into today's notes.

192
00:09:03,680 --> 00:09:06,480
Today we're talking about
molecular orbital theory.

193
00:09:06,480 --> 00:09:10,510
This is a shift, this is a new
topic that we're starting.

194
00:09:10,510 --> 00:09:13,990
So far we've exclusively been
using Lewis structures any

195
00:09:13,990 --> 00:09:17,170
time we've tried to describe
bonding within molecules.

196
00:09:17,170 --> 00:09:19,880
Lewis structures are really
useful, we use them all the

197
00:09:19,880 --> 00:09:21,080
time in chemistry.

198
00:09:21,080 --> 00:09:23,550
And they're useful because,
first of all, they're easy to

199
00:09:23,550 --> 00:09:27,320
depict, they're easy to draw --
relatively easy once we get

200
00:09:27,320 --> 00:09:28,550
all the rules down.

201
00:09:28,550 --> 00:09:31,730
And also they're accurate
over 90% of the time.

202
00:09:31,730 --> 00:09:34,570
But they're not accurate all the
time in predicting bonding

203
00:09:34,570 --> 00:09:37,970
within molecules, and the reason
for this is because

204
00:09:37,970 --> 00:09:39,710
Lewis structures are
not, in fact,

205
00:09:39,710 --> 00:09:41,720
based on quantum mechanics.

206
00:09:41,720 --> 00:09:45,410
So, molecular orbital theory, on
the other hand, is based on

207
00:09:45,410 --> 00:09:46,640
quantum mechanics.

208
00:09:46,640 --> 00:09:49,760
And specifically, MO theory
is the quantum mechanical

209
00:09:49,760 --> 00:09:53,780
description of wave functions
within molecules.

210
00:09:53,780 --> 00:09:56,280
So, saying wave functions within
molecules might sound a

211
00:09:56,280 --> 00:09:59,480
little confusing, but remember
we spent a lot of time talking

212
00:09:59,480 --> 00:10:03,040
about wave functions within
atoms, and we know how to

213
00:10:03,040 --> 00:10:05,320
describe that, we know that a
wave function just means an

214
00:10:05,320 --> 00:10:06,000
atomic orbital.

215
00:10:06,000 --> 00:10:09,210
It's the same thing with
molecules -- a molecular wave

216
00:10:09,210 --> 00:10:11,370
function just means a
molecular orbital.

217
00:10:11,370 --> 00:10:13,600
So, we'll start today talking
about the two kinds of

218
00:10:13,600 --> 00:10:15,910
molecular orbitals, we can
talk about bonding or

219
00:10:15,910 --> 00:10:17,580
anti-bonding orbitals.

220
00:10:17,580 --> 00:10:20,250
Then we're going to actually
use MO theory to describe

221
00:10:20,250 --> 00:10:22,830
bonding within these molecules,
and we'll start

222
00:10:22,830 --> 00:10:25,740
with homonuclear diatomic
molecules.

223
00:10:25,740 --> 00:10:30,070
Diatomic mean it's di atomic,
it's made up of two atoms, and

224
00:10:30,070 --> 00:10:33,270
homonuclear means that those two
are the same atoms. Then

225
00:10:33,270 --> 00:10:35,760
at the end, we'll look at an
example with a heteronuclear

226
00:10:35,760 --> 00:10:37,330
diatomic molecules.

227
00:10:37,330 --> 00:10:40,480
So, again, the same thing, but
now two different atoms.

228
00:10:40,480 --> 00:10:43,560
So, I will point out, in terms
of MO theory, because it

229
00:10:43,560 --> 00:10:46,330
rigorously does take into
account quantum mechanics, it

230
00:10:46,330 --> 00:10:48,650
starts to become complicated
once we go

231
00:10:48,650 --> 00:10:50,830
beyond diatomic molecules.

232
00:10:50,830 --> 00:10:53,930
So we're going to limit in our
discussion in 511-1 for

233
00:10:53,930 --> 00:10:56,760
molecular orbital theory
to diatomic molecules.

234
00:10:56,760 --> 00:10:59,220
However, on Friday we will use a
different approach so we can

235
00:10:59,220 --> 00:11:02,360
talk about bonding within atoms
that have more than two

236
00:11:02,360 --> 00:11:06,920
atoms, molecules with
more than two atoms.

237
00:11:06,920 --> 00:11:09,300
All right, so one thing that I
first want to point out about

238
00:11:09,300 --> 00:11:11,730
MO theory that is a big
difference from Lewis

239
00:11:11,730 --> 00:11:15,350
structures, is that in MO theory
valence electrons are

240
00:11:15,350 --> 00:11:18,710
de-localized over the
entire molecule.

241
00:11:18,710 --> 00:11:21,150
So, when we talked about Lewis
structures, we actually

242
00:11:21,150 --> 00:11:24,330
assigned electrons to individual
atoms or to

243
00:11:24,330 --> 00:11:25,670
individual bonds.

244
00:11:25,670 --> 00:11:28,280
Whereas in molecular orbital
theory, what I'm telling you

245
00:11:28,280 --> 00:11:32,060
is instead we understand that
the electrons are spread all

246
00:11:32,060 --> 00:11:34,780
over the molecule, they're not
just associated with a single

247
00:11:34,780 --> 00:11:37,260
atom or a single bond.

248
00:11:37,260 --> 00:11:40,270
So specifically, what we do
associate them instead is

249
00:11:40,270 --> 00:11:43,970
within molecular orbitals, and
what we say is that they can

250
00:11:43,970 --> 00:11:45,770
be either in bonding or
anti-bonding orbitals.

251
00:11:45,770 --> 00:11:49,210
And again, I want to point out
that a molecular orbital, we

252
00:11:49,210 --> 00:11:50,740
can also call that
a wave function,

253
00:11:50,740 --> 00:11:51,920
they're the same thing.

254
00:11:51,920 --> 00:11:55,370
And these orbitals arise from
the combination of individual

255
00:11:55,370 --> 00:11:55,910
atomic orbital.

256
00:11:55,910 --> 00:11:59,310
So, if we have two atomic
orbitals coming together from

257
00:11:59,310 --> 00:12:02,230
two different atoms and they
combine, what we end up

258
00:12:02,230 --> 00:12:04,060
forming is a molecular
orbital.

259
00:12:04,060 --> 00:12:06,460
The reason that we can talk
about this is remember that

260
00:12:06,460 --> 00:12:08,490
we're talking about wave
functions, we're talking about

261
00:12:08,490 --> 00:12:11,420
waves, so we can have
constructive interference in

262
00:12:11,420 --> 00:12:16,300
which two different orbitals can
constructively interfere,

263
00:12:16,300 --> 00:12:18,630
we can also have destructive
interference.

264
00:12:18,630 --> 00:12:20,970
So, we'll start by taking
a look at constructive

265
00:12:20,970 --> 00:12:24,030
interference, and another way to
explain this is just to say

266
00:12:24,030 --> 00:12:26,540
again, molecular orbitals
are a linear

267
00:12:26,540 --> 00:12:28,120
combination of atomic orbitals.

268
00:12:28,120 --> 00:12:31,970
So, let's start our discussion
of a bonding orbital.

269
00:12:31,970 --> 00:12:34,730
Our simplest case that we can
look at would be if we had two

270
00:12:34,730 --> 00:12:36,620
1 s orbitals coming together.

271
00:12:36,620 --> 00:12:39,160
So let's say, for example,
in a hydrogen atom.

272
00:12:39,160 --> 00:12:42,800
So in hydrogen atom a, I'll
depict that here where the

273
00:12:42,800 --> 00:12:46,500
nucleus is this dot, and then
the circle is what I'm

274
00:12:46,500 --> 00:12:49,070
depicting as the
wave function.

275
00:12:49,070 --> 00:12:51,740
It makes sense to draw the wave
function as a circle,

276
00:12:51,740 --> 00:12:53,440
because we do know
that 1 s orbitals

277
00:12:53,440 --> 00:12:55,220
are spherically symmetric.

278
00:12:55,220 --> 00:12:58,180
So, we can say that a circle is
a good approximation for a

279
00:12:58,180 --> 00:12:59,810
1 s wave function.

280
00:12:59,810 --> 00:13:02,950
Similarly, with the second
hydrogen atom, we've got the

281
00:13:02,950 --> 00:13:06,710
nucleus in the middle, and the 1
s b wave function around it.

282
00:13:06,710 --> 00:13:08,490
So these are atomic orbitals.

283
00:13:08,490 --> 00:13:11,040
What we're going to do in
forming a molecule is just

284
00:13:11,040 --> 00:13:15,650
bring these two orbitals close
together such that now we have

285
00:13:15,650 --> 00:13:18,920
their nucleus, the two nuclei,
at a distance apart that's

286
00:13:18,920 --> 00:13:21,360
equal to the bond length.

287
00:13:21,360 --> 00:13:23,970
And what we end up forming is
a molecular orbital, because

288
00:13:23,970 --> 00:13:27,610
as we bring these two atomic
orbitals close together, the

289
00:13:27,610 --> 00:13:30,500
part between them, that wave
function, constructively

290
00:13:30,500 --> 00:13:33,730
interferes such that in our
molecular orbital, we actually

291
00:13:33,730 --> 00:13:39,440
have a lot of wave function
in between the two nuclei.

292
00:13:39,440 --> 00:13:42,200
So we can go ahead and name our
molecular orbital, just

293
00:13:42,200 --> 00:13:45,270
like we know how to name
our atomic orbitals.

294
00:13:45,270 --> 00:13:47,710
And I'm going to name
this sigma 1 s.

295
00:13:47,710 --> 00:13:50,530
The 1 s just comes from the
fact that the molecular

296
00:13:50,530 --> 00:13:53,920
orbital is a combination of
two 1 s atomic orbitals.

297
00:13:53,920 --> 00:13:56,450
And the sigma tells us something
about the symmetry

298
00:13:56,450 --> 00:13:59,140
of this molecular orbital,
specifically that it's

299
00:13:59,140 --> 00:14:01,770
cylindrically symmetric
about the bond axis.

300
00:14:01,770 --> 00:14:05,340
So that is the bond axis -- it's
just the axis between the

301
00:14:05,340 --> 00:14:06,470
two nuclei.

302
00:14:06,470 --> 00:14:09,340
Sometimes it's also called
the internuclear axis.

303
00:14:09,340 --> 00:14:12,590
So any time you have two atoms
bonding, the bond axis is just

304
00:14:12,590 --> 00:14:15,550
the axis that they're
bonding along.

305
00:14:15,550 --> 00:14:18,520
Another thing I want to point
out about every sigma orbital

306
00:14:18,520 --> 00:14:21,925
that you see, and it will make
more sense when we contrast it

307
00:14:21,925 --> 00:14:23,050
with pi orbitals later.

308
00:14:23,050 --> 00:14:26,610
But in sigma orbitals, you have
no nodal planes along the

309
00:14:26,610 --> 00:14:29,480
bond axis, so if we had a nodal
plane here, we'd see an

310
00:14:29,480 --> 00:14:31,820
area where the wave function
was equal to zero.

311
00:14:31,820 --> 00:14:32,780
We don't see that.

312
00:14:32,780 --> 00:14:35,110
It will make more sense when we
can show you one where it

313
00:14:35,110 --> 00:14:36,400
does have that area.

314
00:14:36,400 --> 00:14:40,210
But keep in mind sigma orbitals
have no nodal planes

315
00:14:40,210 --> 00:14:41,440
along the bond axis.

316
00:14:41,440 --> 00:14:43,160
All right.

317
00:14:43,160 --> 00:14:45,250
So, let's look at this in
another way, sometimes it's

318
00:14:45,250 --> 00:14:47,040
hard to picture these
waves combining.

319
00:14:47,040 --> 00:14:50,200
So let's think of them a little
bit more by graphing

320
00:14:50,200 --> 00:14:53,210
the amplitude of the wave, and
seeing how we can have this

321
00:14:53,210 --> 00:14:54,710
constructive interference.

322
00:14:54,710 --> 00:14:57,550
So again, if we think of a graph
of the wave function, we

323
00:14:57,550 --> 00:15:01,180
had the wave function is at
its highest amplitude when

324
00:15:01,180 --> 00:15:03,320
it's lined up with the nucleus,
and then as we got

325
00:15:03,320 --> 00:15:07,300
further away from the nucleus,
the amplitude of the wave

326
00:15:07,300 --> 00:15:11,700
function ends up tapering off
until -- it never hits zero

327
00:15:11,700 --> 00:15:13,340
exactly, but it goes
down very low.

328
00:15:13,340 --> 00:15:18,030
So we can draw that for 1 s a,
we can also draw it for 1 s b,

329
00:15:18,030 --> 00:15:20,250
and what I'm saying for the
molecular wave function is

330
00:15:20,250 --> 00:15:22,820
that we have the interference
between the two, and we have a

331
00:15:22,820 --> 00:15:25,870
constructive interference, so
we end up adding these two

332
00:15:25,870 --> 00:15:27,940
wave functions together.

333
00:15:27,940 --> 00:15:30,280
So, we're talking about wave
functions and we know that

334
00:15:30,280 --> 00:15:35,140
means orbitals, but this is --
probably the better way to

335
00:15:35,140 --> 00:15:36,460
think about is the physical

336
00:15:36,460 --> 00:15:38,820
interpretation of the wave function.

337
00:15:38,820 --> 00:15:41,720
So what is the wave function
squared going to be equal to?

338
00:15:41,720 --> 00:15:42,342
STUDENT: [INAUDIBLE]

339
00:15:42,342 --> 00:15:46,260
PROFESSOR: Probability
density, yes.

340
00:15:46,260 --> 00:15:49,010
Probability density of finding
an electron within that

341
00:15:49,010 --> 00:15:52,250
molecule in some given volume.

342
00:15:52,250 --> 00:15:54,630
So let's think about that
instead, let's think about

343
00:15:54,630 --> 00:15:55,910
probability density.

344
00:15:55,910 --> 00:15:58,770
So if we're talking about
probability density that's the

345
00:15:58,770 --> 00:16:00,450
wave function squared.

346
00:16:00,450 --> 00:16:03,290
But now we're talking not about
an atomic wave function,

347
00:16:03,290 --> 00:16:05,500
we're talking about a molecular
wave function.

348
00:16:05,500 --> 00:16:08,650
So to talk about it's squared,
we're going to say it's sigma

349
00:16:08,650 --> 00:16:11,580
1 s squared.

350
00:16:11,580 --> 00:16:13,890
Oh, and actually before you skip
your page in the notes, I

351
00:16:13,890 --> 00:16:17,090
realized I should write out for
you what the addition is

352
00:16:17,090 --> 00:16:18,190
to start with.

353
00:16:18,190 --> 00:16:23,350
So, when we're combining two
waves, what we have is 1 s a

354
00:16:23,350 --> 00:16:26,810
that we're adding together
with 1 s for

355
00:16:26,810 --> 00:16:29,150
b, the second atom.

356
00:16:29,150 --> 00:16:32,450
And what we end up for
our molecular wave

357
00:16:32,450 --> 00:16:34,740
function is sigma 1 s.

358
00:16:34,740 --> 00:16:38,020
So this is what we call
our molecular orbital.

359
00:16:38,020 --> 00:16:41,780
All right, so that will now
allow you to turn the page, I

360
00:16:41,780 --> 00:16:44,880
think, and we can take a look
at the probability.

361
00:16:44,880 --> 00:16:48,500
So the probability again,
that's just the orbital

362
00:16:48,500 --> 00:16:50,870
squared, the wave function
squared.

363
00:16:50,870 --> 00:16:54,680
So when we write that out, we
just write sigma 1 s squared,

364
00:16:54,680 --> 00:16:57,350
or we can break it up into its
individual parts, there's no

365
00:16:57,350 --> 00:16:59,080
reason we can't do
that as well.

366
00:16:59,080 --> 00:17:04,320
So just to say that it's 1 s
squared plus 1 s b, all of

367
00:17:04,320 --> 00:17:07,030
that together squared.

368
00:17:07,030 --> 00:17:09,910
So if we write out every term
individually, what we end up

369
00:17:09,910 --> 00:17:12,940
with is essentially just the
probability density for the

370
00:17:12,940 --> 00:17:15,740
first atom, then the probability
density for the

371
00:17:15,740 --> 00:17:19,900
second atom, and then we have
this last term here, and this

372
00:17:19,900 --> 00:17:23,090
is what ends up being the
interference term.

373
00:17:23,090 --> 00:17:25,990
So in this case where we're
adding it together, this is

374
00:17:25,990 --> 00:17:27,970
going to be constructive
interference.

375
00:17:27,970 --> 00:17:31,250
So in this case the cross term
represents constructive

376
00:17:31,250 --> 00:17:37,250
interference between the two
1 s atomic wave functions.

377
00:17:37,250 --> 00:17:38,580
And this again is what
we're going to

378
00:17:38,580 --> 00:17:41,710
call a bonding orbital.

379
00:17:41,710 --> 00:17:44,550
So it can often make a lot more
sense if we think about

380
00:17:44,550 --> 00:17:45,900
things in terms of energy.

381
00:17:45,900 --> 00:17:49,010
We've been discussing energy
diagrams a lot in this class,

382
00:17:49,010 --> 00:17:51,300
it's a very good way to
visualize exactly

383
00:17:51,300 --> 00:17:52,510
what's going on.

384
00:17:52,510 --> 00:17:55,090
So, let's think of the energy
of interaction when we're

385
00:17:55,090 --> 00:17:58,800
comparing atomic orbitals to
molecular bonding orbitals.

386
00:17:58,800 --> 00:18:01,510
And what you find is when you
have a bonding orbital, the

387
00:18:01,510 --> 00:18:05,480
energy decreases compared
to the atomic orbitals.

388
00:18:05,480 --> 00:18:08,890
So you can see here in this
slide we have the atomic

389
00:18:08,890 --> 00:18:12,370
orbitals for the two hydrogen
atoms, each of them have one

390
00:18:12,370 --> 00:18:16,730
electron in them, hydrogen has
one electron in a 1 s orbital.

391
00:18:16,730 --> 00:18:18,650
So, if we look at the molecular
orbital, that's

392
00:18:18,650 --> 00:18:22,050
actually going to be lower in
energy than either of the two

393
00:18:22,050 --> 00:18:23,080
atomic orbitals.

394
00:18:23,080 --> 00:18:26,160
So it's going to be favorable
for the electrons instead to

395
00:18:26,160 --> 00:18:29,690
go to that lower energy
state and be within

396
00:18:29,690 --> 00:18:31,170
the molecular orbital.

397
00:18:31,170 --> 00:18:35,700
So, let's draw in our electrons
there, so we have

398
00:18:35,700 --> 00:18:40,080
our two electrons now in
the molecular orbital.

399
00:18:40,080 --> 00:18:42,180
So any time that you're drawing
these molecular

400
00:18:42,180 --> 00:18:45,070
orbital diagrams, you want to
keep in mind that the number

401
00:18:45,070 --> 00:18:48,090
of electrons that you have in
atomic orbitals, you need to

402
00:18:48,090 --> 00:18:49,620
add those together
and put that many

403
00:18:49,620 --> 00:18:51,640
electrons into your molecule.

404
00:18:51,640 --> 00:18:54,890
Right, we had one from each
atom, so that means we need a

405
00:18:54,890 --> 00:18:57,290
total of two in our
molecular orbital.

406
00:18:57,290 --> 00:18:59,740
And what you can see directly
from looking at this energy

407
00:18:59,740 --> 00:19:02,780
level diagram, is that the
molecule that we have is now

408
00:19:02,780 --> 00:19:05,650
more stable in the individual
atoms. That makes sense

409
00:19:05,650 --> 00:19:07,710
because we're lower in energy,
the electrons are

410
00:19:07,710 --> 00:19:09,810
now lower in energy.

411
00:19:09,810 --> 00:19:13,450
So that's the idea of a bonding
molecular orbital.

412
00:19:13,450 --> 00:19:16,100
Since we're talking about wave
functions, since we're talking

413
00:19:16,100 --> 00:19:19,110
about the properties of waves,
we don't only have

414
00:19:19,110 --> 00:19:21,780
constructive interference, we
can also imagine a case where

415
00:19:21,780 --> 00:19:24,130
we would have destructive
interference.

416
00:19:24,130 --> 00:19:27,090
Just like we see destructive
interference with water waves

417
00:19:27,090 --> 00:19:29,410
or with light waves, we can
also see destructive

418
00:19:29,410 --> 00:19:30,870
interference with orbitals.

419
00:19:30,870 --> 00:19:33,420
So, let's think about what
that would look like.

420
00:19:33,420 --> 00:19:37,640
So in this case we would have
1 s a and 1 s b, and instead

421
00:19:37,640 --> 00:19:41,380
we would subtract one from the
other, and what we would see

422
00:19:41,380 --> 00:19:44,850
is that instead of having
additional, more wave function

423
00:19:44,850 --> 00:19:47,370
in the middle here, we've
actually cancelled out the

424
00:19:47,370 --> 00:19:50,180
wave function and we
end up with a node.

425
00:19:50,180 --> 00:19:53,100
So we can also name this
orbital, and this orbital

426
00:19:53,100 --> 00:19:56,320
we're going to call
sigma 1 s star.

427
00:19:56,320 --> 00:20:00,210
So if we name this orbital,
this is an anti-bonding

428
00:20:00,210 --> 00:20:00,880
molecular orbital.

429
00:20:00,880 --> 00:20:03,160
So we had bonding and now
we're talking about

430
00:20:03,160 --> 00:20:04,520
anti-bonding.

431
00:20:04,520 --> 00:20:08,360
When we talk about anti-bonding,
essentially

432
00:20:08,360 --> 00:20:14,570
we're taking 1 s a and now we're
subtracting 1 s b, and

433
00:20:14,570 --> 00:20:18,520
what we end up with again is
sigma 1 s, and the important

434
00:20:18,520 --> 00:20:21,400
thing to remember is to
write this star here.

435
00:20:21,400 --> 00:20:23,110
So any time you see a
star that means an

436
00:20:23,110 --> 00:20:27,700
anti-bonding orbital.

437
00:20:27,700 --> 00:20:30,600
Again we can look at this in
terms of thinking about a

438
00:20:30,600 --> 00:20:33,510
picture this way, in terms of
drawing the wave function out

439
00:20:33,510 --> 00:20:34,730
on an axis.

440
00:20:34,730 --> 00:20:38,270
So we have 1 s a, and we're
drawing this as having a

441
00:20:38,270 --> 00:20:41,300
positive amplitude, but since
we have destructive

442
00:20:41,300 --> 00:20:45,030
interference we're going to
draw 1 s b as having the

443
00:20:45,030 --> 00:20:47,580
opposite sign, so we
have a plus and a

444
00:20:47,580 --> 00:20:49,380
minus in terms of signs.

445
00:20:49,380 --> 00:20:51,780
So that should make it very easy
to picture that this is

446
00:20:51,780 --> 00:20:53,440
being cancelled out
in the middle.

447
00:20:53,440 --> 00:20:57,600
If we overlay what the actual
molecular orbital is on top of

448
00:20:57,600 --> 00:21:00,490
it, what you see is that in
the center you end up

449
00:21:00,490 --> 00:21:03,650
cancelling out the wave
function entirely.

450
00:21:03,650 --> 00:21:08,480
So this is the 1 s star, sigma 1
s star orbital, and what you

451
00:21:08,480 --> 00:21:12,390
have in the center here is a
node, right in the center

452
00:21:12,390 --> 00:21:15,060
between the two nuclei.

453
00:21:15,060 --> 00:21:17,670
So again if we look at this
in terms of its physical

454
00:21:17,670 --> 00:21:21,170
interpretation or probability
density, what we need to do is

455
00:21:21,170 --> 00:21:22,960
square the wave function.

456
00:21:22,960 --> 00:21:27,970
So if we square sigma 1 s star,
we flip the amplitude so

457
00:21:27,970 --> 00:21:31,280
it's all positive now, but again
we still have this node

458
00:21:31,280 --> 00:21:32,400
right in the middle.

459
00:21:32,400 --> 00:21:34,680
So if we talk about the
probability density and we

460
00:21:34,680 --> 00:21:38,630
write that in, it's going to be
sigma 1 s star squared, so

461
00:21:38,630 --> 00:21:42,730
now we're talking about
1 s a minus 1 s b, all

462
00:21:42,730 --> 00:21:44,670
of that being squared.

463
00:21:44,670 --> 00:21:47,480
And again, if we write out what
all the terms are, we

464
00:21:47,480 --> 00:21:52,270
again have 1 s a squared plus
1 s b squared, but now what

465
00:21:52,270 --> 00:21:54,510
we're doing is we're actually
subtracting the

466
00:21:54,510 --> 00:21:56,200
interference term.

467
00:21:56,200 --> 00:21:59,110
So if we're subtracting the
interference term, what we

468
00:21:59,110 --> 00:22:04,860
have here now is destructive
interference.

469
00:22:04,860 --> 00:22:07,900
So let's think about the energy
of interaction here.

470
00:22:07,900 --> 00:22:11,020
When we were talking about
constructive interference, we

471
00:22:11,020 --> 00:22:14,350
had more electron density
in between the 2 nuclei.

472
00:22:14,350 --> 00:22:17,810
So that lowered the energy
of the molecular orbital.

473
00:22:17,810 --> 00:22:20,360
So, bonding orbitals
are down here.

474
00:22:20,360 --> 00:22:22,910
But when we think about where
anti-bonding orbitals should

475
00:22:22,910 --> 00:22:25,820
be, it should be higher
in energy.

476
00:22:25,820 --> 00:22:29,070
It's increased compared to
the atomic orbitals.

477
00:22:29,070 --> 00:22:33,240
So we would label our
anti-bonding orbital higher in

478
00:22:33,240 --> 00:22:37,110
energy than our 1 s
atomic orbitals.

479
00:22:37,110 --> 00:22:39,190
So, let's think a little bit
about what this means.

480
00:22:39,190 --> 00:22:42,380
First of all, again to repeat,
any time we see the star,

481
00:22:42,380 --> 00:22:46,240
sigma 1 s star, that's an
anti-bonding orbital.

482
00:22:46,240 --> 00:22:48,610
When we talk about that,
basically what we're saying,

483
00:22:48,610 --> 00:22:51,440
and you can see that because of
that negative interference,

484
00:22:51,440 --> 00:22:55,490
we actually have less electron
density between the nuclei

485
00:22:55,490 --> 00:22:58,470
than we did when they were two
separate atoms. So you can see

486
00:22:58,470 --> 00:23:01,670
that this is non-bonding,
this is even worse than

487
00:23:01,670 --> 00:23:03,550
non-bonding, it's anti-bonding,
because we're

488
00:23:03,550 --> 00:23:06,520
actually getting rid of electron
density between the

489
00:23:06,520 --> 00:23:07,200
two nuclei.

490
00:23:07,200 --> 00:23:09,870
And we know that it's electron
density between the nuclei

491
00:23:09,870 --> 00:23:13,290
that holds two atoms
together in a bond.

492
00:23:13,290 --> 00:23:15,770
So what I want to point out is
that it creates an effect that

493
00:23:15,770 --> 00:23:18,080
is exactly opposite of a bond.

494
00:23:18,080 --> 00:23:20,590
You might have thought before
we started talking about

495
00:23:20,590 --> 00:23:23,370
molecular orbital theory that
non-bonding was the opposite

496
00:23:23,370 --> 00:23:26,840
of bonding, it's not,
anti-bonding is the opposite

497
00:23:26,840 --> 00:23:29,960
of bonding, and anti-bonding
is not non-bonding.

498
00:23:29,960 --> 00:23:32,680
We can see that if we just look
at this picture here.

499
00:23:32,680 --> 00:23:35,170
Here is bonding, and here
is non-bonding.

500
00:23:35,170 --> 00:23:40,140
Anti-bonding is even higher in
energy than non-bonding.

501
00:23:40,140 --> 00:23:43,260
And the other thing to point out
is that the energy that an

502
00:23:43,260 --> 00:23:47,650
anti-bonding orbital is raised
by, is the same amount as a

503
00:23:47,650 --> 00:23:49,640
bonding orbital is lowered by.

504
00:23:49,640 --> 00:23:52,990
So any time I draw these
molecular orbitals, I do my

505
00:23:52,990 --> 00:23:55,460
best, and I'm not always
perfect, yet trying to make

506
00:23:55,460 --> 00:23:59,110
this energy different exactly
the same for the anti-bonding

507
00:23:59,110 --> 00:24:01,220
orbital being raised,
versus the bonding

508
00:24:01,220 --> 00:24:02,560
orbital being lowered.

509
00:24:02,560 --> 00:24:07,730
So those should be raised and
lowered by the same energy.

510
00:24:07,730 --> 00:24:09,995
So now let's take a look
at some of -- is there

511
00:24:09,995 --> 00:24:16,130
a question up there?

512
00:24:16,130 --> 00:24:17,930
STUDENT: Why would two atoms
decide to [INAUDIBLE].

513
00:24:17,930 --> 00:24:18,100
PROFESSOR: Well, they
don't want to.

514
00:24:18,100 --> 00:24:19,860
It's a higher energy
situation.

515
00:24:19,860 --> 00:24:22,930
So we'll start to look at
molecules and we'll see if we

516
00:24:22,930 --> 00:24:27,180
take two atoms and we fill in
our molecular orbital and it

517
00:24:27,180 --> 00:24:29,750
turns out that they have more
anti-bonding orbitals than

518
00:24:29,750 --> 00:24:33,610
bonding, that's -- a diatomic
molecule we'll never see.

519
00:24:33,610 --> 00:24:37,060
So it helps us predict, will we
see this, for example, h 2,

520
00:24:37,060 --> 00:24:40,830
which we're going to be about to
do, we'll see is stabilized

521
00:24:40,830 --> 00:24:42,850
because it has more bonding
than anti-bonding.

522
00:24:42,850 --> 00:24:44,730
So we'll predict, yes,
there's a bond here.

523
00:24:44,730 --> 00:24:45,850
That's a really good question.

524
00:24:45,850 --> 00:24:51,480
So, let's go ahead and do this
and take a look at some of the

525
00:24:51,480 --> 00:24:54,640
actual atoms that we can
think about and think

526
00:24:54,640 --> 00:24:56,280
about them in molecules.

527
00:24:56,280 --> 00:24:58,900
So our simplest case that we
started talking about was

528
00:24:58,900 --> 00:25:00,190
molecular hydrogen.

529
00:25:00,190 --> 00:25:03,230
I want to finish this discussion
by including the

530
00:25:03,230 --> 00:25:05,880
anti-bonding orbital, and this
is a tip for you when you're

531
00:25:05,880 --> 00:25:09,890
drawing your molecular orbital
diagrams, any time you draw a

532
00:25:09,890 --> 00:25:12,080
bonding orbital, there is
also an anti-bonding

533
00:25:12,080 --> 00:25:13,490
orbital that exists.

534
00:25:13,490 --> 00:25:15,700
It might not have any electrons
in it, but it still

535
00:25:15,700 --> 00:25:18,960
exists, so you need to draw
these into your molecular

536
00:25:18,960 --> 00:25:20,020
orbital diagram.

537
00:25:20,020 --> 00:25:22,330
So I wanted to make sure you
have a complete set for

538
00:25:22,330 --> 00:25:23,740
hydrogen in your notes.

539
00:25:23,740 --> 00:25:24,940
So let's take a look at this.

540
00:25:24,940 --> 00:25:29,440
Hydrogen, we can first draw
in our atomic electrons.

541
00:25:29,440 --> 00:25:32,850
So there's one electron
in each hydrogen atom.

542
00:25:32,850 --> 00:25:36,030
And then this means we'll have
a total of two electrons in

543
00:25:36,030 --> 00:25:39,910
our hydrogen molecule, so we
can fill both of those into

544
00:25:39,910 --> 00:25:43,260
the sigma 1 s orbital,
the bonding orbital.

545
00:25:43,260 --> 00:25:46,460
We don't have to put anything
into the anti-bonding orbital,

546
00:25:46,460 --> 00:25:47,330
so that's great.

547
00:25:47,330 --> 00:25:51,180
What we've seen is we have a net
lowering of energy of the

548
00:25:51,180 --> 00:25:56,330
molecule versus the
individual atoms.

549
00:25:56,330 --> 00:26:00,090
So let's draw the electron
configuration of hydrogen, the

550
00:26:00,090 --> 00:26:02,480
molecule, molecular hydrogen.

551
00:26:02,480 --> 00:26:05,200
What you saw, what we've done
a lot of is drawing the

552
00:26:05,200 --> 00:26:08,520
electron configurations for
different atoms, we can do the

553
00:26:08,520 --> 00:26:10,430
same thing for a molecule.

554
00:26:10,430 --> 00:26:13,850
So, if we take h 2, and we
want to draw the electron

555
00:26:13,850 --> 00:26:15,900
configuration, it's
very short.

556
00:26:15,900 --> 00:26:20,500
All it is sigma 1 s, and then
we have two electrons in it,

557
00:26:20,500 --> 00:26:23,890
so it's sigma 1 s squared.

558
00:26:23,890 --> 00:26:25,990
So this is our electron
configuration.

559
00:26:25,990 --> 00:26:27,620
Let's take a look at
another example.

560
00:26:27,620 --> 00:26:30,700
Let's draw the molecular
diagram for h e 2 now.

561
00:26:30,700 --> 00:26:35,880
So again, we can fill in our
atomic orbitals here, there's

562
00:26:35,880 --> 00:26:39,490
going to be two electrons in
each of our atomic orbitals.

563
00:26:39,490 --> 00:26:42,240
So now let's go ahead and fill
in our molecular orbitals.

564
00:26:42,240 --> 00:26:45,950
We need to fill in a total
of four electrons.

565
00:26:45,950 --> 00:26:49,280
So we have two electrons in
our bonding orbital, but

566
00:26:49,280 --> 00:26:53,130
because we use the same rules to
fill up molecular orbitals

567
00:26:53,130 --> 00:26:56,810
as we do atomic orbitals, so the
Pauli exclusion principle

568
00:26:56,810 --> 00:26:58,760
tells us we can't have more
than two electrons per

569
00:26:58,760 --> 00:27:00,910
orbital, so we have
to go up to our

570
00:27:00,910 --> 00:27:02,870
anti-bonding orbital here.

571
00:27:02,870 --> 00:27:06,130
So this means that we have two
of the electrons are lowered

572
00:27:06,130 --> 00:27:09,690
in energy, but two are
raised in energy.

573
00:27:09,690 --> 00:27:12,470
So would this be a stabilized
molecule then?

574
00:27:12,470 --> 00:27:14,520
STUDENT: [INAUDIBLE]

575
00:27:14,520 --> 00:27:15,320
PROFESSOR: No.

576
00:27:15,320 --> 00:27:18,050
So, compared to the atoms, it
should be somewhat the same

577
00:27:18,050 --> 00:27:20,940
energy, we shouldn't get any
extra stabilization from

578
00:27:20,940 --> 00:27:21,730
forming the molecule.

579
00:27:21,730 --> 00:27:25,100
So lets go ahead and write
what the electron

580
00:27:25,100 --> 00:27:31,680
configuration would
be of h e 2.

581
00:27:31,680 --> 00:27:34,660
And again, we're just filling in
the different orbitals, so

582
00:27:34,660 --> 00:27:39,060
we have sigma 1 s, that's going
to be squared, and now

583
00:27:39,060 --> 00:27:44,730
we have sigma 1 s
star squared.

584
00:27:44,730 --> 00:27:48,440
So we can compare the two
electron configurations, and

585
00:27:48,440 --> 00:27:52,220
we can actually think about --
what we figure out from them,

586
00:27:52,220 --> 00:27:55,320
we see that two are lowered in
energy, two electrons are

587
00:27:55,320 --> 00:27:58,930
raised in energy, so we have no
net gain or no net loss in

588
00:27:58,930 --> 00:28:01,830
energy for h e 2.

589
00:28:01,830 --> 00:28:04,810
And there's actually a way that
we can make predictions

590
00:28:04,810 --> 00:28:07,630
here, and what I'll tell you
is molecular orbital theory

591
00:28:07,630 --> 00:28:10,970
predicts that h e 2 does not
exist because it's not

592
00:28:10,970 --> 00:28:14,830
stabilized in terms of
forming the molecule.

593
00:28:14,830 --> 00:28:17,070
The way that we can figure this
out is using something

594
00:28:17,070 --> 00:28:21,260
called bond order, and bond
order is equal to 1/2 times

595
00:28:21,260 --> 00:28:23,990
the number of bonding electrons,
minus the number of

596
00:28:23,990 --> 00:28:25,550
anti-bonding electrons.

597
00:28:25,550 --> 00:28:28,350
And the bond order you get out
will either be, for example,

598
00:28:28,350 --> 00:28:31,165
zero, which would mean that you
have no bond, or you could

599
00:28:31,165 --> 00:28:33,330
have 1, a single bond, 1 .

600
00:28:33,330 --> 00:28:37,490
5, a 1 and 1/2 bond, 2, a
double bond, and so on.

601
00:28:37,490 --> 00:28:42,130
So let's figure out the bond
order for our two molecules

602
00:28:42,130 --> 00:28:45,670
here that we figured out the
electron configuration for.

603
00:28:45,670 --> 00:28:47,220
So I guess we'll start
with helium 2.

604
00:28:47,220 --> 00:28:53,900
So the bond order is going to
be equal to 1/2, and then it

605
00:28:53,900 --> 00:28:56,400
will be 2 minus 2.

606
00:28:56,400 --> 00:29:00,250
So our bond order for h e 2
is going to be equal to 0.

607
00:29:00,250 --> 00:29:04,330
So it has a 0 bond, there's
no bond in h e 2.

608
00:29:04,330 --> 00:29:06,120
Let's look for hydrogen.

609
00:29:06,120 --> 00:29:14,260
For hydrogen our bond order is
going to equal 1/2, 2 minus 0.

610
00:29:14,260 --> 00:29:16,850
So we would predict
a bond order of 1.

611
00:29:16,850 --> 00:29:19,590
What kind of a bond is
a bond order of 1?

612
00:29:19,590 --> 00:29:23,780
Yeah, we'd expect to see a
single bond in hydrogen.

613
00:29:23,780 --> 00:29:27,660
So what actually turns out the
reality is that h e 2 does

614
00:29:27,660 --> 00:29:31,300
exist, but it exists as the
weakest chemical bond known,

615
00:29:31,300 --> 00:29:35,370
and it wasn't, in fact, even
found to exist until 1993, so

616
00:29:35,370 --> 00:29:39,000
I can assure you this is not a
bond that you see very often

617
00:29:39,000 --> 00:29:42,210
in nature, and it is a
very, very weak bond.

618
00:29:42,210 --> 00:29:45,320
It only has a dissociation
energy of 0 .

619
00:29:45,320 --> 00:29:47,180
1 kilojoules per mole.

620
00:29:47,180 --> 00:29:50,210
So that should make sense,
because we saw no energy

621
00:29:50,210 --> 00:29:53,780
difference between the actual
atoms and the molecules.

622
00:29:53,780 --> 00:29:57,330
Molecular orbital theory, even
at this very basic level,

623
00:29:57,330 --> 00:30:00,340
allowed us to predict that no,
we're not going to see a true

624
00:30:00,340 --> 00:30:02,220
bond here, a strong bond.

625
00:30:02,220 --> 00:30:06,930
In contrast, the dissociation
energy of a bond for hydrogen,

626
00:30:06,930 --> 00:30:10,710
and molecular hydrogen is
everywhere around us, we see

627
00:30:10,710 --> 00:30:12,720
432 kilojoules per mole.

628
00:30:12,720 --> 00:30:16,880
All right, so we can now see a
little bit of what the power

629
00:30:16,880 --> 00:30:20,180
of molecular orbital theory is
in predicting what kind of

630
00:30:20,180 --> 00:30:23,110
bonds we're going to see in
molecules, or whether or not

631
00:30:23,110 --> 00:30:25,610
we'll see this bonding
occur at all.

632
00:30:25,610 --> 00:30:28,540
So let's look at another
example, let's take lithium 2

633
00:30:28,540 --> 00:30:30,710
and see what we can
figure out here.

634
00:30:30,710 --> 00:30:34,430
In lithium 2, we have two atoms
of lithium, each have

635
00:30:34,430 --> 00:30:36,450
three electrons in them.

636
00:30:36,450 --> 00:30:40,670
So now we have to include both
the 1 s orbitals and also the

637
00:30:40,670 --> 00:30:42,250
2 s orbitals.

638
00:30:42,250 --> 00:30:45,390
So any time in a molecular
orbital diagram you draw in

639
00:30:45,390 --> 00:30:46,790
orbitals, you need to draw the

640
00:30:46,790 --> 00:30:49,630
corresponding molecular orbitals.

641
00:30:49,630 --> 00:30:54,450
So, this means we need to have
sigma 1 s, sigma 1 s star, and

642
00:30:54,450 --> 00:30:58,210
now sigma 2 s and
sigma 2 s star.

643
00:30:58,210 --> 00:31:01,490
Something I'll also point out
as you see these dashed line

644
00:31:01,490 --> 00:31:04,370
that tell you where the
individual molecular orbitals

645
00:31:04,370 --> 00:31:08,050
are arising from, as you get
to higher and higher atomic

646
00:31:08,050 --> 00:31:12,380
numbers of molecules that you're
making, it makes a lot

647
00:31:12,380 --> 00:31:14,760
more sense to look at a diagram
when you draw these

648
00:31:14,760 --> 00:31:16,460
dotted lines in, because
they can start to get

649
00:31:16,460 --> 00:31:17,510
a little bit confusing.

650
00:31:17,510 --> 00:31:20,010
So when you go ahead and draw
these on your problem-sets or

651
00:31:20,010 --> 00:31:22,820
on your exams, it's a good idea
to put these dashed lines

652
00:31:22,820 --> 00:31:25,670
in, both for you and for people
reading it to see

653
00:31:25,670 --> 00:31:29,050
exactly where your molecular
orbitals are coming from.

654
00:31:29,050 --> 00:31:32,390
So, this means we have a total
of six electrons that we need

655
00:31:32,390 --> 00:31:34,550
to put into molecular
orbitals.

656
00:31:34,550 --> 00:31:37,260
So again we just start filling
those up -- we have two in the

657
00:31:37,260 --> 00:31:42,050
1 s, two in the sigma 1 s star,
and then we have two in

658
00:31:42,050 --> 00:31:44,220
the sigma 2 s.

659
00:31:44,220 --> 00:31:46,890
So we should be able to also
calculate the bond order, just

660
00:31:46,890 --> 00:31:49,330
like we did for hydrogen
and helium.

661
00:31:49,330 --> 00:31:52,120
First we can do that by
knowing the electron

662
00:31:52,120 --> 00:31:56,070
configuration, we can write it
out just by going up the table

663
00:31:56,070 --> 00:31:58,560
here, up the energy levels.

664
00:31:58,560 --> 00:32:01,270
And you can go ahead and tell
me what you think the bond

665
00:32:01,270 --> 00:32:22,730
order is going to be
for this molecule.

666
00:32:22,730 --> 00:32:22,920
All right.

667
00:32:22,920 --> 00:32:36,460
Let's take 10 more
seconds on this.

668
00:32:36,460 --> 00:32:37,960
OK, good, we're back on
track a little bit

669
00:32:37,960 --> 00:32:39,170
with our clicker answers.

670
00:32:39,170 --> 00:32:46,180
So it's selection three or
one is the bond order.

671
00:32:46,180 --> 00:32:49,250
So let's switch back to our
class notes and look at what

672
00:32:49,250 --> 00:32:49,900
this means.

673
00:32:49,900 --> 00:32:54,010
So we know that it's 1, because
we have 1, 2, 3, 4

674
00:32:54,010 --> 00:32:58,000
bonding, minus 2 anti-bonding,
and 1/2 of that is a bond

675
00:32:58,000 --> 00:32:58,900
order of 1.

676
00:32:58,900 --> 00:33:01,800
We would predict to see a single
bond between lithium,

677
00:33:01,800 --> 00:33:04,000
and it turns out that's
what we see.

678
00:33:04,000 --> 00:33:07,060
And so you have for a reference,
the dissociation

679
00:33:07,060 --> 00:33:10,680
energy of lithium 2 is 105
kilojoules per mole.

680
00:33:10,680 --> 00:33:14,040
So let's keep moving along the
periodic table and keep

681
00:33:14,040 --> 00:33:16,440
applying our molecular
orbitals.

682
00:33:16,440 --> 00:33:22,100
For example now, with b e 2,
so beryllium 2 has four

683
00:33:22,100 --> 00:33:24,840
electrons in terms
of each atom.

684
00:33:24,840 --> 00:33:28,040
So you can start by filling
those in, and now we can fill

685
00:33:28,040 --> 00:33:30,110
in our molecular orbitals
as well.

686
00:33:30,110 --> 00:33:34,090
This means we need a total
of eight electrons in our

687
00:33:34,090 --> 00:33:35,480
molecular orbitals.

688
00:33:35,480 --> 00:33:40,220
So we have two in 1 s, two in
the sigma 1 s star, two in the

689
00:33:40,220 --> 00:33:44,460
sigma 2 s, and two in
the sigma 2 s star.

690
00:33:44,460 --> 00:33:48,270
So let's go ahead and figure
out the bonding order for

691
00:33:48,270 --> 00:33:57,030
beryllium here.

692
00:33:57,030 --> 00:34:00,720
So when we figure it out for
beryllium -- let's see if I

693
00:34:00,720 --> 00:34:06,610
wrote in your notes what
the actual -- electron

694
00:34:06,610 --> 00:34:08,830
configuration, OK that's already
in your notes for you.

695
00:34:08,830 --> 00:34:12,450
So let's go right to the bond
order for beryllium.

696
00:34:12,450 --> 00:34:16,210
So for the bond order we want
to take 1/2 of the total

697
00:34:16,210 --> 00:34:20,140
number of bonding electrons, so
that's going to be 4 minus

698
00:34:20,140 --> 00:34:24,660
anti-bonding is 4, so we end up
getting a bond order that's

699
00:34:24,660 --> 00:34:25,940
equal to 0.

700
00:34:25,940 --> 00:34:28,530
So what I want to point out with
this case in beryllium is

701
00:34:28,530 --> 00:34:31,450
that you don't have to use all
of the electrons to figure out

702
00:34:31,450 --> 00:34:35,320
the bond order, and in fact,
once you get to molecules that

703
00:34:35,320 --> 00:34:39,240
are from atoms with atomic
numbers of 8 or 10, you're not

704
00:34:39,240 --> 00:34:42,190
going to want to maybe
draw out the full

705
00:34:42,190 --> 00:34:44,010
molecular orbital diagram.

706
00:34:44,010 --> 00:34:46,600
So what I want to tell you is
we also always get the same

707
00:34:46,600 --> 00:34:49,050
bond order if we instead
only deal

708
00:34:49,050 --> 00:34:50,810
with the valence electrons.

709
00:34:50,810 --> 00:34:53,620
So let's just prove that to
ourselves and figure out the

710
00:34:53,620 --> 00:34:57,030
bond order just using
valence electrons.

711
00:34:57,030 --> 00:34:59,940
So this would mean the bond
order is equal to 1/2, and in

712
00:34:59,940 --> 00:35:02,370
terms of valence electrons,
how many bonding valence

713
00:35:02,370 --> 00:35:02,990
electrons do we have?

714
00:35:02,990 --> 00:35:03,440
STUDENT: [INAUDIBLE]

715
00:35:03,440 --> 00:35:06,690
PROFESSOR: All right, what
about anti-bonding?

716
00:35:06,690 --> 00:35:07,840
STUDENT: [INAUDIBLE]

717
00:35:07,840 --> 00:35:08,270
PROFESSOR: Two.

718
00:35:08,270 --> 00:35:08,630
OK, good.

719
00:35:08,630 --> 00:35:11,780
So again, we're going to
see that we have a

720
00:35:11,780 --> 00:35:13,820
bonding order of 0.

721
00:35:13,820 --> 00:35:18,330
So we would not predict
to see a b e 2 bond.

722
00:35:18,330 --> 00:35:23,150
So what we see is a bond order
of 0, and again, the bond is

723
00:35:23,150 --> 00:35:24,180
very, very weak.

724
00:35:24,180 --> 00:35:26,320
Essentially we're not going
to see this, it's 9

725
00:35:26,320 --> 00:35:27,450
kilojoules per mole.

726
00:35:27,450 --> 00:35:29,990
All right.

727
00:35:29,990 --> 00:35:33,060
So, so far we've looked only
at molecules that involve

728
00:35:33,060 --> 00:35:36,110
atoms that have only
s orbitals in them.

729
00:35:36,110 --> 00:35:38,560
I'm sure you're thinking well,
what do we do in the case of p

730
00:35:38,560 --> 00:35:40,900
orbitals, and, in fact, we
can do the same thing.

731
00:35:40,900 --> 00:35:43,480
Again, we're going to take the
linear combination of those p

732
00:35:43,480 --> 00:35:47,700
atomic orbitals and make what
are called pi or some more

733
00:35:47,700 --> 00:35:49,990
sigma molecular orbitals.

734
00:35:49,990 --> 00:35:52,670
So let's look at the first case
where we have either the

735
00:35:52,670 --> 00:35:57,200
2 p x or 2 p y type of orbitals
that we're combining.

736
00:35:57,200 --> 00:35:59,760
So they're the same shape,
this is the shape of the

737
00:35:59,760 --> 00:36:03,090
orbital or the shape of the wave
function, and we can call

738
00:36:03,090 --> 00:36:07,840
this either 2 p x a being
combined with 2 p x b, or we

739
00:36:07,840 --> 00:36:11,085
could say since it's the same
shape, it's 2 p y a being

740
00:36:11,085 --> 00:36:13,780
combined with 2 p y b.

741
00:36:13,780 --> 00:36:16,530
And in either case if we first
talk about constructive

742
00:36:16,530 --> 00:36:19,310
interference, what again we're
going to see is that where

743
00:36:19,310 --> 00:36:22,380
these two orbitals come
together, we're going to see

744
00:36:22,380 --> 00:36:25,430
increased wave function in
that area, so we saw

745
00:36:25,430 --> 00:36:27,530
constructive interference.

746
00:36:27,530 --> 00:36:31,740
So again, we can name these
molecular orbitals and these

747
00:36:31,740 --> 00:36:35,220
we're going to call -- also to
point out there is now a bond

748
00:36:35,220 --> 00:36:38,650
axis along this nodal plane,
which is something we didn't

749
00:36:38,650 --> 00:36:41,600
see before when we were
combining the s orbitals.

750
00:36:41,600 --> 00:36:43,670
So when we go ahead and name
these, we're going to call

751
00:36:43,670 --> 00:36:45,260
these pi orbitals.

752
00:36:45,260 --> 00:36:49,520
We'll call it either pi 2 p x,
if we're combining the x

753
00:36:49,520 --> 00:36:53,910
orbitals, or pi 2 p y.

754
00:36:53,910 --> 00:36:57,280
The reason that I wanted to
point out this nodal plane

755
00:36:57,280 --> 00:37:00,840
here is because this is why
it is called a pi orbital.

756
00:37:00,840 --> 00:37:04,630
Pi orbitals are a molecular
orbital that have a nodal

757
00:37:04,630 --> 00:37:07,220
plane through the bond axis.

758
00:37:07,220 --> 00:37:10,750
Remember this is our bond axis
here, and you can see there is

759
00:37:10,750 --> 00:37:13,640
this area where the wave
function is equal to zero all

760
00:37:13,640 --> 00:37:16,190
along that plane, that's
a nodal plane.

761
00:37:16,190 --> 00:37:18,290
So that's why these
are pi orbitals

762
00:37:18,290 --> 00:37:20,420
instead of sigma orbitals.

763
00:37:20,420 --> 00:37:23,410
So again, we can think about
the probability density in

764
00:37:23,410 --> 00:37:25,480
terms of squaring the
wave function.

765
00:37:25,480 --> 00:37:28,410
So now what it is that we're
squaring is if we're talking

766
00:37:28,410 --> 00:37:34,390
about x orbital, it's pi 2 p
x squared, and this is just

767
00:37:34,390 --> 00:37:42,980
equal to the 2 p x a plus the 2
p x b all squared, or if we

768
00:37:42,980 --> 00:37:48,360
write out all of the terms we
have 2 p x a squared plus 2 p

769
00:37:48,360 --> 00:37:52,330
x b squared, and then this term
here, and again, this is

770
00:37:52,330 --> 00:37:53,760
our interference term.

771
00:37:53,760 --> 00:37:56,200
In this case is it constructive
or destructive

772
00:37:56,200 --> 00:37:57,000
interference?

773
00:37:57,000 --> 00:37:57,336
STUDENT: [INAUDIBLE]

774
00:37:57,336 --> 00:37:59,410
PROFESSOR: Constructive
interference.

775
00:37:59,410 --> 00:38:02,030
We're seeing that the wave
function's adding together and

776
00:38:02,030 --> 00:38:06,680
giving us more wave function
in the center here.

777
00:38:06,680 --> 00:38:07,010
All right.

778
00:38:07,010 --> 00:38:09,390
So we see constructive
interference, of course, we

779
00:38:09,390 --> 00:38:12,060
can also see destructive
interference.

780
00:38:12,060 --> 00:38:15,490
So I changed the colors here
to show that these are 2 p

781
00:38:15,490 --> 00:38:19,150
orbitals with an opposite phase
or an opposite sign.

782
00:38:19,150 --> 00:38:24,490
So what happens when we add a 2
p a and we subtract from it

783
00:38:24,490 --> 00:38:29,970
a 2 p x b, or the same with a 2
p y a subtracting a 2 p y b,

784
00:38:29,970 --> 00:38:33,290
is that we're actually going
to cancel out the wave

785
00:38:33,290 --> 00:38:36,830
function in the center, so we
now have 2 nodal planes.

786
00:38:36,830 --> 00:38:39,530
So again, this is an
anti-bonding orbital, and what

787
00:38:39,530 --> 00:38:43,470
you see is that there is now
less electron density between

788
00:38:43,470 --> 00:38:49,040
the two nuclei than there was
when you had non-bonding.

789
00:38:49,040 --> 00:38:53,320
So we're going to call this the
sigma 2 p x star, or if

790
00:38:53,320 --> 00:38:58,400
we're talking about the 2 p y
orbitals we'll call this the

791
00:38:58,400 --> 00:39:05,880
pi 2 p x star, and the
pi 2 p y star.

792
00:39:05,880 --> 00:39:09,200
And the pi star orbitals result
from any time you have

793
00:39:09,200 --> 00:39:12,600
destructive interference from
2 p orbitals that are either

794
00:39:12,600 --> 00:39:16,370
the p x or the p y.

795
00:39:16,370 --> 00:39:19,030
So now we can move on to an
example where we do, in fact,

796
00:39:19,030 --> 00:39:23,790
have to use some p orbitals,
so this would be b 2.

797
00:39:23,790 --> 00:39:26,990
How many electrons
are in boron?

798
00:39:26,990 --> 00:39:27,590
Five.

799
00:39:27,590 --> 00:39:29,590
I see some hands going up.

800
00:39:29,590 --> 00:39:32,740
There's five electrons So what
you'll notice here is that I

801
00:39:32,740 --> 00:39:35,240
only filled in 3 electrons.

802
00:39:35,240 --> 00:39:37,140
What do these electrons
represent?

803
00:39:37,140 --> 00:39:38,750
STUDENT: Valence.

804
00:39:38,750 --> 00:39:39,740
PROFESSOR: Valence electrons.

805
00:39:39,740 --> 00:39:41,910
OK, sometimes you're going to
be asked to draw a molecular

806
00:39:41,910 --> 00:39:44,790
orbital diagram where you're
asked to include all

807
00:39:44,790 --> 00:39:48,080
electrons, and sometimes it
will specifically say only

808
00:39:48,080 --> 00:39:50,110
include valence electrons.

809
00:39:50,110 --> 00:39:53,190
That happens because of space
issues that you were asked to

810
00:39:53,190 --> 00:39:55,880
do that, because you can always
assume that all of the

811
00:39:55,880 --> 00:39:59,050
core orbitals are already
going to be filled.

812
00:39:59,050 --> 00:40:01,310
So, in this case, we're just
drawing the molecular orbital

813
00:40:01,310 --> 00:40:03,940
diagram for the valence
electrons, so we

814
00:40:03,940 --> 00:40:05,320
have three for each.

815
00:40:05,320 --> 00:40:09,330
And what we see here is now when
we're combining the p, we

816
00:40:09,330 --> 00:40:13,200
have our 2 p x and our 2 p y
orbitals that are lower in

817
00:40:13,200 --> 00:40:16,900
energy, and then our pi
anti-bonding orbitals that are

818
00:40:16,900 --> 00:40:18,580
higher in energy.

819
00:40:18,580 --> 00:40:22,090
You might be asking where the 2
p z orbital is and we'll get

820
00:40:22,090 --> 00:40:24,410
to that soon once we need it.

821
00:40:24,410 --> 00:40:28,170
Let's just first fill in
this for the b 2 case.

822
00:40:28,170 --> 00:40:32,360
So we can start at the bottom,
two electrons in sigma 2 s,

823
00:40:32,360 --> 00:40:35,700
two electrons in
sigma 2 s star.

824
00:40:35,700 --> 00:40:40,220
Now we need to jump up to using
these pi orbitals, and

825
00:40:40,220 --> 00:40:43,910
what we're going to do is put
one electron into each of our

826
00:40:43,910 --> 00:40:47,790
pi 2 p x and 2 p y orbitals.

827
00:40:47,790 --> 00:40:50,690
So again you can see as we're
filling up our molecular

828
00:40:50,690 --> 00:40:53,750
orbitals, we're using the exact
same principle we used

829
00:40:53,750 --> 00:40:55,110
to fill up atomic orbitals.

830
00:40:55,110 --> 00:41:00,530
So let's think about what
the valence electron

831
00:41:00,530 --> 00:41:03,170
configuration is here.

832
00:41:03,170 --> 00:41:07,980
So now we're looking
at the case of b 2.

833
00:41:07,980 --> 00:41:11,500
And what we're looking at is a
valence electron molecular

834
00:41:11,500 --> 00:41:13,640
orbital diagram, so let's
just draw the electron

835
00:41:13,640 --> 00:41:16,880
configuration for the valence
orbitals, so that will be

836
00:41:16,880 --> 00:41:25,940
sigma 2 s 2, sigma 2 s star 2,
and now we start in with our

837
00:41:25,940 --> 00:41:34,350
pi 2 p x 1, and our
pi 2 p y 1.

838
00:41:34,350 --> 00:41:36,440
So this is our valence electron

839
00:41:36,440 --> 00:41:38,800
configuration for b 2.

840
00:41:38,800 --> 00:41:41,250
All right.

841
00:41:41,250 --> 00:41:48,670
So what would you expect the
bonding order for b 2 to be?

842
00:41:48,670 --> 00:41:50,030
Shout it out if you know.

843
00:41:50,030 --> 00:41:51,440
STUDENT: one.

844
00:41:51,440 --> 00:41:55,220
PROFESSOR: And I didn't write up
there but it is one, and we

845
00:41:55,220 --> 00:42:00,200
can see that it's 1, because
it's 1/2 of 2, 4 minus 2, so

846
00:42:00,200 --> 00:42:04,130
1/2 of 2, the bonding order is
going to be equal to one.

847
00:42:04,130 --> 00:42:06,900
So let's move on to another
example, let's talk about

848
00:42:06,900 --> 00:42:07,680
carbon here.

849
00:42:07,680 --> 00:42:10,230
Again, we're just talking about
the valence electrons.

850
00:42:10,230 --> 00:42:13,660
So carbon has four valence
electrons, so if we talk about

851
00:42:13,660 --> 00:42:17,220
c 2, again we're going to start
filling in our molecular

852
00:42:17,220 --> 00:42:21,100
orbitals, and now we're going
to have eight electrons to

853
00:42:21,100 --> 00:42:22,400
fill into our molecular
orbitals.

854
00:42:22,400 --> 00:42:27,130
So, we'll put two in the sigma
2 s, two in the sigma 2 s

855
00:42:27,130 --> 00:42:30,870
star, and now we're going to
fill one and one into each of

856
00:42:30,870 --> 00:42:35,540
our pi 2 p x and 2 p y, but we
still have two electrons left,

857
00:42:35,540 --> 00:42:38,560
so what we're going to do is
double up in terms of our 2 p

858
00:42:38,560 --> 00:42:40,120
x and our 2 p y.

859
00:42:40,120 --> 00:42:43,640
So let's think about what this
valence electron configuration

860
00:42:43,640 --> 00:42:48,230
is for c 2.

861
00:42:48,230 --> 00:42:51,270
And again, I want you to have
practiced drawing these out in

862
00:42:51,270 --> 00:42:54,460
the form -- you always need to
start with the sigma and then

863
00:42:54,460 --> 00:42:56,710
write the number
of the orbital.

864
00:42:56,710 --> 00:43:02,170
So, sigma 2 s has two electrons,
sigma 2 s star with

865
00:43:02,170 --> 00:43:06,560
two electrons, and now we have
sigma 2 p x -- how many

866
00:43:06,560 --> 00:43:07,630
electrons here?

867
00:43:07,630 --> 00:43:09,760
STUDENT: Two.

868
00:43:09,760 --> 00:43:10,560
PROFESSOR: Two.

869
00:43:10,560 --> 00:43:15,710
And sigma 2 p y, two
electrons here.

870
00:43:15,710 --> 00:43:20,960
Oh excuse me, pi 2 p y, thank
you -- pi 2 p x and pi 2 p y.

871
00:43:20,960 --> 00:43:23,540
So let's talk about what
the bonding order is

872
00:43:23,540 --> 00:43:25,110
going to be for c 2.

873
00:43:25,110 --> 00:43:30,640
So what's the bonding
order for c 2?

874
00:43:30,640 --> 00:43:31,460
STUDENT: Two.

875
00:43:31,460 --> 00:43:32,320
PROFESSOR: two?

876
00:43:32,320 --> 00:43:40,880
OK, so we have 2, 4, 6 minus 2,
so we have 1/2 of 6 minus

877
00:43:40,880 --> 00:43:45,390
2, so that's 1/2 half 4, so we
have a bonding order of two

878
00:43:45,390 --> 00:43:46,870
for carbon 2.

879
00:43:46,870 --> 00:43:50,330
So we would expect to see a
double bond for a c 2 where we

880
00:43:50,330 --> 00:43:54,680
would expect to see a -- double
bond for c 2 and a

881
00:43:54,680 --> 00:43:58,060
single bond for b 2.

882
00:43:58,060 --> 00:44:01,810
And that is, in fact, what we
can surmise if we look at the

883
00:44:01,810 --> 00:44:04,940
different dissociation energies
for the two bonds.

884
00:44:04,940 --> 00:44:08,490
So for b 2, which is a single
bond, that's 289 kilojoules

885
00:44:08,490 --> 00:44:12,130
per mole to break it, and it
takes us more energy to break

886
00:44:12,130 --> 00:44:14,690
this double bond for carbon,
which is 599

887
00:44:14,690 --> 00:44:17,000
kilojoules per mole.

888
00:44:17,000 --> 00:44:20,080
So, in general what we see,
and this is always true if

889
00:44:20,080 --> 00:44:22,420
we're comparing the same atom,
and in general, if we're

890
00:44:22,420 --> 00:44:25,470
comparing different types of
molecules, but we know that a

891
00:44:25,470 --> 00:44:27,950
single bond is always weaker
than a double bond, which is

892
00:44:27,950 --> 00:44:29,490
weaker than a triple bond.

893
00:44:29,490 --> 00:44:33,380
And obviously, no bond is the
weakest of all is not bonding.

894
00:44:33,380 --> 00:44:34,470
All right.

895
00:44:34,470 --> 00:44:37,790
So let's look now at the case
where we do have 2 p z

896
00:44:37,790 --> 00:44:39,570
orbitals that we're
talking about.

897
00:44:39,570 --> 00:44:41,850
So again, what we're talking
about is the linear

898
00:44:41,850 --> 00:44:45,710
combination of atomic 2 p
orbitals, and now we're

899
00:44:45,710 --> 00:44:47,440
talking about 2 p z.

900
00:44:47,440 --> 00:44:50,680
So if we have constructive
interference between the two,

901
00:44:50,680 --> 00:44:54,610
what we're going to see is our
molecular orbital looks

902
00:44:54,610 --> 00:44:56,570
something like this.

903
00:44:56,570 --> 00:44:59,790
Do you predict that this will
be a sigma or a pi orbital?

904
00:44:59,790 --> 00:45:02,420
STUDENT: [INAUDIBLE]

905
00:45:02,420 --> 00:45:03,613
PROFESSOR: All right, I'm
hearing a little of both, but

906
00:45:03,613 --> 00:45:05,640
I'm very encouraged to
hear quite a few

907
00:45:05,640 --> 00:45:07,310
people saying sigma.

908
00:45:07,310 --> 00:45:10,230
This is, in fact, a sigma
2 p z orbital is what

909
00:45:10,230 --> 00:45:12,210
this orbital is called.

910
00:45:12,210 --> 00:45:15,270
The reason that it's sigma is
if you look at the bonding

911
00:45:15,270 --> 00:45:18,410
axis here, is that there
is no nodal plane

912
00:45:18,410 --> 00:45:20,820
along the bonding axis.

913
00:45:20,820 --> 00:45:25,430
Also, it is cylindrically
symmetric around the bonding

914
00:45:25,430 --> 00:45:28,390
axis, so this is how we know
that it's a sigma orbital.

915
00:45:28,390 --> 00:45:32,660
So some p orbitals form pi
molecular orbitals, and some

916
00:45:32,660 --> 00:45:34,540
form sigma p orbitals.

917
00:45:34,540 --> 00:45:38,030
Specifically, it's always the
z that forms the sigma

918
00:45:38,030 --> 00:45:41,600
orbital, and the reason is at
least at a minimum for this

919
00:45:41,600 --> 00:45:45,740
class we always define the
internuclear axis as the z

920
00:45:45,740 --> 00:45:50,290
axis, so this is always the z
axis, so it's always going to

921
00:45:50,290 --> 00:45:53,440
be the 2 p z's that are coming
together head-on.

922
00:45:53,440 --> 00:45:56,370
The reason that there is
increased electron density

923
00:45:56,370 --> 00:45:59,490
here is you can see that these
two orbitals come together and

924
00:45:59,490 --> 00:46:02,450
constructively interfere.

925
00:46:02,450 --> 00:46:05,210
We can also talk about
anti-bonding orbitals where we

926
00:46:05,210 --> 00:46:07,190
have destructive interference.

927
00:46:07,190 --> 00:46:10,250
So instead, these would be
canceling out wave functions

928
00:46:10,250 --> 00:46:13,820
between the two, so we would end
up with a nodal plane down

929
00:46:13,820 --> 00:46:15,190
the center.

930
00:46:15,190 --> 00:46:18,390
Would this be a sigma or a pi?

931
00:46:18,390 --> 00:46:19,840
It's still sigma.

932
00:46:19,840 --> 00:46:22,670
So even though we see a nodal
plane down the center, I just

933
00:46:22,670 --> 00:46:25,110
want to really point out that
it's only when we have a nodal

934
00:46:25,110 --> 00:46:27,940
plane in the internuclear or
the bond axis that we're

935
00:46:27,940 --> 00:46:30,660
calling that a pi orbital.

936
00:46:30,660 --> 00:46:32,360
So this is still a
sigma -- it's a

937
00:46:32,360 --> 00:46:35,360
sigma 2 p z star orbital.

938
00:46:35,360 --> 00:46:38,370
We have destructive
interference here.

939
00:46:38,370 --> 00:46:41,270
So now let's look at an example
where we talk about

940
00:46:41,270 --> 00:46:45,210
using these 2 p z orbitals,
so let's look at oxygen.

941
00:46:45,210 --> 00:46:48,280
So the first thing I want to
point out is that the 2 p z,

942
00:46:48,280 --> 00:46:53,400
the sigma 2 p z is even lower in
energy than the pi orbitals

943
00:46:53,400 --> 00:46:57,340
here, and the anti-bonding sigma
orbital is going to be

944
00:46:57,340 --> 00:47:03,010
higher in energy than the pi 2
p orbitals that we have here.

945
00:47:03,010 --> 00:47:05,690
So in oxygen again, this is
just showing the valence

946
00:47:05,690 --> 00:47:09,570
electrons, so we end up having
six valence electrons from

947
00:47:09,570 --> 00:47:11,070
each oxygen atom.

948
00:47:11,070 --> 00:47:14,380
We can fill right up our table
just like we did before, but

949
00:47:14,380 --> 00:47:18,610
now we have included our
2 p z orbital here.

950
00:47:18,610 --> 00:47:23,080
So we have two electrons in
sigma 2 s, two in sigma 2 s

951
00:47:23,080 --> 00:47:29,730
star, in sigma 2 p z we have two
-- those are filled first,

952
00:47:29,730 --> 00:47:33,780
and now we're going to put
one into pi 2 p x, and

953
00:47:33,780 --> 00:47:37,480
one into pi 2 p y.

954
00:47:37,480 --> 00:47:41,860
So we can write out what the
electron configuration is

955
00:47:41,860 --> 00:47:44,250
here, and I think that I have
already written that out for

956
00:47:44,250 --> 00:47:45,890
you in your notes.

957
00:47:45,890 --> 00:47:50,400
What is the bond order of o 2?

958
00:47:50,400 --> 00:47:54,200
It's two.

959
00:47:54,200 --> 00:47:56,090
Oh excuse me, I didn't fill
in all of my electrons.

960
00:47:56,090 --> 00:47:57,140
All right.

961
00:47:57,140 --> 00:48:00,220
So we had a total
of 2, 4, 6, 8.

962
00:48:00,220 --> 00:48:01,990
So we had a total of 12.

963
00:48:01,990 --> 00:48:07,640
So we filled in four here --
we need to keep going.

964
00:48:07,640 --> 00:48:10,630
All right, so I did this not at
all purposely, but this can

965
00:48:10,630 --> 00:48:13,570
point out for you that you need
to make sure that the

966
00:48:13,570 --> 00:48:17,480
number of electrons that you
have in your molecular orbital

967
00:48:17,480 --> 00:48:19,840
does match up with the total
number that you have in your

968
00:48:19,840 --> 00:48:21,170
atomic orbitals.

969
00:48:21,170 --> 00:48:24,160
So I did not do any counting up
here, you should make sure

970
00:48:24,160 --> 00:48:25,910
you do counting, I apologize.

971
00:48:25,910 --> 00:48:29,850
So we need to fill all the
way up to the pi 2 p x,

972
00:48:29,850 --> 00:48:31,220
and the pi 2 p y.

973
00:48:31,220 --> 00:48:34,760
All right, so the bonding order,
you're correct, should

974
00:48:34,760 --> 00:48:38,040
be 2, if we subtract the
number of bonding minus

975
00:48:38,040 --> 00:48:42,380
anti-bonding electrons
and take that in 1/2.

976
00:48:42,380 --> 00:48:45,560
And what I want to point out
that we just figured out for

977
00:48:45,560 --> 00:48:49,120
molecular orbital theory, is
that o 2 is a biradical,

978
00:48:49,120 --> 00:48:51,180
because remember, the definition
of a radical is

979
00:48:51,180 --> 00:48:53,550
when we have an unpaired
electron.

980
00:48:53,550 --> 00:48:57,680
You can see that we have two
unpaired electrons in this

981
00:48:57,680 --> 00:49:02,880
molecule here -- one in the pi
2 p x star, and one in the pi

982
00:49:02,880 --> 00:49:05,020
2 p y star orbital.

983
00:49:05,020 --> 00:49:07,570
This was something we could
not predict using Lewis

984
00:49:07,570 --> 00:49:11,520
structures, but we can predict
using MO theory that we have a

985
00:49:11,520 --> 00:49:13,190
radical species here.

986
00:49:13,190 --> 00:49:15,850
So that's a really important
type of an application that we

987
00:49:15,850 --> 00:49:18,440
can use MO theory for that we
weren't able to do with our

988
00:49:18,440 --> 00:49:20,340
Lewis structures.

989
00:49:20,340 --> 00:49:23,380
All right, I want to do one more
at homonuclear example

990
00:49:23,380 --> 00:49:25,520
here, and this is n 2.

991
00:49:25,520 --> 00:49:28,710
The first thing that I need to
point out is you can actually

992
00:49:28,710 --> 00:49:33,440
see an n 2 versus o 2 that we
flip-flopped the energy of the

993
00:49:33,440 --> 00:49:36,590
sigma and the pi 2 p orbitals.

994
00:49:36,590 --> 00:49:39,610
So this is a glitch, just like
sometimes we had glitches in

995
00:49:39,610 --> 00:49:41,040
filling up our atomic
orbitals.

996
00:49:41,040 --> 00:49:43,100
This is something that
you need to remember.

997
00:49:43,100 --> 00:49:47,670
And what you need to remember is
if the z is equal to eight

998
00:49:47,670 --> 00:49:51,370
or greater, such as oxygen being
the cut-off point, this

999
00:49:51,370 --> 00:49:56,030
sigma 2 p orbital is actually
lower in energy than the pi 2

1000
00:49:56,030 --> 00:49:57,650
p orbitals, the molecular
orbitals.

1001
00:49:57,650 --> 00:50:01,660
But for anything 7 or
less, so what is the

1002
00:50:01,660 --> 00:50:03,220
atomic number for nitrogen?

1003
00:50:03,220 --> 00:50:05,400
STUDENT: Five.

1004
00:50:05,400 --> 00:50:07,330
PROFESSOR: five -- there's five
valence electrons, but

1005
00:50:07,330 --> 00:50:09,990
the atomic number is
actually seven.

1006
00:50:09,990 --> 00:50:13,950
So z equals 7 -- this is the
cut-off where, in fact, the

1007
00:50:13,950 --> 00:50:18,450
sigma orbital is going to be
higher in energy than the pi 2

1008
00:50:18,450 --> 00:50:19,410
p orbitals.

1009
00:50:19,410 --> 00:50:21,330
This is something that you
just need to remember.

1010
00:50:21,330 --> 00:50:24,120
I wrote it down your notes, if
you can put a big star next to

1011
00:50:24,120 --> 00:50:25,890
it so you don't forget this.

1012
00:50:25,890 --> 00:50:27,930
This is something you're going
to be responsible for in

1013
00:50:27,930 --> 00:50:29,850
drawing out your molecular
orbitals.

1014
00:50:29,850 --> 00:50:32,650
So let's fill it out in this
way, keeping in mind that

1015
00:50:32,650 --> 00:50:36,630
we're going to fill out the
pi 2 p's before the sigma.

1016
00:50:36,630 --> 00:50:42,410
So we have a total of 2, 4, 6,
8, 10 valence electrons, so

1017
00:50:42,410 --> 00:50:44,590
I'll make sure I count to 10
as we fill up our molecular

1018
00:50:44,590 --> 00:50:45,760
orbitals here.

1019
00:50:45,760 --> 00:50:48,050
We have two, then
we have four.

1020
00:50:48,050 --> 00:50:51,710
Now we're going to start in
with that pi 2 p orbitals,

1021
00:50:51,710 --> 00:50:55,960
which gives us 1 each, and then
two each in those, and

1022
00:50:55,960 --> 00:51:00,490
then after that, we'll go up
to our sigma 2 p z orbital.

1023
00:51:00,490 --> 00:51:04,210
So this is going to be our
molecular orbital diagram.

1024
00:51:04,210 --> 00:51:06,340
And again, I've written for you,
but you can figure out

1025
00:51:06,340 --> 00:51:08,320
what the electron configuration
is just by

1026
00:51:08,320 --> 00:51:10,940
writing up in this order here.

1027
00:51:10,940 --> 00:51:13,480
And what is the bond order
going to be n 2?

1028
00:51:13,480 --> 00:51:15,280
STUDENT: [INAUDIBLE]

1029
00:51:15,280 --> 00:51:16,190
PROFESSOR: It's going
to be three.

1030
00:51:16,190 --> 00:51:18,850
So, you can go ahead and
calculate that, if you can't

1031
00:51:18,850 --> 00:51:20,390
see that right away.

1032
00:51:20,390 --> 00:51:22,370
So we'll end here, we'll
finish up with the

1033
00:51:22,370 --> 00:51:25,230
heteronuclear example
on Friday.