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Today I would like to start by discussing a timeline.
And you will see in a moment what this timeline has to do
with. It is obviously only a partial
timeline. But let's start here in 1916,
as we have done this semester, by talking about the Lewis
theory of electronic structure.
And his electron pair theory is something we are going to come
back to a couple of times during lecture today.
Let's move on to 1954. 1954 was an important year in
electronic structure theory, because in that year there was
awarded, to Linus Pauling, the Nobel Prize in chemistry.
Let me write down Pauling here.
And if you are interested in knowing something about what
Pauling was awarded the Nobel Prize in chemistry for,
I will show you over here on the side boards.
What you are going to see here, if you read this citation for
Linus Carl Pauling in 1954 for the Nobel Prize in chemistry,
his prize was awarded principally for his
contributions to our understanding of the nature of
the chemical bond. If you think back to the
elegant title of the paper by Lewis that we started out our
discussion of acid-base theory with, it was a paper entitled
"The Atom and the Molecule." And now we have gotten to Pauling,
in 1954, who is being awarded a Nobel Prize in chemistry for the
nature of the chemical bond. That also is the title of a
very famous chemistry book by Linus Pauling entitled "The
Nature of the Chemical Bond." That was published by Cornell
University Press originally, because it stemmed from his set
of lectures at Cornell, the Baker lectures,
in the 1950s. As we talk about electronic
structure theory, I would like you to keep in
mind the way in which these different geniuses were
approaching the problem, a problem that we are going to
launch in on today and spend the next few lectures on.
We will move up here to 1966.
In 1966 there was awarded a Nobel Prize to Mulliken.
Not to be confused with Milliken.
We are going from 1954 to 1966.
You are going to find, as you explore the Nobel Prize
website, that there are a lot of informational links on these
people. You can go and read
biographies. You can read some of their
writings. In the case of Linus Pauling,
you have links to all the pages of all of his research
notebooks, spanning more than 60 years of research.
Those are pretty interesting supportive materials.
In the case of Robert S. Mulliken, he is being cited for
his contributions to the molecular orbital method,
which we will also call the molecular orbital theory.
We have the Lewis theory. We have, in the case of
Pauling, I am going to say the nature of the chemical bond,
described in terms of valance bond theory.
We will come back to that in a moment.
And then, in the case of Mulliken, we have a Nobel Prize
for molecular orbital theory. And I just would like to show
you something kind of neat, here.
This has to do with the fact that if I go to the section
labeled other resources, I can click on MIT digital
thesis library. Then I can choose a page of
Mulliken's thesis to display. And that is because Robert S.
Mulliken was Course 5 1917. Let's hear it for Course 5
chemistry. [APPLAUSE] Robert S.
Mulliken was one of you guys, and he graduated in 1917.
His undergraduate chemistry thesis at MIT was entitled "The
Effective Structure on the Activity of the Hydroxyl Group
in Alcohols." Submitted by Robert S.
Mulliken. There is his signature.
Isn't it cool to have your undergraduate thesis linked in
from the Nobel Prize website? Robert S.
Mulliken for molecular orbital theory.
And you can see, even as you read his
undergraduate thesis, he was talking about the effect
of structure on the activity of the hydroxyl group.
He had the idea that if you knew something about the
structure of the molecule, even back then,
you could make predictions about the properties of the
molecule. And that is what we really want
to be able to do in chemistry, because we want to be able to
control function as much as possible.
I will take that way for now and we'll come back in a moment
because I am going to mention to you that in 1998 there was
another Nobel Prize given for advances in our understanding of
electronic structure of molecules.
And this one was a shared prize, rather than these three
other ones that I mentioned. Well, two others.
Lewis was neglected from that category, unfortunately.
In 1998 Kohn and Pople shared the Nobel Prize for furthering
our understanding of how to describe electronic structure of
molecules. And this is a theory that we
are not going to be talking about too much explicitly here
in 5.112 this semester, but if you go on in chemistry,
you will be exposed to it more and more.
It is called density functional theory.
It is one of the most expedient ways to use computers to get
electronic structure information about molecules.
And so, that method has become extremely important.
And I will just show you a little piece of information from
that website, so we go to 1998.
And, under the John Pople section, I am going to go to
interview. He has given an interview on
different topics relating to his involvement in chemistry.
One short piece of that interview is entitled "Interest
in Quantum Mechanics and Development of Computer
Techniques." We are going to take a look at
that and hopefully, if the audio and video are both
working, you will be able to see John Pople talking a little bit
about this important area of chemistry.
We just don't have time for fixing audio/video problems in
real-time here, unfortunately.
Therefore, what I would like you to do is go to
NobelPrize.org, Chemistry Laureates on Pople,
and actually watch that five-minute segment of his
interview that has to do with his feelings about electronic
structure theory and advice to students on that topic.
And I will summarize his comments here --
-- by saying that the goal of studying electronic structure of
molecules is to try to get predictive power about molecular
systems. And we want predictive power in
terms of the 3D structure of molecules.
We know how to represent connectivity in molecules in two
dimensions. We have been doing that already
quite a bit this semester. But we would like to know,
if you know which atoms are bonded to which.
And then how does that translate into the intricate
three-dimensional structures that molecules can have?
Also, molecules can have color. That is an important property
of a molecular system. In addition to which,
molecules can be magnetic. So, magnetism is one of the
important properties of molecular systems.
And, as they aggregate into extended solid materials,
the way in which magnetic molecules interact to produce
macroscopic magnetic phenomena is very much an area of interest
to chemists. People want to design molecular
magnets in order to be able to make materials that have desired
properties that will be useful to us in building things.
And then, of course, we have molecules that are
redox-active. And redox properties are very
important. We would like to be able to sit
down with our computer and draw out a structure.
We would like to be able to pop it into its optimum 3D geometry
and find out what that is. We would like to then know how
easy is it to remove an electron from that system or how easy it
is to add an electron to that system.
Can we sit down and, right from the start,
use theory to predict properties like the energies
associated with electron transfer to and from a molecular
system? That would be important if we
are going to do what I talked about last time in terms of
inventing systems to transform light energy into chemical
energy in terms of the water splitting reaction I discussed
last time. Also, molecules have acid-base
chemistry. And this is one of the most
pervasive forms of chemical reactivity that we can discuss.
And so, we really have been talking, so far in my lectures,
about redox chemistry and acid-base chemistry.
And, as I go on, during the next few lectures,
we are going to be also talking about properties like color and
magnetism and 3D structure from theoretical considerations.
Acid-base is one type of reactivity, but then also there
are all kinds of different modes of reactivity that can be
classified in different ways. Just to give you an example,
there is a class of reactions in organic chemistry called
electrocyclic reactions. We will be talking a little bit
about reactions of that sort. And then there is something
that Professor Ceyer referred to earlier in the semester as
stability and the idea that this can take on both kinetic and
thermodynamic forms. And so, we would want,
from first principles, to be able to sit down and
consider a molecular system composed of whatever elements
from whatever part of the periodic table it is composed,
and just how these properties follow naturally from the
collection of elements that you have put together into a
molecule. This is really chemistry and
this is what we would like to be able to do.
In this next part, what I would like to do is just
spend a little time right here in 1957 because that is when
Ronald Gillespie published his VSEPR theory.
Ronald Gillespie is now kind of in the twilight of his career.
He has published on his "Lifetime in Chemistry." And so,
you can Google Ronald Gillespie and find information about him
and his VSEPR theory that will go well beyond what you will
find in that section devoted to it in your textbook.
This VSEPR theory, it is an acronym.
And it stands for Valance-Shell Electron-Pair Repulsion theory.
I tell you, the closer you get to the board the less easily you
can see the things on that board.
When we talk about VSEPR theory, Ronald Gillespie
formulates it simply in terms of five basic considerations.
The first of these, you can tell very easily from
the name, and that is that electron pairs repel each other.
And note here I am underlining the word "pairs." And that is
because we know that electrons are all negatively charged
particles. And so they should all
individually repel each other. And they do,
in fact. But, based on the ideas of
Lewis, you will see that Gillespie is formulating this
theory, taking the notion of the electron pair as the fundamental
unit to consider. And he is saying that electron
pairs are somehow organized in space in a manner that they
repel each other, and they try to occupy
different regions of space from one another.
And this is going to be useful in terms of predicting the 3D
structure of molecules, and this is what this theory is
devoted to. And, two molecules can have
single bonds, or they can have double bonds,
or they can have triple bonds between pairs of atoms.
Maybe we will see this semester also that molecules can have
quadruple bonds between pairs of atoms if the orbitals are
available for that. But in the VSEPR theory,
in this context multiple bonds are treated like single bonds.
You might suspect that that type of approximation is a
little crude and that it might lead to certain guesses that
might turn out not to be quite right, but actually it is a
useful enough approximation for the prediction of the
three-dimensional structures of a lot of different molecules
that we are actually going to adopt for the purposes of our
treatment of VSEPR theory. Number three:
if you have multiple central atoms, --
- they are treated independently.
And you will see what I mean by that in a moment.
You should see, from that statement,
that in the context of VSEPR theory, we are going to be
trying to identify central atoms and peripheral atoms that are
attached all to the central atom.
And there may be one or more central atoms in a molecule that
themselves are interconnected. And, four, we have two kinds of
electron pairs that we consider in VSEPR theory.
We have lone pairs, and we have bond pairs.
And lone pairs occupy more space --
-- than bond pairs do.
And we will discuss the reason for that in a moment.
Finally, I want to give you rule number five for 3D
structure prediction using VSEPR.
That is that lone pairs are not included in the description of
the structure. And you will see what I mean by
that in a moment. The idea is that the names that
we give to different molecular structures have to do with the
3D arrangement in space of the nuclei only and not the
electrons.
The lone pairs are not included in the structure description.
This is reserved for the nuclei.
Now, let's do a couple of examples.
And, in introducing these examples, I will also be giving
you some more of the shorthand that is associated with VSEPR
treatment of molecular structure.
Let's talk about this one here.
I have drawn here a very simple Lewis dot structure for a
hydrogen sulfide molecule, H2S.
And for a molecule like this, we really only have two
possibilities for the structure because you have three nuclei.
And so, either they can all be arranged -- we are going to
assume that nuclei are not going to fuse together and be one on
top of another because those positively charged nuclei do
indeed repel each other very successfully -- and so,
therefore, we could either have a linear or a bent structure.
And we can approach that question using the VSEPR theory
very nicely. We start out by recognizing
that we have two lone pairs.
That would be this one and this one in the Lewis dot structure
that are not interacting with both hydrogen and sulfur nuclei.
And we will call those E. And then we have two bond
pairs.
And we will refer to those each as X.
And then we have a single central atom.
We have a central sulfur atom. And the central atom is usually
given the label A. And so, that means that we have
a system here of the type AX two E two.
And if you look at the general class of molecules of the type
AX two E two, it turns out that we can draw
their structures this way.
What I am trying to indicate in this structure is that one of
these lone pairs is coming up and out of the board this way
and the other one is going back behind the board the other way.
These are our two bond pairs that I am representing as lines.
Bond pairs occupy less space than lone pairs do,
and that is because you have two electrons interacting with
two positively charged nuclei. Whereas, in the case of a lone
pair, you have a single pair of electrons interacting only with
a singly positively charged nuclei.
Two nuclei cause a greater localization in space of bond
pairs, as compared with lone pairs.
And the angle here that this vector associated with the lone
pair direction makes to the hydrogen is something
approximately tetrahedral. Actually, probably larger than
tetrahedral in this case because the H-S-H angle is smaller than
tetrahedral in H two S. But this is an angle certainly
greater than 90 degrees. And that is one of our angles
of the type E-A-X that describes the interaction of a lone pair
with a bond pair. What we want to do is maximize
those E-A-E and E-A-X angles because, as I was saying
earlier, a lone pair of electrons requires a greater
amount of space than does a bond pair of electrons.
The magnitude of the repulsions, if we get back to
the word repulsion in the name of this theory,
the greatest repulsions are found between lone pairs.
And so, next we have repulsions between lone pairs and bond
pairs. And then, finally,
the weakest repulsions in the system will be between bond
pairs. And so, the best
three-dimensional structure given by this theory is that
which minimizes these different repulsions in the system.
If we considered the linear structure, then what we would
have to do is put all the electrons in the same plane of
the molecule. And these angles here would
have to be 90. And, overall,
this would be a higher energy structure because of the
necessity of putting in an E lone pair at 90 degrees to a
couple of bond pairs and so on around the molecule.
Three dimensionally in space, this quasi-tetrahedral geometry
gets the four pairs of electrons of the molecule the farthest
apart in space and minimizes electron pair repulsion.
And that leads, therefore, to a description of
the structure as bent. The structure is called bent
rather than tetrahedral because we include only the nuclei in
the way that we refer to the structure of the molecule.
And we do not include those electron pairs.
Let me give you a feel for how this looks.
And in this picture that I am going to show you,
which will recall to mind some that I showed you in my first
couple of lectures, you will see that what I have
here is an electron density isosurface for the H two S
molecule. And you can see here one of the
S-H bonds. Here is another S-H bond.
Over here is that region in space where the electron density
isosurface is associated with lone pairs.
And you can see that certainly the electron density is a lot
more tightly contracted in the region between the sulfurs and
the hydrogens than it is elsewhere, where it bulges out.
And you can see that effect of getting the eight valance
electrons in this molecule as far apart from each other in
space as you can. And then, furthermore,
the coloring in this diagram represents the propensity of
electrons at that point in space to come together as pairs.
In effect, that coloring is the three-dimensional manifestation
of the Pauli principle mapped onto an electron density
isosurface for the H two S *molecule.
This type of picture is very nicely associated with the VSEPR
representation of molecular structure.
And I am going to go through another example.
I am numbering this off so as not to distract you with that
picture.
This next example is SF four.
Let me draw out a Lewis dot structure of this.
As you are looking at this Lewis dot structure,
one of the things you should do is to see if the number of
electrons that I am including in my drawing is,
in fact, the correct number of valance electrons for this
system. And that is easy to do.
You know that fluorine is in Group 19 of the Periodic Table.
You know that sulfur is in Group 6 of the Periodic Table.
And so you can quickly figure out how many valance electrons
there should be. And, hopefully,
I have indicated all of them on my drawing, and no more than all
of them. What you might not like about a
drawing like this is that while each fluorine has been
represented as an octet, as being associated with eight
electrons, four pairs of electrons, the central sulfur
atom seems to be, in this drawing,
associated with ten electrons, --
-- doesn't it? That seems to be a violation of
the octet rule. And I will defer that
observation for now, but it is an interesting
feature of this. And, when you do yourself write
down Lewis structures as a prelude to subjecting them to
the valence bond theory of Pauling or to the valence shell
electron pair repulsion theory of Gillespie or the molecular
orbital theory of Mulliken or the density functional theory of
Kohn and Pople, you should be sticking with the
basics here and making sure you are working with the right
number of valance electrons -- -- because your whole initial
description of the molecular system is going to revolve
around the correct distribution in space of this number of
valance electrons that these atoms that you are including in
the molecule bring into play. And then you are going to see
if you can predict properties based on that.
That is what we do first. And, in terms of bond pairs,
based on that structure, we have four.
And, in terms of lone pairs, we have one.
Therefore, the type of system that we are working with here is
AX four E. This is one of the possible
types, when you have five units, surrounding a central atom.
And the most typical type of geometry that arises when we
have five units surrounding a central atom is as follows.
The atom A at the center is intended to be here.
And then I am going to draw five balls.
You can think of them as representing either lone pairs
or fluorine atoms. And I am going to color two of
them to distinguish them from the others.
And this structure is called TBP.
And that standards for trigonal bipyramidal.
And the reason I have colored this type different from that
type is that in a trigonal bipyramidal structure,
there are two possible environments,
either for a lone pair of electrons or for a bond pair of
electrons. You can have axial,
and the axial position is easily distinguished from the
equatorial position --
-- by virtue of the fact that an atom or a lone pair in the
axial position makes 90 degree angles, three of them to its
neighbors. Whereas, an atom in the
equatorial position makes two 90 degree angles with respect to
its neighbors. It is three versus two that
will help you distinguish axial from equatorial.
And understanding that about this molecular geometry,
you can see that for the SF four molecule there are
two possibilities. Note that when I am drawing a
wedge here that means that the atom connected to the central
atom is coming out of the plane at us.
And the dashed bond means that it is going back behind the
plane so that viewed from the top, this thing would look
simply like a Mercedes Benz symbol, just to understand that
about the wedges and dash nomenclature on these systems.
And so, the two possibilities that we have for our system is,
we can either put our lone pair E up here and our four bond
pairs X down here. Or, we can have the lone pair
equatorial and our bond pairs, two of them axial and two of
them equatorial. As in the case of H two S,
we had two structures to distinguish between linear
and bent. Over here, we have a structure
with an equatorial lone pair or with an axial lone pair for SF
four. And when you look at the top
one and realize that you have only two of these very bad lone
pair-bond pair contacts at 90 degrees, whereas,
on the bottom one we have three of these bad lone pair-bond pair
contacts at 90 degrees, you might be inclined to pick,
in fact, this top one.
And that would be right because it minimizes the number of the
worst kind of repulsions. In this case,
lone pair bond pair at 90 degrees.
And when we give this structure a name, we are not going to call
it trigonal bipyramidal because we do not include the lone pair.
We only include the positions of the nuclei in the naming of
the molecular structure. This one is called a seesaw.
Some of you may be aware that there is a piece of playground
equipment known as a seesaw. You probably don't get a chance
to play on them anymore very much.
Neither do I. This is more fun,
anyway. And what I am showing you now
on these side screens is a picture of the electron density
isosurface for the SF four molecule.
And hopefully, you can see that it looks like
a seesaw. These two fluorines down here
would be the legs of the seesaw. And then you would sit either
here or here and then lean forward and put your hands on
the lone pair and then rock up and down somehow.
I don't know. Anyway.
In this system, you should be able to see that
the lone pair on the sulfur, which is here,
is definitely in this equatorial position,
so the electro-density isosurface has a nice dark-blue
color where we find that lone pair on the sulfur.
And then the four flourines are organized, according to the
predictions of VSEPR theory, with these 90 degree angles to
the flourines that are oriented in the axial.
The two flourines are axial. And then here is our two
equatorial flourines here spinning around in the belt of
this system. We could also say that you
would be sitting on the axial positions if you were going to
ride on this particular seesaw. Now, I would like to proceed in
time briefly back from '57 to
Because we need to discuss some of the issues of the valance
bond theory that Pauling brought into the quantum mechanical
treatment of molecules.
What I am representing here are a couple of hydrogen atoms 1S
orbitals at a distance. We have (H)A 1s and we have the
1s of hydrogen labeled B.
And we are going to say that at some infinite separation between
the two, they would not really know much about the spin of the
electron on the partner hydrogen.
But as we bring them close together, the spin is going to
become very important. And that is by virtue of the
Pauli principle. And you should remember that
one of the ways of formulating the Pauli principle is that no
two electrons in a quantum mechanical system can have the
same set of four quantum numbers.
As these two hydrogens get close together,
the stable situation for the electrons coming from the two
have opposite spin, so I am drawing with spin-up
and one with spin-down. And then you are going to
notice that here in the center of our H two molecule,
now, is a region of overlap and of constructive interference of
those 1s-orbital wave functions from the two sides.
In this representation of the ground state of the molecule,
the Pauli principle is satisfied.
And we can put this pair of electrons into an orbital.
And when that orbital is represented that way,
it is cylindrically symmetric.
And we call that a sigma bond.
In chemistry we talk often about the properties of sigma
bonds. We talk about also the
properties of things called pi bonds.
And we can even have delta bonds.
Just as I was talking about bond multiplicity a moment ago
with reference to VSEPR, let me give you here an
x,y-plane. I am drawing in perspective an
x,y-plane. And in this x,y-plane we are
going to have, actually, six atomic nuclei.
And our z direction is perpendicular to this plane
drawn in perspective. And I am drawing in here the
positions of four hydrogen and two carbon nuclei.
And when I draw them in like that, you are going to see that
all the valence orbitals of this system, except for two,
lie in that x,y-plane. And the two that lie out of
that x,y-plane, I will show you here,
are p orbitals that go above and below the plane.
And I am shading in the negative phase lobe of these pz
orbitals. This is pz from carbon A and
this is a pz from carbon B. And you can see that these are
oriented in a side-on fashion, so that the overlap area that
can occur is a side-to-side overlap of two neighboring P
orbitals, like this. And the distinguishing feature
here, as compared to my description of the sigma bond
over there, is that it is not cylindrically symmetric.
This bond has a nodal surface, which is the x,y-plane,
where the phase changes as you pass from above that plane to
below that plane. We have a nodal surface,
a node containing the internuclear axis.
The type of bond that I have drawn there is distinct from a
sigma bond. It is a pi bond.
That bond over there, the sigma bond,
has no nodal surfaces passing through the internuclear axis.
If I draw the internuclear axis here, you can see that it has
the same phase no matter where you are with respect to that
axis. Plus, plus, plus everywhere.
And here, if these lobes of these two pz orbitals are
considered to be positive in the positive z direction,
then as we go this way, we pass through the x,y-plane
and get down into negative z. We now have negative phase,
as indicated by the purple shading down here.
The fact that that happens only once with respect to this
internuclear axis is what tells us that it is a pi bond.
If there were two such nodal surfaces, then we would have a
delta bond, and so on. And next time,
we are going to start talking about the progression from these
ideas onto hybridization. And then from there onto
molecular orbital theory.