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Today I would like to start by
discussing a timeline.

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And you will see in a moment
what this timeline has to do

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with.
It is obviously only a partial

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timeline.
But let's start here in 1916,

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as we have done this semester,
by talking about the Lewis

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theory of electronic structure.

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And his electron pair theory is
something we are going to come

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back to a couple of times during
lecture today.

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Let's move on to 1954.
1954 was an important year in

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electronic structure theory,
because in that year there was

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awarded, to Linus Pauling,
the Nobel Prize in chemistry.

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Let me write down Pauling here.

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And if you are interested in
knowing something about what

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Pauling was awarded the Nobel
Prize in chemistry for,

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I will show you over here on
the side boards.

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What you are going to see here,
if you read this citation for

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Linus Carl Pauling in 1954 for
the Nobel Prize in chemistry,

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his prize was awarded
principally for his

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contributions to our
understanding of the nature of

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the chemical bond.
If you think back to the

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elegant title of the paper by
Lewis that we started out our

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discussion of acid-base theory
with, it was a paper entitled

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"The Atom and the Molecule." And
now we have gotten to Pauling,

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in 1954, who is being awarded a
Nobel Prize in chemistry for the

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nature of the chemical bond.
That also is the title of a

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very famous chemistry book by
Linus Pauling entitled "The

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Nature of the Chemical Bond."
That was published by Cornell

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University Press originally,
because it stemmed from his set

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of lectures at Cornell,
the Baker lectures,

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in the 1950s.
As we talk about electronic

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structure theory,
I would like you to keep in

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mind the way in which these
different geniuses were

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approaching the problem,
a problem that we are going to

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launch in on today and spend the
next few lectures on.

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We will move up here to 1966.

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In 1966 there was awarded a
Nobel Prize to Mulliken.

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Not to be confused with
Milliken.

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We are going from 1954 to 1966.

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You are going to find,
as you explore the Nobel Prize

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website, that there are a lot of
informational links on these

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people.
You can go and read

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biographies.
You can read some of their

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writings.
In the case of Linus Pauling,

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you have links to all the pages
of all of his research

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notebooks, spanning more than 60
years of research.

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Those are pretty interesting
supportive materials.

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In the case of Robert S.
Mulliken, he is being cited for

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his contributions to the
molecular orbital method,

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which we will also call the
molecular orbital theory.

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We have the Lewis theory.
We have, in the case of

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Pauling, I am going to say the
nature of the chemical bond,

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described in terms of valance
bond theory.

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We will come back to that in a
moment.

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And then, in the case of
Mulliken, we have a Nobel Prize

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for molecular orbital theory.
And I just would like to show

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you something kind of neat,
here.

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This has to do with the fact
that if I go to the section

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labeled other resources,
I can click on MIT digital

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thesis library.
Then I can choose a page of

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Mulliken's thesis to display.
And that is because Robert S.

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Mulliken was Course 5 1917.
Let's hear it for Course 5

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chemistry.
[APPLAUSE] Robert S.

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Mulliken was one of you guys,
and he graduated in 1917.

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His undergraduate chemistry
thesis at MIT was entitled "The

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Effective Structure on the
Activity of the Hydroxyl Group

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in Alcohols."
Submitted by Robert S.

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Mulliken.
There is his signature.

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Isn't it cool to have your
undergraduate thesis linked in

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from the Nobel Prize website?
Robert S.

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Mulliken for molecular orbital
theory.

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And you can see,
even as you read his

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undergraduate thesis,
he was talking about the effect

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of structure on the activity of
the hydroxyl group.

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He had the idea that if you
knew something about the

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structure of the molecule,
even back then,

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you could make predictions
about the properties of the

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molecule.
And that is what we really want

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to be able to do in chemistry,
because we want to be able to

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control function as much as
possible.

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I will take that way for now
and we'll come back in a moment

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because I am going to mention to
you that in 1998 there was

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another Nobel Prize given for
advances in our understanding of

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electronic structure of
molecules.

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And this one was a shared
prize, rather than these three

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other ones that I mentioned.
Well, two others.

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Lewis was neglected from that
category, unfortunately.

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In 1998 Kohn and Pople shared
the Nobel Prize for furthering

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our understanding of how to
describe electronic structure of

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molecules.
And this is a theory that we

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are not going to be talking
about too much explicitly here

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in 5.112 this semester,
but if you go on in chemistry,

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you will be exposed to it more
and more.

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It is called density functional
theory.

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It is one of the most expedient
ways to use computers to get

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electronic structure information
about molecules.

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And so, that method has become
extremely important.

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And I will just show you a
little piece of information from

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that website,
so we go to 1998.

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And, under the John Pople
section, I am going to go to

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interview.
He has given an interview on

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different topics relating to his
involvement in chemistry.

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One short piece of that
interview is entitled "Interest

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in Quantum Mechanics and
Development of Computer

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Techniques."
We are going to take a look at

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that and hopefully,
if the audio and video are both

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working, you will be able to see
John Pople talking a little bit

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about this important area of
chemistry.

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We just don't have time for
fixing audio/video problems in

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real-time here,
unfortunately.

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Therefore, what I would like
you to do is go to

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NobelPrize.org,
Chemistry Laureates on Pople,

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and actually watch that
five-minute segment of his

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interview that has to do with
his feelings about electronic

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structure theory and advice to
students on that topic.

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And I will summarize his
comments here --

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-- by saying that the goal of
studying electronic structure of

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molecules is to try to get
predictive power about molecular

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systems.
And we want predictive power in

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terms of the 3D structure of
molecules.

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We know how to represent
connectivity in molecules in two

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dimensions.
We have been doing that already

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quite a bit this semester.
But we would like to know,

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if you know which atoms are
bonded to which.

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And then how does that
translate into the intricate

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three-dimensional structures
that molecules can have?

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Also, molecules can have color.
That is an important property

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of a molecular system.
In addition to which,

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molecules can be magnetic.
So, magnetism is one of the

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important properties of
molecular systems.

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And, as they aggregate into
extended solid materials,

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the way in which magnetic
molecules interact to produce

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macroscopic magnetic phenomena
is very much an area of interest

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to chemists.
People want to design molecular

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magnets in order to be able to
make materials that have desired

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properties that will be useful
to us in building things.

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And then, of course,
we have molecules that are

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redox-active.
And redox properties are very

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important.
We would like to be able to sit

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down with our computer and draw
out a structure.

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We would like to be able to pop
it into its optimum 3D geometry

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and find out what that is.
We would like to then know how

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easy is it to remove an electron
from that system or how easy it

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is to add an electron to that
system.

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Can we sit down and,
right from the start,

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use theory to predict
properties like the energies

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associated with electron
transfer to and from a molecular

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system?
That would be important if we

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are going to do what I talked
about last time in terms of

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inventing systems to transform
light energy into chemical

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energy in terms of the water
splitting reaction I discussed

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last time.
Also, molecules have acid-base

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chemistry.
And this is one of the most

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pervasive forms of chemical
reactivity that we can discuss.

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And so, we really have been
talking, so far in my lectures,

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about redox chemistry and
acid-base chemistry.

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And, as I go on,
during the next few lectures,

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we are going to be also talking
about properties like color and

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magnetism and 3D structure from
theoretical considerations.

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Acid-base is one type of
reactivity, but then also there

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are all kinds of different modes
of reactivity that can be

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classified in different ways.
Just to give you an example,

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there is a class of reactions
in organic chemistry called

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electrocyclic reactions.
We will be talking a little bit

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about reactions of that sort.
And then there is something

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that Professor Ceyer referred to
earlier in the semester as

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stability and the idea that this
can take on both kinetic and

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thermodynamic forms.
And so, we would want,

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from first principles,
to be able to sit down and

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consider a molecular system
composed of whatever elements

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from whatever part of the
periodic table it is composed,

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and just how these properties
follow naturally from the

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collection of elements that you
have put together into a

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molecule.
This is really chemistry and

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this is what we would like to be
able to do.

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In this next part,
what I would like to do is just

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spend a little time right here
in 1957 because that is when

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Ronald Gillespie published his
VSEPR theory.

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Ronald Gillespie is now kind of
in the twilight of his career.

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He has published on his
"Lifetime in Chemistry." And so,

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you can Google Ronald Gillespie
and find information about him

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and his VSEPR theory that will
go well beyond what you will

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find in that section devoted to
it in your textbook.

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This VSEPR theory,
it is an acronym.

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And it stands for Valance-Shell
Electron-Pair Repulsion theory.

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I tell you, the closer you get
to the board the less easily you

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can see the things on that
board.

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When we talk about VSEPR
theory, Ronald Gillespie

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formulates it simply in terms of
five basic considerations.

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The first of these,
you can tell very easily from

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the name, and that is that
electron pairs repel each other.

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And note here I am underlining
the word "pairs." And that is

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because we know that electrons
are all negatively charged

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particles.
And so they should all

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individually repel each other.
And they do,

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in fact.
But, based on the ideas of

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Lewis, you will see that
Gillespie is formulating this

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theory, taking the notion of the
electron pair as the fundamental

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unit to consider.
And he is saying that electron

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pairs are somehow organized in
space in a manner that they

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repel each other,
and they try to occupy

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different regions of space from
one another.

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And this is going to be useful
in terms of predicting the 3D

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structure of molecules,
and this is what this theory is

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devoted to.
And, two molecules can have

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single bonds,
or they can have double bonds,

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or they can have triple bonds
between pairs of atoms.

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Maybe we will see this semester
also that molecules can have

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quadruple bonds between pairs of
atoms if the orbitals are

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available for that.
But in the VSEPR theory,

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in this context multiple bonds
are treated like single bonds.

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You might suspect that that
type of approximation is a

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little crude and that it might
lead to certain guesses that

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might turn out not to be quite
right, but actually it is a

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useful enough approximation for
the prediction of the

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three-dimensional structures of
a lot of different molecules

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that we are actually going to
adopt for the purposes of our

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treatment of VSEPR theory.
Number three:

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if you have multiple central
atoms, --

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- they are treated
independently.

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And you will see what I mean by
that in a moment.

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You should see,
from that statement,

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that in the context of VSEPR
theory, we are going to be

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trying to identify central atoms
and peripheral atoms that are

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attached all to the central
atom.

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And there may be one or more
central atoms in a molecule that

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themselves are interconnected.
And, four, we have two kinds of

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electron pairs that we consider
in VSEPR theory.

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We have lone pairs,
and we have bond pairs.

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And lone pairs occupy more
space --

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-- than bond pairs do.

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And we will discuss the reason
for that in a moment.

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Finally, I want to give you
rule number five for 3D

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structure prediction using
VSEPR.

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That is that lone pairs are not
included in the description of

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the structure.
And you will see what I mean by

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that in a moment.
The idea is that the names that

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we give to different molecular
structures have to do with the

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3D arrangement in space of the
nuclei only and not the

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electrons.

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The lone pairs are not included
in the structure description.

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This is reserved for the
nuclei.

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Now, let's do a couple of
examples.

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And, in introducing these
examples, I will also be giving

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you some more of the shorthand
that is associated with VSEPR

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treatment of molecular
structure.

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Let's talk about this one here.

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I have drawn here a very simple
Lewis dot structure for a

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hydrogen sulfide molecule,
H2S.

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And for a molecule like this,
we really only have two

275
00:21:35 --> 00:21:40
possibilities for the structure
because you have three nuclei.

276
00:21:40 --> 00:21:44
And so, either they can all be
arranged -- we are going to

277
00:21:44 --> 00:21:48
assume that nuclei are not going
to fuse together and be one on

278
00:21:48 --> 00:21:52
top of another because those
positively charged nuclei do

279
00:21:52 --> 00:21:56
indeed repel each other very
successfully -- and so,

280
00:21:56 --> 00:22:02
therefore, we could either have
a linear or a bent structure.

281
00:22:02 --> 00:22:11


282
00:22:11 --> 00:22:19
And we can approach that
question using the VSEPR theory

283
00:22:19 --> 00:22:25
very nicely.
We start out by recognizing

284
00:22:25 --> 00:22:30
that we have two lone pairs.

285
00:22:30 --> 00:22:35


286
00:22:35 --> 00:22:39
That would be this one and this
one in the Lewis dot structure

287
00:22:39 --> 00:22:44
that are not interacting with
both hydrogen and sulfur nuclei.

288
00:22:44 --> 00:22:49
And we will call those E.
And then we have two bond

289
00:22:49 --> 00:22:50
pairs.

290
00:22:50 --> 00:22:58


291
00:22:58 --> 00:23:02
And we will refer to those each
as X.

292
00:23:02 --> 00:23:07
And then we have a single
central atom.

293
00:23:07 --> 00:23:15
We have a central sulfur atom.
And the central atom is usually

294
00:23:15 --> 00:23:22
given the label A.
And so, that means that we have

295
00:23:22 --> 00:23:30
a system here of the type AX two
E two.

296
00:23:30 --> 00:23:36
And if you look at the general
class of molecules of the type

297
00:23:36 --> 00:23:42
AX two E two,
it turns out that we can draw

298
00:23:42 --> 00:23:46
their structures this way.

299
00:23:46 --> 00:23:52


300
00:23:52 --> 00:23:55
What I am trying to indicate in
this structure is that one of

301
00:23:55 --> 00:23:59
these lone pairs is coming up
and out of the board this way

302
00:23:59 --> 00:24:04
and the other one is going back
behind the board the other way.

303
00:24:04 --> 00:24:08
These are our two bond pairs
that I am representing as lines.

304
00:24:08 --> 00:24:12
Bond pairs occupy less space
than lone pairs do,

305
00:24:12 --> 00:24:16
and that is because you have
two electrons interacting with

306
00:24:16 --> 00:24:20
two positively charged nuclei.
Whereas, in the case of a lone

307
00:24:20 --> 00:24:25
pair, you have a single pair of
electrons interacting only with

308
00:24:25 --> 00:24:29
a singly positively charged
nuclei.

309
00:24:29 --> 00:24:34
Two nuclei cause a greater
localization in space of bond

310
00:24:34 --> 00:24:37
pairs, as compared with lone
pairs.

311
00:24:37 --> 00:24:43
And the angle here that this
vector associated with the lone

312
00:24:43 --> 00:24:48
pair direction makes to the
hydrogen is something

313
00:24:48 --> 00:24:53
approximately tetrahedral.
Actually, probably larger than

314
00:24:53 --> 00:24:59
tetrahedral in this case because
the H-S-H angle is smaller than

315
00:24:59 --> 00:25:07
tetrahedral in H two S.
But this is an angle certainly

316
00:25:07 --> 00:25:12
greater than 90 degrees.
And that is one of our angles

317
00:25:12 --> 00:25:18
of the type E-A-X that describes
the interaction of a lone pair

318
00:25:18 --> 00:25:23
with a bond pair.
What we want to do is maximize

319
00:25:23 --> 00:25:28
those E-A-E and E-A-X angles
because, as I was saying

320
00:25:28 --> 00:25:33
earlier, a lone pair of
electrons requires a greater

321
00:25:33 --> 00:25:40
amount of space than does a bond
pair of electrons.

322
00:25:40 --> 00:25:43
The magnitude of the
repulsions, if we get back to

323
00:25:43 --> 00:25:46
the word repulsion in the name
of this theory,

324
00:25:46 --> 00:25:50
the greatest repulsions are
found between lone pairs.

325
00:25:50 --> 00:25:54
And so, next we have repulsions
between lone pairs and bond

326
00:25:54 --> 00:25:56
pairs.
And then, finally,

327
00:25:56 --> 00:26:00
the weakest repulsions in the
system will be between bond

328
00:26:00 --> 00:26:03
pairs.
And so, the best

329
00:26:03 --> 00:26:08
three-dimensional structure
given by this theory is that

330
00:26:08 --> 00:26:13
which minimizes these different
repulsions in the system.

331
00:26:13 --> 00:26:18
If we considered the linear
structure, then what we would

332
00:26:18 --> 00:26:23
have to do is put all the
electrons in the same plane of

333
00:26:23 --> 00:26:27
the molecule.
And these angles here would

334
00:26:27 --> 00:26:31
have to be 90.
And, overall,

335
00:26:31 --> 00:26:35
this would be a higher energy
structure because of the

336
00:26:35 --> 00:26:40
necessity of putting in an E
lone pair at 90 degrees to a

337
00:26:40 --> 00:26:44
couple of bond pairs and so on
around the molecule.

338
00:26:44 --> 00:26:49
Three dimensionally in space,
this quasi-tetrahedral geometry

339
00:26:49 --> 00:26:54
gets the four pairs of electrons
of the molecule the farthest

340
00:26:54 --> 00:27:00
apart in space and minimizes
electron pair repulsion.

341
00:27:00 --> 00:27:03
And that leads,
therefore, to a description of

342
00:27:03 --> 00:27:06
the structure as bent.
The structure is called bent

343
00:27:06 --> 00:27:11
rather than tetrahedral because
we include only the nuclei in

344
00:27:11 --> 00:27:15
the way that we refer to the
structure of the molecule.

345
00:27:15 --> 00:27:18
And we do not include those
electron pairs.

346
00:27:18 --> 00:27:22
Let me give you a feel for how
this looks.

347
00:27:22 --> 00:27:36


348
00:27:36 --> 00:27:40
And in this picture that I am
going to show you,

349
00:27:40 --> 00:27:46
which will recall to mind some
that I showed you in my first

350
00:27:46 --> 00:27:51
couple of lectures,
you will see that what I have

351
00:27:51 --> 00:27:57
here is an electron density
isosurface for the H two S

352
00:27:57 --> 00:28:02
molecule.
And you can see here one of the

353
00:28:02 --> 00:28:04
S-H bonds.
Here is another S-H bond.

354
00:28:04 --> 00:28:08
Over here is that region in
space where the electron density

355
00:28:08 --> 00:28:11
isosurface is associated with
lone pairs.

356
00:28:11 --> 00:28:15
And you can see that certainly
the electron density is a lot

357
00:28:15 --> 00:28:19
more tightly contracted in the
region between the sulfurs and

358
00:28:19 --> 00:28:23
the hydrogens than it is
elsewhere, where it bulges out.

359
00:28:23 --> 00:28:26
And you can see that effect of
getting the eight valance

360
00:28:26 --> 00:28:30
electrons in this molecule as
far apart from each other in

361
00:28:30 --> 00:28:34
space as you can.
And then, furthermore,

362
00:28:34 --> 00:28:39
the coloring in this diagram
represents the propensity of

363
00:28:39 --> 00:28:44
electrons at that point in space
to come together as pairs.

364
00:28:44 --> 00:28:49
In effect, that coloring is the
three-dimensional manifestation

365
00:28:49 --> 00:28:53
of the Pauli principle mapped
onto an electron density

366
00:28:53 --> 00:28:58
isosurface for the H two S
*molecule.

367
00:28:58 --> 00:29:03
This type of picture is very
nicely associated with the VSEPR

368
00:29:03 --> 00:29:06
representation of molecular
structure.

369
00:29:06 --> 00:29:10
And I am going to go through
another example.

370
00:29:10 --> 00:29:15
I am numbering this off so as
not to distract you with that

371
00:29:15 --> 00:29:17
picture.

372
00:29:17 --> 00:29:22


373
00:29:22 --> 00:29:30
This next example is SF four.

374
00:29:30 --> 00:29:42


375
00:29:42 --> 00:29:46
Let me draw out a Lewis dot
structure of this.

376
00:29:46 --> 00:30:04


377
00:30:04 --> 00:30:07
As you are looking at this
Lewis dot structure,

378
00:30:07 --> 00:30:11
one of the things you should do
is to see if the number of

379
00:30:11 --> 00:30:14
electrons that I am including in
my drawing is,

380
00:30:14 --> 00:30:18
in fact, the correct number of
valance electrons for this

381
00:30:18 --> 00:30:20
system.
And that is easy to do.

382
00:30:20 --> 00:30:25
You know that fluorine is in
Group 19 of the Periodic Table.

383
00:30:25 --> 00:30:30
You know that sulfur is in
Group 6 of the Periodic Table.

384
00:30:30 --> 00:30:34
And so you can quickly figure
out how many valance electrons

385
00:30:34 --> 00:30:37
there should be.
And, hopefully,

386
00:30:37 --> 00:30:41
I have indicated all of them on
my drawing, and no more than all

387
00:30:41 --> 00:30:45
of them.
What you might not like about a

388
00:30:45 --> 00:30:49
drawing like this is that while
each fluorine has been

389
00:30:49 --> 00:30:53
represented as an octet,
as being associated with eight

390
00:30:53 --> 00:30:57
electrons, four pairs of
electrons, the central sulfur

391
00:30:57 --> 00:31:00
atom seems to be,
in this drawing,

392
00:31:00 --> 00:31:04
associated with ten electrons,
--

393
00:31:04 --> 00:31:07
-- doesn't it?
That seems to be a violation of

394
00:31:07 --> 00:31:10
the octet rule.
And I will defer that

395
00:31:10 --> 00:31:13
observation for now,
but it is an interesting

396
00:31:13 --> 00:31:16
feature of this.
And, when you do yourself write

397
00:31:16 --> 00:31:21
down Lewis structures as a
prelude to subjecting them to

398
00:31:21 --> 00:31:25
the valence bond theory of
Pauling or to the valence shell

399
00:31:25 --> 00:31:29
electron pair repulsion theory
of Gillespie or the molecular

400
00:31:29 --> 00:31:34
orbital theory of Mulliken or
the density functional theory of

401
00:31:34 --> 00:31:37
Kohn and Pople,
you should be sticking with the

402
00:31:37 --> 00:31:42
basics here and making sure you
are working with the right

403
00:31:42 --> 00:31:47
number of valance electrons --
-- because your whole initial

404
00:31:47 --> 00:31:50
description of the molecular
system is going to revolve

405
00:31:50 --> 00:31:53
around the correct distribution
in space of this number of

406
00:31:53 --> 00:31:56
valance electrons that these
atoms that you are including in

407
00:31:56 --> 00:31:59
the molecule bring into play.
And then you are going to see

408
00:31:59 --> 00:32:02
if you can predict properties
based on that.

409
00:32:02 --> 00:32:12
That is what we do first.
And, in terms of bond pairs,

410
00:32:12 --> 00:32:20
based on that structure,
we have four.

411
00:32:20 --> 00:32:30
And, in terms of lone pairs,
we have one.

412
00:32:30 --> 00:32:37
Therefore, the type of system
that we are working with here is

413
00:32:37 --> 00:32:42
AX four E.
This is one of the possible

414
00:32:42 --> 00:32:49
types, when you have five units,
surrounding a central atom.

415
00:32:49 --> 00:32:56
And the most typical type of
geometry that arises when we

416
00:32:56 --> 00:33:04
have five units surrounding a
central atom is as follows.

417
00:33:04 --> 00:33:08
The atom A at the center is
intended to be here.

418
00:33:08 --> 00:33:13
And then I am going to draw
five balls.

419
00:33:13 --> 00:33:18
You can think of them as
representing either lone pairs

420
00:33:18 --> 00:33:23
or fluorine atoms.
And I am going to color two of

421
00:33:23 --> 00:33:29
them to distinguish them from
the others.

422
00:33:29 --> 00:33:33
And this structure is called
TBP.

423
00:33:33 --> 00:33:41
And that standards for trigonal
bipyramidal.

424
00:33:41 --> 00:33:47


425
00:33:47 --> 00:33:51
And the reason I have colored
this type different from that

426
00:33:51 --> 00:33:54
type is that in a trigonal
bipyramidal structure,

427
00:33:54 --> 00:33:56
there are two possible
environments,

428
00:33:56 --> 00:34:00
either for a lone pair of
electrons or for a bond pair of

429
00:34:00 --> 00:34:04
electrons.
You can have axial,

430
00:34:04 --> 00:34:10
and the axial position is
easily distinguished from the

431
00:34:10 --> 00:34:13
equatorial position --

432
00:34:13 --> 00:34:18


433
00:34:18 --> 00:34:23
-- by virtue of the fact that
an atom or a lone pair in the

434
00:34:23 --> 00:34:28
axial position makes 90 degree
angles, three of them to its

435
00:34:28 --> 00:34:31
neighbors.
Whereas, an atom in the

436
00:34:31 --> 00:34:35
equatorial position makes two 90
degree angles with respect to

437
00:34:35 --> 00:34:38
its neighbors.
It is three versus two that

438
00:34:38 --> 00:34:42
will help you distinguish axial
from equatorial.

439
00:34:42 --> 00:34:45
And understanding that about
this molecular geometry,

440
00:34:45 --> 00:34:49
you can see that for the SF
four molecule there are

441
00:34:49 --> 00:34:53
two possibilities.
Note that when I am drawing a

442
00:34:53 --> 00:34:57
wedge here that means that the
atom connected to the central

443
00:34:57 --> 00:35:01
atom is coming out of the plane
at us.

444
00:35:01 --> 00:35:06
And the dashed bond means that
it is going back behind the

445
00:35:06 --> 00:35:12
plane so that viewed from the
top, this thing would look

446
00:35:12 --> 00:35:17
simply like a Mercedes Benz
symbol, just to understand that

447
00:35:17 --> 00:35:23
about the wedges and dash
nomenclature on these systems.

448
00:35:23 --> 00:35:29
And so, the two possibilities
that we have for our system is,

449
00:35:29 --> 00:35:35
we can either put our lone pair
E up here and our four bond

450
00:35:35 --> 00:35:41
pairs X down here.
Or, we can have the lone pair

451
00:35:41 --> 00:35:47
equatorial and our bond pairs,
two of them axial and two of

452
00:35:47 --> 00:35:51
them equatorial.
As in the case of H two S,

453
00:35:51 --> 00:35:57
we had two structures
to distinguish between linear

454
00:35:57 --> 00:36:01
and bent.
Over here, we have a structure

455
00:36:01 --> 00:36:06
with an equatorial lone pair or
with an axial lone pair for SF

456
00:36:06 --> 00:36:09
four.
And when you look at the top

457
00:36:09 --> 00:36:14
one and realize that you have
only two of these very bad lone

458
00:36:14 --> 00:36:17
pair-bond pair contacts at 90
degrees, whereas,

459
00:36:17 --> 00:36:22
on the bottom one we have three
of these bad lone pair-bond pair

460
00:36:22 --> 00:36:27
contacts at 90 degrees,
you might be inclined to pick,

461
00:36:27 --> 00:36:30
in fact, this top one.

462
00:36:30 --> 00:36:35


463
00:36:35 --> 00:36:39
And that would be right because
it minimizes the number of the

464
00:36:39 --> 00:36:41
worst kind of repulsions.
In this case,

465
00:36:41 --> 00:36:43
lone pair bond pair at 90
degrees.

466
00:36:43 --> 00:36:48
And when we give this structure
a name, we are not going to call

467
00:36:48 --> 00:36:52
it trigonal bipyramidal because
we do not include the lone pair.

468
00:36:52 --> 00:36:56
We only include the positions
of the nuclei in the naming of

469
00:36:56 --> 00:37:01
the molecular structure.
This one is called a seesaw.

470
00:37:01 --> 00:37:06


471
00:37:06 --> 00:37:11
Some of you may be aware that
there is a piece of playground

472
00:37:11 --> 00:37:17
equipment known as a seesaw.
You probably don't get a chance

473
00:37:17 --> 00:37:20
to play on them anymore very
much.

474
00:37:20 --> 00:37:23
Neither do I.
This is more fun,

475
00:37:23 --> 00:37:27
anyway.
And what I am showing you now

476
00:37:27 --> 00:37:32
on these side screens is a
picture of the electron density

477
00:37:32 --> 00:37:38
isosurface for the SF four
molecule.

478
00:37:38 --> 00:37:41
And hopefully,
you can see that it looks like

479
00:37:41 --> 00:37:43
a seesaw.
These two fluorines down here

480
00:37:43 --> 00:37:48
would be the legs of the seesaw.
And then you would sit either

481
00:37:48 --> 00:37:52
here or here and then lean
forward and put your hands on

482
00:37:52 --> 00:37:55
the lone pair and then rock up
and down somehow.

483
00:37:55 --> 00:37:58
I don't know.
Anyway.

484
00:37:58 --> 00:38:01
In this system,
you should be able to see that

485
00:38:01 --> 00:38:04
the lone pair on the sulfur,
which is here,

486
00:38:04 --> 00:38:08
is definitely in this
equatorial position,

487
00:38:08 --> 00:38:12
so the electro-density
isosurface has a nice dark-blue

488
00:38:12 --> 00:38:16
color where we find that lone
pair on the sulfur.

489
00:38:16 --> 00:38:20
And then the four flourines are
organized, according to the

490
00:38:20 --> 00:38:25
predictions of VSEPR theory,
with these 90 degree angles to

491
00:38:25 --> 00:38:30
the flourines that are oriented
in the axial.

492
00:38:30 --> 00:38:35
The two flourines are axial.
And then here is our two

493
00:38:35 --> 00:38:40
equatorial flourines here
spinning around in the belt of

494
00:38:40 --> 00:38:43
this system.
We could also say that you

495
00:38:43 --> 00:38:49
would be sitting on the axial
positions if you were going to

496
00:38:49 --> 00:38:55
ride on this particular seesaw.
Now, I would like to proceed in

497
00:38:55.659 --> 1954.
time briefly back from '57 to

498
1954. --> 00:39:00


499
00:39:00 --> 00:39:02
Because we need to discuss some
of the issues of the valance

500
00:39:02 --> 00:39:05
bond theory that Pauling brought
into the quantum mechanical

501
00:39:05 --> 00:39:07
treatment of molecules.

502
00:39:07 --> 00:39:36


503
00:39:36 --> 00:39:42
What I am representing here are
a couple of hydrogen atoms 1S

504
00:39:42 --> 00:39:47
orbitals at a distance.
We have (H)A 1s and we have the

505
00:39:47 --> 00:39:51
1s of hydrogen labeled B.

506
00:39:51 --> 00:39:58
And we are going to say that at
some infinite separation between

507
00:39:58 --> 00:40:04
the two, they would not really
know much about the spin of the

508
00:40:04 --> 00:40:09
electron on the partner
hydrogen.

509
00:40:09 --> 00:40:13
But as we bring them close
together, the spin is going to

510
00:40:13 --> 00:40:17
become very important.
And that is by virtue of the

511
00:40:17 --> 00:40:20
Pauli principle.
And you should remember that

512
00:40:20 --> 00:40:25
one of the ways of formulating
the Pauli principle is that no

513
00:40:25 --> 00:40:29
two electrons in a quantum
mechanical system can have the

514
00:40:29 --> 00:40:33
same set of four quantum
numbers.

515
00:40:33 --> 00:40:36
As these two hydrogens get
close together,

516
00:40:36 --> 00:40:42
the stable situation for the
electrons coming from the two

517
00:40:42 --> 00:40:46
have opposite spin,
so I am drawing with spin-up

518
00:40:46 --> 00:40:50
and one with spin-down.
And then you are going to

519
00:40:50 --> 00:40:56
notice that here in the center
of our H two molecule,

520
00:40:56 --> 00:41:02
now, is a region of overlap and
of constructive interference of

521
00:41:02 --> 00:41:08
those 1s-orbital wave functions
from the two sides.

522
00:41:08 --> 00:41:12
In this representation of the
ground state of the molecule,

523
00:41:12 --> 00:41:14
the Pauli principle is
satisfied.

524
00:41:14 --> 00:41:18
And we can put this pair of
electrons into an orbital.

525
00:41:18 --> 00:41:22
And when that orbital is
represented that way,

526
00:41:22 --> 00:41:25
it is cylindrically symmetric.

527
00:41:25 --> 00:41:35


528
00:41:35 --> 00:41:37
And we call that a sigma bond.

529
00:41:37 --> 00:41:46


530
00:41:46 --> 00:41:50
In chemistry we talk often
about the properties of sigma

531
00:41:50 --> 00:41:53
bonds.
We talk about also the

532
00:41:53 --> 00:41:56
properties of things called pi
bonds.

533
00:41:56 --> 00:42:00
And we can even have delta
bonds.

534
00:42:00 --> 00:42:07
Just as I was talking about
bond multiplicity a moment ago

535
00:42:07 --> 00:42:13
with reference to VSEPR,
let me give you here an

536
00:42:13 --> 00:42:18
x,y-plane.
I am drawing in perspective an

537
00:42:18 --> 00:42:23
x,y-plane.
And in this x,y-plane we are

538
00:42:23 --> 00:42:30
going to have,
actually, six atomic nuclei.

539
00:42:30 --> 00:42:35
And our z direction is
perpendicular to this plane

540
00:42:35 --> 00:42:40
drawn in perspective.
And I am drawing in here the

541
00:42:40 --> 00:42:46
positions of four hydrogen and
two carbon nuclei.

542
00:42:46 --> 00:42:52
And when I draw them in like
that, you are going to see that

543
00:42:52 --> 00:42:58
all the valence orbitals of this
system, except for two,

544
00:42:58 --> 00:43:04
lie in that x,y-plane.
And the two that lie out of

545
00:43:04 --> 00:43:08
that x,y-plane,
I will show you here,

546
00:43:08 --> 00:43:14
are p orbitals that go above
and below the plane.

547
00:43:14 --> 00:43:20
And I am shading in the
negative phase lobe of these pz

548
00:43:20 --> 00:43:24
orbitals.
This is pz from carbon A and

549
00:43:24 --> 00:43:30
this is a pz from carbon B.
And you can see that these are

550
00:43:30 --> 00:43:35
oriented in a side-on fashion,
so that the overlap area that

551
00:43:35 --> 00:43:40
can occur is a side-to-side
overlap of two neighboring P

552
00:43:40 --> 00:43:44
orbitals, like this.
And the distinguishing feature

553
00:43:44 --> 00:43:49
here, as compared to my
description of the sigma bond

554
00:43:49 --> 00:43:55
over there, is that it is not
cylindrically symmetric.

555
00:43:55 --> 00:44:01
This bond has a nodal surface,
which is the x,y-plane,

556
00:44:01 --> 00:44:09
where the phase changes as you
pass from above that plane to

557
00:44:09 --> 00:44:14
below that plane.
We have a nodal surface,

558
00:44:14 --> 00:44:19
a node containing the
internuclear axis.

559
00:44:19 --> 00:44:27
The type of bond that I have
drawn there is distinct from a

560
00:44:27 --> 00:44:32
sigma bond.
It is a pi bond.

561
00:44:32 --> 00:44:37


562
00:44:37 --> 00:44:39
That bond over there,
the sigma bond,

563
00:44:39 --> 00:44:42
has no nodal surfaces passing
through the internuclear axis.

564
00:44:42 --> 00:44:46
If I draw the internuclear axis
here, you can see that it has

565
00:44:46 --> 00:44:50
the same phase no matter where
you are with respect to that

566
00:44:50 --> 00:44:52
axis.
Plus, plus, plus everywhere.

567
00:44:52 --> 00:44:55
And here, if these lobes of
these two pz orbitals are

568
00:44:55 --> 00:44:58
considered to be positive in the
positive z direction,

569
00:44:58 --> 00:45:02
then as we go this way,
we pass through the x,y-plane

570
00:45:02 --> 00:45:06
and get down into negative z.
We now have negative phase,

571
00:45:06 --> 00:45:10
as indicated by the purple
shading down here.

572
00:45:10 --> 00:45:14
The fact that that happens only
once with respect to this

573
00:45:14 --> 00:45:18
internuclear axis is what tells
us that it is a pi bond.

574
00:45:18 --> 00:45:22
If there were two such nodal
surfaces, then we would have a

575
00:45:22 --> 00:45:24
delta bond, and so on.
And next time,

576
00:45:24 --> 00:45:29
we are going to start talking
about the progression from these

577
00:45:29 --> 00:45:33
ideas onto hybridization.
And then from there onto

578
00:45:33.743 --> 45:36
molecular orbital theory.