WEBVTT

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Prof: So this is where
we were at the end last time,

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trying to decide when a high
HOMO, or a low LUMO,

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is unusual in its energy;
because, as the world is,

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things like to be at low
energy.

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We'll talk about that later,
why that's so.

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But that means that electrons
tend to be in the occupied,

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the low -- occupy the
low-energy orbitals and not the

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high-energy orbitals.

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So that empty orbitals are
almost always higher than any

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occupied orbitals.

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So if you want to get good
energy match,

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and therefore mixing,
and therefore bonding,

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the occupied orbital that
you're interested in must be

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unusually high,
and the vacant orbital must be

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unusually low.

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So the task we have is to
recognize what orbitals should

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be unusually high and what ones
should be unusually low,

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and if we can find the unusual
ones,

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then we'll know what's
reactive, be able to identify

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functional groups.

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Okay, so unusual,
compared to what?

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Compared to normal occupied and
vacant orbitals.

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That is, in organic chemistry,
or in most kinds of chemistry

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actually, carbon-carbon,
carbon-hydrogen bonds are

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occupied orbitals;
not unusually high,

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they're our standard of usual.

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And the antibonds,
corresponding antibonds are

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unusual -- are the usual vacant
orbitals.

01:36.849 --> 01:40.989
So what can make things
unusually low or unusually high?

01:40.989 --> 01:43.269
When the valence-shell orbitals
that,

01:43.269 --> 01:45.559
if they bonded,
would go down and up,

01:45.560 --> 01:48.080
don't bond with anything,
don't mix with anything,

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then they'll be unusual.

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Second, if the orbitals don't
overlap, then they don't go down

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and go up.

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Third, if you have an unusual
atomic orbital.

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These are made of carbon and
hydrogen, going down.

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But if you start with something
that's unusual,

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unusually high or unusually
low, then the things that come

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from it will be unusually high
or unusually low.

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And finally, electrical charge.

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So right at the end last time
we were looking at the first

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example: unmixed valence-shell
atomic orbitals.

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So we saw that the simplest of
all acids, H^+,

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of course is unusually -- if it
were occupied,

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it would be unusually high for
an occupied orbital.

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Right?

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Because it hasn't gone down.

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But it's vacant,
and it's unusually low,

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for a vacant orbital,
because it hasn't gone up.

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And so on with these others:
an unshared pair on nitrogen;

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or a little less so on oxygen.

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A vacant orbital on boron
that's not bonding with anything

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is an unusually low LUMO;
even though orbitals on boron

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are not unusually low,
because the nuclear charge

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isn't very big for something
that's using the second,

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n=2, quantum level
orbitals,

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valence orbitals.

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It's an unusually low nuclear
charge for that.

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So the orbitals are unusually
high in energy,

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not being attracted by more
protons.

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But it's low for a vacant
orbital, if it hasn't mixed with

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anything.

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Okay, and finally notice that
some of these are charged:

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H^+;
plus means that's a good place

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to put an electron,
so unusually low;

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OH^-, unusually high because of
the negative charge;

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CH_3^-, especially high.

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So this slide also shows the
fourth point,

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that electrical charge makes a
difference on how normal

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occupied and vacant orbitals
are.

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Okay, so these unusually low
vacant orbitals are acids,

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like H^+.

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Unusually high occupied
orbitals are bases,

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like OH^-, as we just showed on
the previous slide.

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That means that you can mix the
high HOMO of OH^-,

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with the low LUMO of H^+,
and two electrons,

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the ones that were on the OH^-,
go down in energy,

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and that makes a bond.

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And our notation for showing
that is to draw a curved arrow,

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and it gives water.

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Now think carefully about what
a curved arrow means;

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it's not the same as a straight
arrow.

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A curved arrow designates a
shift of electron pairs.

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It doesn't show that this atom
moves from here to here.

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It shows that a pair of
electrons shifts,

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and that pair of electrons goes
from being on the oxygen,

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to being between oxygen and
hydrogen,

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to form the bond.

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So you start the curved arrow
where the electron pair is at

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the beginning,
and you end the arrow,

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put its point,
where it's going to be in the

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product.

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Right?

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So it's not showing that an
atom moves from here to there.

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It's showing that the electrons
that were formerly on oxygen are

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now between oxygen and hydrogen.

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The effect of that is,
of course, to pull all the

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hydrogen to the oxygen.

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But that's not what's being
shown by the arrow.

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What's being shown by the arrow
is how the electrons are moving

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in our picture.

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Okay, so there's a case.

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Now here's another base with
the same acid,

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and we can draw a curved arrow
there and show making an

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ammonium ion out of ammonia.

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Or we could use the same base
with a different acid,

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the low vacant orbital of BH_3,
and draw the same curved arrow,

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and make this anion,
make the boron-oxygen bond.

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Or we could start with
completely different ones.

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We could start with ammonia,
not OH^-, not Arrhenius's base,

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but ammonia;
not Arrhenius acid,

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H^+, but BH_3.

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But it's exactly the same
reaction.

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The high HOMO mixes with the
low LUMO to form a new bond.

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Okay?

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So that's what curved arrows
show, and don't confuse it by

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trying to draw molecules or
atoms moving,

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and showing a curved arrow.

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If you want to show them
moving, draw some other kind of

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arrow;
draw dotted arrows or a

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straight arrow or a wiggly
arrow, or something.

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But the curved arrows have a
very specific meaning.

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Now the second reason that
things could be unusually high

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or low is because they don't
have much overlap.

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Notice in the first case,
it was just an extreme case of

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that.

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There was no overlap at all,
the orbitals were just there.

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But even though the orbitals
are mixed with something else,

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if the overlap is poor,
they haven't changed very much,

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they still look very much like
they did originally.

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Right?

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So a good example of not having
very good overlap is the

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side-to-side overlap of p
orbitals.

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The π overlap -- you
remember from looking at those

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curves of amount of overlap for
different orbitals versus

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distance --
the π overlap isn't

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very big.

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So even though the p
orbitals start a little higher

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on carbon than they do on
hydrogen,

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or normal bonds of carbon that
have s character in them,

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they start a little higher,
but they don't mix very much.

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Right?

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So the π orbital is
unusually high,

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and the π*
antibonding orbital is unusually

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low,
because they didn't go down or

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up very much.

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Okay?

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Now, which of those do you
think is more remarkable,

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in its highness or lowness?

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So for this reason,
the carbon-carbon double bond

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could behave either as an acid
or as a base.

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Right?

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High occupied orbital makes it
a base;

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low vacant orbital makes it an
acid.

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And indeed, it does have both
kinds of reactivity.

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But which do you think is more
pronounced?

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Which would be more familiar,
how high the occupied one is,

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or how low the vacant one is?

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Lucas, what do you say?

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Student:  How low the
vacant one is.

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Prof: And why do you say
so?

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Student:  Because
electrons have to sort of --

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they would likely move into a
position of an energy as close

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as possible to it.

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Prof: Yes,
but on the other hand,

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the electrons of the
π want to move into

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something else.

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Student:  There are lots
and lots and lots of electrons

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going up.

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Prof: Well there are
lots -- there are even more

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vacant orbitals than there are
electrons.

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Right?

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Student:  Because you
also have starring electrons

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that will -- like in a normal
carbon atom.

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Prof: Let's just look at
the picture.

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Yes Catherine?

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Student:  I think the
HOMO is more unusual because

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it's farther away from the usual
--

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Prof: Ah,
the HOMO is further above the

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normal bonds,
than the LUMO is below the

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normal antibonds.

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Why?

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Student:  Because the
p orbital started --

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Prof: Can't hear very
well.

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Student:  Because the
p orbital started a

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little higher.

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Prof: Ah,
because they started a little

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higher.

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Right?

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So most reactions that we'll
study,

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or at least many reactions that
we'll study of the carbon-carbon

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double bond,
it's reactive because of the

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high HOMO,
not because of the low LUMO;

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although there are cases where
the low LUMO makes it reactive.

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But it's this π
orbital, here,

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that makes it particularly
remarkable, because they started

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a little high.

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Okay, so the high HOMO makes it
unusually reactive.

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Now how about the C=O double
bond?

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Right?

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So it starts with the same
p orbital on the carbon,

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which has π overlap
and therefore not much shifting

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up and down,
with a p orbital of

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oxygen, which of course is lower
than that of carbon,

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because of the higher nuclear
charge.

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Which of these will be most
unusual?

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Somebody got a suggestion?

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So what would you think the
characteristic reactivity of a

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C=O double bond --
would it be reactive mostly as

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a high HOMO --
that is, as a base -- or mostly

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as a low LUMO?

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Which is more unusual,
compared with what we compare

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things with?

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Andrew?

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Student:  I think it's a
low LUMO.

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Prof: Why?

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Student:  First of all
it can't -- it's further away

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from its origin.

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Prof: And why is it
further down,

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compared to what we usually
compare?

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Why does the π*,
C double bond O,

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why is that orbital so very
low?

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Pardon me, one reason it's low
is because the overlap isn't

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very much.

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So it didn't go up so much.

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Right?

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That's the same,
true with a C-C double bond.

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But what's special about the
C-O double bond Andrew?

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Student:  I thought the
atoms are different,

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there's a --
Prof: Because of the bad

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energy match,
it didn't go up very much from

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the carbon, or down very much
from the oxygen.

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But the average is low,
that it starts from.

11:21.940 --> 11:27.140
So what's special here is the
π is not so unusual,

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not so far from here.

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But this one,
π*,

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is very far from here.

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So what should make a carbonyl
especially reactive is its low

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vacant orbital,
because of poor overlap;

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and that it started with an
oxygen, an unusually low

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orbital, atomic orbital.

11:49.009 --> 11:50.609
Okay?

11:50.610 --> 11:52.760
We saw another example here.

11:52.759 --> 11:57.499
The three-membered carbon ring
is unusually reactive,

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for a carbon-carbon bond.

11:59.970 --> 12:04.230
That is, the electrons in that
carbon-carbon bond are not

12:04.231 --> 12:09.001
shifted down so much,
and the antibond is not shifted

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up so much,
as in normal carbon-carbon

12:11.839 --> 12:12.269
bonds.

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Why?

12:14.918 --> 12:18.528
What's special about the bonds
in the three-membered ring?

12:18.529 --> 12:19.919
Kevin?

12:19.918 --> 12:23.408
Student:  Well two of
them are bent.

12:23.409 --> 12:24.329
Prof: Ah, they're bent.

12:24.330 --> 12:26.220
And what does that mean?

12:27.820 --> 12:30.000
Prof: Yes,
but they're bent,

12:29.999 --> 12:30.639
so what?

12:30.639 --> 12:31.989
Student:  It overlaps,
there are better overlaps.

12:31.990 --> 12:33.410
Prof: Does it overlap as
well?

12:33.408 --> 12:35.268
So it doesn't go up and down as
much.

12:35.267 --> 12:35.677
Right?

12:35.678 --> 12:40.128
So another example of poor
overlap.

12:40.129 --> 12:44.149
Okay, or you could have an
unusual atomic energy orbital in

12:44.154 --> 12:45.824
the molecular orbital.

12:45.820 --> 12:49.390
For example,
how about a C-F single bond?

12:49.385 --> 12:50.095
Right?

12:50.100 --> 12:52.100
So the overlap can be perfectly
good.

12:52.100 --> 12:54.690
It's a regular old
σ bond,

12:54.688 --> 12:55.508
straight on.

12:55.505 --> 12:56.115
Right?

12:56.120 --> 13:00.110
But the fluorine starts very
low.

13:00.110 --> 13:01.930
There's bad energy match.

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So the π* isn't so
very different from a vacant

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orbital on carbon;
unusually low as a vacant

13:10.222 --> 13:10.972
orbital.

13:10.970 --> 13:13.330
So it should act as an acid.

13:13.330 --> 13:17.880
Things that have high HOMOs
should come up and react with

13:17.875 --> 13:20.305
that σ* of C-F.

13:20.309 --> 13:22.719
It's an unusually low LUMO.

13:22.720 --> 13:25.040
Can you think of what the flip
side of that --

13:25.038 --> 13:26.268
how could you have something
like this,

13:26.269 --> 13:31.189
a carbon bonding to something,
that for the same or analogous

13:31.190 --> 13:35.700
reason would have an unusually
high occupied orbital?

13:35.700 --> 13:40.410
What would you want the carbon
to bond with?

13:40.409 --> 13:42.919
Choose an element.

13:42.919 --> 13:43.759
Student:  Lithium.

13:43.759 --> 13:45.129
Prof: Lithium.

13:45.129 --> 13:46.219
Why lithium?

13:46.220 --> 13:51.620
Student:  Because --
Prof: Because you looked

13:51.620 --> 13:52.210
at the PowerPoint?

13:52.210 --> 13:53.110
Student:  No.

13:53.110 --> 13:54.610
Prof:
>

13:54.610 --> 13:55.140
Student:  I didn't look
at it.

13:55.139 --> 13:56.479
Prof: Why lithium?

13:56.480 --> 14:04.320
Student:  Because its
valence electron -- it's easy

14:04.317 --> 14:10.367
for the valence electron to be
given away.

14:10.370 --> 14:11.790
Prof: Why?

14:11.788 --> 14:14.668
Student:  Because it
would be as stable as a lithium

14:14.666 --> 14:15.406
plus one ion.

14:15.409 --> 14:17.759
Prof: Why?

14:17.759 --> 14:22.189
That's restating the same
thing, right?

14:22.190 --> 14:29.400
What's different about lithium?

14:29.399 --> 14:34.369
Why are orbitals on lithium,
as an atom, unusually high in

14:34.374 --> 14:37.694
energy, compared to
carbon-hydrogen?

14:37.690 --> 14:38.800
Catherine?

14:38.798 --> 14:40.578
Student:  Because it has
a low nuclear charge.

14:40.580 --> 14:42.870
Prof: Because it has a
low nuclear charge.

14:42.868 --> 14:43.248
Right?

14:43.250 --> 14:46.610
It's right at the left end of
the table.

14:46.610 --> 14:47.270
Okay?

14:47.269 --> 14:51.039
So its orbitals aren't very
stable because it doesn't have

14:51.042 --> 14:52.832
very high nuclear charge.

14:52.830 --> 14:53.990
So it's a high energy.

14:53.990 --> 14:56.720
And therefore it has bad energy
match.

14:56.720 --> 14:59.410
Or it could've been lithium
that I drew here.

14:59.408 --> 15:02.498
I happened to draw boron,
which is, for the same reason,

15:02.500 --> 15:04.580
a lower nuclear charge than
carbon;

15:04.580 --> 15:08.340
therefore higher energy as an
atomic orbital.

15:08.340 --> 15:11.790
When they mix,
what's special here is the

15:11.793 --> 15:14.563
occupied orbital,
σ,

15:14.556 --> 15:18.956
which is unusually high,
because the average started

15:18.960 --> 15:19.910
high.

15:19.909 --> 15:21.079
Okay.

15:21.080 --> 15:24.410
So boron.

15:24.408 --> 15:28.368
You may remember that in the
first slide we showed,

15:28.371 --> 15:32.961
boron had a vacant orbital;
that p orbital on boron

15:32.960 --> 15:33.800
is vacant.

15:33.799 --> 15:35.509
Unusually low.

15:35.509 --> 15:40.209
Therefore what, acid or base?

15:40.210 --> 15:44.110
Unusually low vacant orbitals,
which does that make it?

15:44.110 --> 15:44.840
Student:  Acid.

15:44.840 --> 15:45.370
Prof: Acid.

15:45.370 --> 15:48.500
So BH_3 should be an acid.

15:48.504 --> 15:49.354
Right?

15:49.350 --> 15:51.670
Well what I just showed you is
what Shai?

15:51.669 --> 15:54.419
On the previous slide;
we'll go back there.

15:54.418 --> 15:55.378
Student:  That it had a
big B-H;

15:55.379 --> 15:56.139
yes the B-H.

15:56.139 --> 15:57.849
Prof: It has an
unusually high HOMO,

15:57.845 --> 15:58.125
BH_3.

15:58.129 --> 16:01.559
So what does that make it Shai?

16:01.558 --> 16:03.488
Student:  It would make
it a base but --

16:03.490 --> 16:06.590
Prof: So is it an acid
or a base?

16:06.590 --> 16:08.460
Student:  Both.

16:08.460 --> 16:09.980
Prof: Wilson?

16:09.980 --> 16:10.600
Student:  Both.

16:10.600 --> 16:12.380
Prof: It's both.

16:12.379 --> 16:19.619
And what does that suggest,
if the same molecule is both an

16:19.621 --> 16:21.871
acid and a base?

16:21.870 --> 16:24.490
What do acids react with?

16:24.490 --> 16:25.780
Students:  Bases.

16:25.778 --> 16:28.278
Prof: So what if the
same molecule is an acid and a

16:28.282 --> 16:28.592
base?

16:28.590 --> 16:29.910
<<Students speak over one
another>>

16:29.908 --> 16:31.678
Prof: It's going to
react with itself.

16:31.678 --> 16:34.218
Two of the molecules will react
with one another.

16:34.220 --> 16:39.820
Okay, and that's why you can't
do a crystal structure of BH_3,

16:39.817 --> 16:43.577
because BH_3_ becomes
B_2H_6.

16:43.580 --> 16:45.210
Let's look at how it happens.

16:45.210 --> 16:49.120
So there's the low LUMO that
makes BH_3 an acid.

16:49.120 --> 16:53.390
What's the high HOMO?

16:53.389 --> 16:57.869
What's the high HOMO of BH_3?

16:57.870 --> 16:59.030
In localized terms.

16:59.029 --> 17:04.169
I don't mean these big things
that go over the whole molecule.

17:04.170 --> 17:05.910
It's the B-H bond -- right?

17:05.910 --> 17:08.530
-- which was poorly matched in
energy and so on.

17:08.529 --> 17:09.459
So there.

17:09.460 --> 17:13.930
Notice that the B-H bonding
electrons are big on hydrogen,

17:13.926 --> 17:15.256
small on boron.

17:15.259 --> 17:17.239
We saw that last lecture.

17:17.240 --> 17:18.060
Okay?

17:18.058 --> 17:20.488
So they should overlap like
this, right?

17:20.490 --> 17:26.310
And the vacant orbital on the B
should stabilize these

17:26.307 --> 17:30.697
high-energy electrons in the B-H
bond.

17:30.700 --> 17:35.720
But now, you could imagine many
different orientations of the

17:35.721 --> 17:39.071
top molecule that would allow
overlap.

17:39.068 --> 17:48.718
Do you know why I chose this
particular orientation?

17:48.720 --> 17:55.850
Which one acted as the acid and
which one is the base?

17:55.848 --> 17:57.408
The one on the bottom,
the vacant orbital,

17:57.406 --> 17:58.126
acted as an acid.

17:58.130 --> 18:02.070
The one on the top acted as a
base.

18:02.068 --> 18:04.918
So what other possibility is
there?

18:04.920 --> 18:06.840
Yoonjoo?

18:06.838 --> 18:10.138
Student:  So then there
also -- you could reverse the

18:10.144 --> 18:11.044
roles of them.

18:11.039 --> 18:11.549
Prof: Ah ha!

18:11.548 --> 18:13.048
You could have -- so that would
make --

18:13.048 --> 18:15.678
notice incidentally,
what I forgot to mention here,

18:15.680 --> 18:20.650
is that there are three nuclei
being held together by that pair

18:20.654 --> 18:22.184
of electrons now.

18:22.180 --> 18:25.550
Originally the top molecule,
that pair of electrons,

18:25.551 --> 18:29.521
mostly on hydrogen but partly
on boron, held the hydrogen and

18:29.519 --> 18:31.039
the boron together.

18:31.038 --> 18:36.258
Now that same pair of electrons
is attracted -- is helping form

18:36.255 --> 18:39.615
a bond with a boron,
the bottom boron.

18:39.618 --> 18:43.258
So in fact that's an unusual
kind of bond,

18:43.256 --> 18:46.976
because it's bonding three
nuclei together,

18:46.981 --> 18:48.491
not just two.

18:48.490 --> 18:51.210
It's doing double,
or perhaps triple duty.

18:51.210 --> 18:54.920
So we need a new symbol to talk
about such bonds,

18:54.921 --> 18:59.561
and a reasonable one would be a
bond that looks like that.

18:59.559 --> 19:02.929
It's a Y bond.

19:02.930 --> 19:05.800
We could make it blue.

19:05.799 --> 19:07.699
Okay?

19:07.700 --> 19:09.990
But now we have,
as Yoonjoo said,

19:09.990 --> 19:14.360
the vacant orbital on the top
and the high occupied orbital on

19:14.359 --> 19:18.299
the bottom, and they can do
exactly the same thing.

19:18.298 --> 19:21.768
So we have two of these
three-center,

19:21.765 --> 19:23.585
two-electron bonds.

19:23.593 --> 19:24.463
Right?

19:24.460 --> 19:27.420
Two electrons holding three
atoms together.

19:27.424 --> 19:27.994
Right?

19:27.990 --> 19:30.830
Or we can draw it that way.

19:30.832 --> 19:31.572
Right?

19:31.568 --> 19:36.168
And that's the structure of
B_2H_6.

19:36.170 --> 19:41.080
Two of the pairs of electrons
are each bonding three atoms

19:41.079 --> 19:43.319
together instead of two.

19:43.319 --> 19:47.029
Any questions about this?

19:47.029 --> 19:47.859
Yes Alison?

19:47.858 --> 19:49.958
Student:  Is that what
the dotted line means for --

19:49.960 --> 19:51.370
Prof: Yes,
the dotted just means it's a

19:51.373 --> 19:51.973
little different.

19:51.970 --> 19:54.130
You could draw the solid Y if
you want to.

19:54.130 --> 19:58.180
There's no really standard
notation for that.

19:58.180 --> 19:59.490
But it's clear what it means.

19:59.490 --> 20:02.810
It's just that a pair of
electrons is being shared among

20:02.813 --> 20:04.463
three nuclei,
rather than two,

20:04.461 --> 20:05.871
and their electron density is
--

20:05.868 --> 20:07.598
correspondingly,
if you did a difference density

20:07.602 --> 20:09.512
map,
if you could do an X-ray of

20:09.513 --> 20:12.763
this, you'd expect electron
density to build up in the

20:12.759 --> 20:14.169
middle of all three.

20:14.170 --> 20:16.090
Yes Claire?

20:16.088 --> 20:19.008
Student:  This may seem
like a stupid question but a

20:19.005 --> 20:22.015
high HOMO, we've talked about as
a base, and a low LUMO we've

20:22.021 --> 20:23.431
talked about as an acid.

20:23.430 --> 20:24.080
Prof: Yes.

20:24.078 --> 20:25.748
Student:  And the low
LUMO is unoccupied.

20:25.750 --> 20:29.030
If you think about it,
it's sort of receiving

20:29.034 --> 20:29.934
electrons.

20:29.930 --> 20:30.610
Prof: Right.

20:30.608 --> 20:33.348
Student:  But generally,
bases are supposed to receive

20:33.352 --> 20:35.092
electrons, instead of acids,
and --

20:35.088 --> 20:36.278
Prof: No,
you got it backwards.

20:36.279 --> 20:38.389
Student:  Do I?

20:38.390 --> 20:39.280
Prof: Yes.

20:39.279 --> 20:40.059
Student:  Oh okay.

20:40.058 --> 20:43.908
Prof: Because H^+ is an
acid.

20:43.910 --> 20:44.640
Right?

20:44.640 --> 20:45.030
Student:  Right.

20:45.029 --> 20:47.259
Prof: So it obviously
can't give up electrons.

20:47.259 --> 20:48.979
There aren't any electrons.

20:48.980 --> 20:52.860
An acid accepts electrons.

20:52.859 --> 20:53.769
Okay?

20:53.769 --> 20:56.779
Think about it a little bit in
the privacy of your room,

20:56.777 --> 20:57.977
and you'll see that.

20:57.980 --> 20:58.590
Okay?

20:58.588 --> 21:00.928
Student:  Does the bond
between three nuclei only happen

21:00.931 --> 21:01.941
--
Prof: I can't hear very

21:01.935 --> 21:02.095
well.

21:02.098 --> 21:04.508
Student:  Does the bond
between the three nuclei only

21:04.506 --> 21:06.706
happen here because of the
geometry of the molecule?

21:06.710 --> 21:07.010
Student:  Yes.

21:07.009 --> 21:11.109
And to get that,
you have to have overlap.

21:11.108 --> 21:14.248
So if you didn't have -- if the
top BH_3_ were

21:14.246 --> 21:17.666
oriented so that the B-H bond
were vertical and the boron was

21:17.667 --> 21:20.987
way up at the top,
it wouldn't overlap the other

21:20.991 --> 21:21.341
one.

21:21.338 --> 21:23.958
So you have to -- always to get
a bond,

21:23.960 --> 21:26.560
you have to have overlap,
because otherwise the orbitals

21:26.557 --> 21:29.057
don't mix and you just have the
original orbitals,

21:29.059 --> 21:29.599
as we've seen.

21:29.598 --> 21:31.348
Student:  Is this kind
of bond very common?

21:31.349 --> 21:31.739
Prof: Pardon me?

21:31.740 --> 21:33.750
Student:  Is this kind
of bond very common?

21:33.750 --> 21:36.350
Prof: No,
it's not very common,

21:36.346 --> 21:39.846
because there are not many
really low energy vacant

21:39.854 --> 21:41.544
orbitals running around.

21:41.538 --> 21:42.308
Right?

21:42.309 --> 21:44.139
Boron is a very special case.

21:44.140 --> 21:47.320
But a lithium can do the same
thing.

21:47.318 --> 21:50.818
But lithium doesn't have
energy, orbital energies as low

21:50.818 --> 21:53.868
as those of Boron,
because it doesn't have as big

21:53.873 --> 21:55.213
a nuclear charge.

21:55.210 --> 22:01.060
So boron is particularly good
at getting this kind of thing.

22:01.058 --> 22:05.358
And this answers the puzzle
about Lewis structures that we

22:05.362 --> 22:09.212
raised in Lecture two,
about how can BH_3 react with

22:09.211 --> 22:09.591
BH_3?

22:09.588 --> 22:10.418
Right?

22:10.420 --> 22:14.290
That's how it does it,
by making three-center bonds.

22:14.288 --> 22:17.438
Now here's a True and False
quiz.

22:17.440 --> 22:24.540
On the basis of what you know,
is it true that low energy

22:24.537 --> 22:29.477
molecular orbitals result in
bonding?

22:29.480 --> 22:32.370
True or false?

22:32.368 --> 22:34.128
I don't think you trust me
anymore.

22:34.130 --> 22:35.990
>

22:35.990 --> 22:40.260
We've been saying that when you
get those low orbitals -- things

22:40.261 --> 22:43.181
come together,
you get a low orbital -- that

22:43.178 --> 22:44.668
results in a bond.

22:44.670 --> 22:46.070
Lots of overlap.

22:46.069 --> 22:49.019
>

22:49.019 --> 22:50.839
I can't talk you into it?

22:50.839 --> 22:52.359
Good.

22:52.359 --> 22:53.769
That's false.

22:53.769 --> 22:57.539
What makes a bond is
lowered energy

22:57.544 --> 22:58.414
orbitals.

22:58.410 --> 23:01.370
It's when things come together
and the electrons get more

23:01.373 --> 23:01.853
stable.

23:01.848 --> 23:05.138
It's not how low they are,
it's how much they're lowered

23:05.142 --> 23:08.372
by the coming together,
because then pulling apart they

23:08.374 --> 23:10.114
have to go back up again.

23:10.108 --> 23:14.278
So it's not whether they're
high or low, it's whether they

23:14.276 --> 23:15.296
get lowered.

23:15.299 --> 23:16.939
Okay?

23:16.940 --> 23:19.450
Now, compared to what?

23:19.450 --> 23:22.230
What do they have to get lower
compared to?

23:22.230 --> 23:25.760
Student:  By the size.

23:25.759 --> 23:28.179
Prof: Yoonjoo?

23:28.180 --> 23:30.480
Student:  So it's kind
of like how in Erwin and

23:30.476 --> 23:32.726
Goldilocks you showed the
antibonding and bonding.

23:32.730 --> 23:35.790
So wouldn't it be the reactants?

23:35.788 --> 23:37.968
Prof: You can say
something in fewer words than

23:37.971 --> 23:38.261
that.

23:38.259 --> 23:39.859
What do you compare to?

23:39.858 --> 23:44.978
When you say energy is lowered,
and that makes a bond,

23:44.980 --> 23:48.170
what's it lowered,
compared to?

23:48.170 --> 23:49.300
Christopher?

23:49.298 --> 23:50.968
Student:  The atoms in
their standard states.

23:50.970 --> 23:53.150
Prof: Well yes.

23:53.150 --> 23:55.920
It wouldn't necessarily be
between atoms,

23:55.921 --> 23:59.871
it could be between two
molecules, like BH_3 with BH_3.

23:59.869 --> 24:01.619
But you're right.

24:01.618 --> 24:06.318
What it's lowered compared to
is the things it was before they

24:06.317 --> 24:07.397
came together.

24:07.395 --> 24:08.085
Right?

24:08.088 --> 24:10.968
Now these things,
before they came together,

24:10.970 --> 24:13.650
one of them had electrons,
one didn't.

24:13.650 --> 24:16.210
Those might've been very high.

24:16.211 --> 24:16.811
Right?

24:16.809 --> 24:17.759
So they came together.

24:17.759 --> 24:20.059
The electrons went
substantially down,

24:20.060 --> 24:21.990
but still aren't so very low.

24:21.990 --> 24:26.080
They could've been very
low-energy orbitals to begin

24:26.082 --> 24:30.502
with, but not gone down very
much, because there was bad

24:30.496 --> 24:31.776
overlap say.

24:31.778 --> 24:35.558
So these, even though they're
lower than the ones we talked

24:35.557 --> 24:38.097
about first, would not be so
bonding.

24:38.098 --> 24:41.018
It's these that were bonding,
because they came down a lot,

24:41.019 --> 24:42.379
when the mixing happened.

24:42.380 --> 24:43.400
So it's lowering.

24:43.400 --> 24:44.770
Compared to what?

24:44.769 --> 24:48.699
Compared to the separated
components, before you made this

24:48.702 --> 24:49.052
bond.

24:49.048 --> 24:49.668
Right?

24:49.670 --> 24:53.080
So when things come together,
and that results in the

24:53.075 --> 24:56.935
electrons going way down in
energy, that's a strong bond.

24:56.940 --> 24:58.580
Yes, Chenyu?

24:58.579 --> 24:59.139
Pardon me?

24:59.140 --> 25:01.010
Student:  How far does
it have to go down?

25:01.009 --> 25:02.799
Prof: Well that's what
we're going to have to learn.

25:02.798 --> 25:04.398
That's a question of lore.

25:04.398 --> 25:04.828
Right?

25:04.828 --> 25:09.428
And it has to be at least
enough to overcome the fact that

25:09.434 --> 25:12.914
when they come together other
electrons,

25:12.910 --> 25:14.620
other orbitals,
filled orbitals are

25:14.615 --> 25:17.355
overlapping,
which is net repulsive.

25:17.358 --> 25:20.608
So it may not be that there's
an absolute criterion.

25:20.609 --> 25:21.119
Right?

25:21.118 --> 25:24.978
It may be that if there are a
lot of other things opposing the

25:24.978 --> 25:27.958
coming together,
filled orbital with filled

25:27.962 --> 25:30.342
orbital,
then you have to have really

25:30.335 --> 25:31.595
enormous going down.

25:31.598 --> 25:34.708
So you can't make a simple
answer to that.

25:34.710 --> 25:37.820
But we'll learn as we see
examples.

25:37.819 --> 25:39.469
Okay.

25:39.470 --> 25:47.030
So now, HOMO/LUMO mixing,
for reactivity and resonance.

25:47.029 --> 25:49.749
So reactivity means between
molecules.

25:49.750 --> 25:53.640
So far we've been talking
mostly about atoms coming

25:53.636 --> 25:55.966
together and forming a bond.

25:55.970 --> 25:59.180
But molecules have high
orbitals and low orbitals,

25:59.181 --> 26:00.821
as in the case of BH_3.

26:00.818 --> 26:04.388
The B-H was a molecular
orbital, or not an atomic

26:04.394 --> 26:04.994
orbital.

26:04.989 --> 26:05.659
Right?

26:05.660 --> 26:08.690
So when things come together,
orbitals are orbitals.

26:08.690 --> 26:11.580
If you have an unusually high
energy and an unusually low

26:11.583 --> 26:14.583
energy, and they overlap and go
down, that makes a bond.

26:14.578 --> 26:16.508
So that's between
molecules.

26:16.509 --> 26:20.829
But it turns out that what
resonance is,

26:20.830 --> 26:26.150
is HOMO/LUMO mixing,
within a molecule.

26:26.150 --> 26:30.930
Now you might say the molecules
have certain molecular orbitals.

26:30.930 --> 26:32.710
How can you mix them? Right?

26:32.710 --> 26:35.880
The idea is that we made our
first analysis on the basis of

26:35.880 --> 26:38.560
localized orbitals:
σ,σ*

26:38.557 --> 26:40.317
here;
σ,σ*

26:40.316 --> 26:42.256
here;
not these big Chladni things

26:42.259 --> 26:44.069
that go over the whole thing.

26:44.068 --> 26:46.938
But it may be that this
σ,σ*,

26:46.940 --> 26:48.450
and this
σ,σ*,

26:48.450 --> 26:50.840
are near one another and
overlap.

26:50.838 --> 26:53.358
So that when we made our
initial analysis,

26:53.358 --> 26:56.898
and looked only at this and
only with this,

26:56.900 --> 27:00.250
we didn't take into account
that this one might interact

27:00.252 --> 27:04.372
with this one,
and give still lower energy.

27:04.368 --> 27:07.998
When that kind of thing is
important, that's when you have

27:07.996 --> 27:10.346
to draw other resonance
structures.

27:10.349 --> 27:13.509
And I'll show you an example.

27:13.509 --> 27:17.369
But first I'm going to show you
reactivity, and then we'll go on

27:17.369 --> 27:18.289
to resonance.

27:18.288 --> 27:23.478
Okay, now let's look at the
frontier orbitals for H-F.

27:23.480 --> 27:25.040
Okay?

27:25.038 --> 27:30.528
So it has four valence electron
pairs and five valence atomic

27:30.531 --> 27:34.261
orbitals;
2s, 2p_x_y_z on

27:34.262 --> 27:39.432
fluorine, and a 1s on
hydrogen, and four pairs of

27:39.429 --> 27:40.649
electrons.

27:40.650 --> 27:43.290
So there are going to be four
occupied orbitals.

27:43.288 --> 27:46.898
And this is what the lowest
orbital looks like.

27:46.900 --> 27:50.320
What does it look like?

27:50.318 --> 27:53.598
Prof: Well it's a 2s
orbital, the 1s being

27:53.602 --> 27:54.822
the core on fluorine.

27:54.818 --> 27:56.818
But it's made up of atomic
orbitals.

27:56.818 --> 28:01.038
Is it exactly a 2s of
fluorine?

28:01.038 --> 28:03.018
Does it look like sphere on
fluorine?

28:03.019 --> 28:04.719
Alison, you're shaking your
head.

28:04.720 --> 28:06.520
Student:  It's a little
bit distorted.

28:06.519 --> 28:09.019
Prof: And how did it get
a little distorted?

28:09.019 --> 28:11.609
What did we mix with the F
orbital?

28:11.609 --> 28:12.529
Student:  The H.

28:12.528 --> 28:14.538
Prof: A little bit of
the 1s on hydrogen.

28:14.538 --> 28:17.048
It's mostly the F on
fluorine.

28:17.049 --> 28:18.039
Why?

28:18.038 --> 28:21.048
Because the fluorine's way down
in energy.

28:21.048 --> 28:23.158
So the best combination is
mostly this.

28:23.160 --> 28:25.820
But you can see that it's a
little bit egg shaped,

28:25.823 --> 28:28.273
a little bit drawn out toward
the hydrogen.

28:28.269 --> 28:31.669
Okay, so it's mostly a
2s of fluorine,

28:31.669 --> 28:34.839
but a little bit of 1s
on hydrogen.

28:34.836 --> 28:35.606
Right?

28:35.609 --> 28:37.249
Now here's the next one.

28:37.250 --> 28:38.740
What's that mostly?

28:38.740 --> 28:40.240
Can you see?

28:40.240 --> 28:47.960
<<Students speak over one
another>>

28:47.960 --> 28:49.180
Prof: Tyler,
what do you say?

28:49.180 --> 28:50.370
Student:  I would say a
2p.

28:50.368 --> 28:52.088
Prof: It looks like a
2p on fluorine.

28:52.088 --> 28:54.278
Does it look exactly like a
2p on fluorine,

28:54.281 --> 28:56.521
or is it just hard for you to
see that it's not?

28:56.519 --> 28:57.659
It's very similar.

28:57.660 --> 28:59.640
Student:  I don't know,
it looks pretty close,

28:59.644 --> 29:01.214
but the blue one might be a bit
bigger.

29:01.210 --> 29:02.540
Prof: Yes,
the blue one is a little bit

29:02.535 --> 29:04.505
bigger,
because it's got a little bit

29:04.508 --> 29:07.628
of the 1s of hydrogen
lowering the energy of the

29:07.633 --> 29:09.083
2p of fluorine.

29:09.079 --> 29:10.209
Okay?

29:10.210 --> 29:13.780
And now the next two orbitals
are these.

29:13.779 --> 29:17.049
What are those?

29:17.049 --> 29:19.329
Steve, what do you say?

29:19.328 --> 29:20.678
Student:  The
2p_y and 2p_z.

29:20.680 --> 29:22.340
Prof: Yes,
the 2p_y and 2p_z

29:22.336 --> 29:22.816
of fluorine.

29:22.819 --> 29:25.879
Is there hydrogen in those too?

29:25.880 --> 29:26.920
Student:  Not very much.

29:26.920 --> 29:27.920
Prof: Why not?

29:27.920 --> 29:30.000
Student:  Because they
don't overlap with the one --

29:30.000 --> 29:32.130
Prof: Ah,
they're orthogonal.

29:32.130 --> 29:33.720
It's a π versus a
σ.

29:33.720 --> 29:35.920
There's no overlap,
therefore no mixing.

29:35.920 --> 29:38.660
So those are the occupied
orbitals.

29:38.660 --> 29:42.350
And the 2p's have the
same energy.

29:42.348 --> 29:46.028
Okay, and then remember there
are going to be five molecular

29:46.032 --> 29:46.722
orbitals.

29:46.720 --> 29:50.990
And now you make the last one,
which is going to have another

29:50.994 --> 29:52.924
node, with the leftovers.

29:52.920 --> 29:57.160
What's left over,
after we made the occupied

29:57.155 --> 29:58.235
orbitals?

29:58.240 --> 30:01.280
What's it mostly left over?

30:01.278 --> 30:04.638
We used up the 2p's of
fluorine to make those HOMOs.

30:04.640 --> 30:06.440
Those were pure, right?

30:06.440 --> 30:10.220
But what was left over from the
bottom?

30:10.220 --> 30:10.920
Students:  1s.

30:10.920 --> 30:14.520
Prof: We used very
little of 1s on hydrogen,

30:14.519 --> 30:17.619
and there's a little bit of
2p fluorine and 2s

30:17.616 --> 30:20.186
fluorine that we didn't use in
the bottom ones.

30:20.190 --> 30:21.730
So they're back in the top.

30:21.730 --> 30:25.240
So what we have is mostly a
1s on hydrogen,

30:25.238 --> 30:29.818
but a little bit of some kind
of sp hybrid on fluorine.

30:29.819 --> 30:31.589
Is that clear to everyone?

30:31.589 --> 30:33.829
So that's the vacant orbital.

30:33.828 --> 30:38.438
Is it unusual energy,
that vacant orbital?

30:38.440 --> 30:41.670
Student:  It's low.

30:41.670 --> 30:42.690
Prof: It's low.

30:42.690 --> 30:44.310
Is it unusually low?

30:44.309 --> 30:48.089
Kate, do you have an idea?

30:48.088 --> 30:51.168
What kind of criteria do we
have for whether an orbital

30:51.173 --> 30:52.663
should be unusually low?

30:52.660 --> 30:56.590
What do we look for?

30:56.588 --> 31:01.438
Student:  We look for
overlap and energy match.

31:01.440 --> 31:02.740
Prof: Overlap.

31:02.740 --> 31:03.730
Energy match.

31:03.730 --> 31:06.930
How about this case,
good overlap?

31:06.930 --> 31:08.010
Quite good overlap.

31:08.009 --> 31:10.849
It's a hybrid orbital on
fluorine pointed right toward a

31:10.851 --> 31:11.421
hydrogen.

31:11.420 --> 31:12.020
Good overlap.

31:12.019 --> 31:13.479
How about the energy match?

31:13.480 --> 31:16.230
Kate?

31:16.230 --> 31:20.920
Student:  Sure.

31:20.920 --> 31:21.970
Prof: Sure what?

31:21.970 --> 31:25.980
Sure it's good or sure it's bad?

31:25.980 --> 31:26.860
One of them's hydrogen.

31:26.859 --> 31:27.989
What's the other one?

31:27.990 --> 31:29.240
Student:  The other one
is fluorine.

31:29.240 --> 31:31.140
Prof: Where's fluorine,
compared to hydrogen?

31:31.140 --> 31:31.830
Student:  Fluorine is
going to be lower.

31:31.829 --> 31:32.389
Prof: Why?

31:32.390 --> 31:33.900
Student:  It has greater
nuclear charge.

31:33.900 --> 31:34.710
Prof: Right.

31:34.710 --> 31:36.630
Okay, good energy match or bad
energy match?

31:36.630 --> 31:37.420
Student:  Not great.

31:37.420 --> 31:38.580
Prof: Not very good.

31:38.579 --> 31:41.149
So you don't get much mixing.

31:41.150 --> 31:43.330
And you know that already by
looking at the picture,

31:43.327 --> 31:44.947
because you didn't mix it very
much.

31:44.950 --> 31:47.820
It's almost all 1s of
hydrogen.

31:47.818 --> 31:50.788
So it's unusually low for a
σ*;

31:50.788 --> 31:54.098
it didn't go up very much from
hydrogen.

31:54.098 --> 31:56.788
So indeed -- now it's got an
unusually low vacant orbital.

31:56.788 --> 31:59.418
What does that make it,
an acid or a base?

31:59.420 --> 32:00.880
Student:  An acid.

32:00.880 --> 32:01.710
Prof: It's an acid.

32:01.710 --> 32:04.030
Are you surprised that H-F is
an acid?

32:04.029 --> 32:04.719
Student:  No.

32:04.720 --> 32:05.620
Prof: Why?

32:05.619 --> 32:08.019
What's its name?

32:08.019 --> 32:09.559
Student:  Hydrofluoric
acid.

32:09.559 --> 32:10.849
Prof: Hydrofluoric acid.

32:10.848 --> 32:12.818
And that's what makes it an
acid.

32:12.818 --> 32:18.018
Arrhenius would say it's an
acid because it gives up H^+.

32:18.019 --> 32:21.789
We say it's an acid because
it's an unusually low vacant

32:21.785 --> 32:22.325
orbital.

32:22.333 --> 32:22.953
Right?

32:22.950 --> 32:27.480
So notice that those three are
made up of three atomic

32:27.482 --> 32:30.822
orbitals: the 1s of
hydrogen,

32:30.818 --> 32:34.408
the 2s of fluorine,
and a 2p orbital of

32:34.410 --> 32:35.170
fluorine.

32:35.170 --> 32:37.290
And they're in different
mixtures in three of these.

32:37.288 --> 32:39.548
Usually we've looked at just
two things, right?

32:39.548 --> 32:42.228
There's one atom,
atomic orbital,

32:42.227 --> 32:44.647
and another one,
and they mix.

32:44.653 --> 32:45.493
Right?

32:45.490 --> 32:46.220
A pair.

32:46.220 --> 32:48.700
Here there are three going in,
to give three molecular

32:48.703 --> 32:49.223
orbitals.

32:49.220 --> 32:51.850
But still you can see quite
easily why they should be the

32:51.854 --> 32:54.794
way they are;
why the bottom ones are almost

32:54.791 --> 32:58.071
pure fluorine,
and the top one is almost pure

32:58.066 --> 32:58.956
hydrogen.

32:58.960 --> 33:01.360
Okay.

33:01.358 --> 33:03.518
And so that top one is
σ*;

33:03.519 --> 33:07.429
the LUMO, the unusually low
LUMO.

33:07.430 --> 33:08.440
Lucas?

33:08.440 --> 33:11.660
Student:  How can we be
sure that the 1s of the

33:11.655 --> 33:14.925
low nuclear-charge hydrogen is
going to be that much different

33:14.925 --> 33:18.245
from the really high nuclear
charge 2s of fluorine?

33:18.250 --> 33:19.840
Prof: Yes,
this you have to learn.

33:19.838 --> 33:24.068
And I'm going to show you very
soon how we can tell that kind

33:24.065 --> 33:24.835
of thing.

33:24.838 --> 33:29.688
Okay, there's a different
picture, that was made in 1973,

33:29.688 --> 33:31.418
of the same thing.

33:31.420 --> 33:33.600
These pictures were drawn just
a year or two ago,

33:33.595 --> 33:35.585
but this is -- you can see the
same thing.

33:35.588 --> 33:38.388
It's drawn at a different
contour level.

33:38.390 --> 33:41.730
It was based on a different
calculation.

33:41.730 --> 33:43.850
But you can see it's the same
thing.

33:43.848 --> 33:47.618
And we'll notice that -- how
many nodes does this thing have,

33:47.615 --> 33:49.305
that are clearly visible?

33:49.309 --> 33:49.969
Students:  Two.

33:49.970 --> 33:50.780
Prof: Two nodes, right?

33:50.779 --> 33:52.879
Between the H and F.

33:52.880 --> 33:55.480
That one is antibonding. Right?

33:55.480 --> 33:58.610
When they came together they
cancelled in the middle,

33:58.613 --> 34:00.183
rather than reinforcing.

34:00.180 --> 34:02.350
There's another node there.

34:02.348 --> 34:05.628
But notice that that didn't
have anything to do with the

34:05.633 --> 34:06.233
bonding.

34:06.230 --> 34:10.060
That was already there in the
atomic orbital you started with.

34:10.059 --> 34:12.649
So it didn't have anything to
do with lowering.

34:12.650 --> 34:14.910
It didn't have anything to do
with whether the thing was

34:14.911 --> 34:15.941
bonding or antibonding.

34:15.940 --> 34:19.050
The pink node had to do with
whether it was bonding.

34:19.050 --> 34:21.350
That came when they came
together.

34:21.351 --> 34:21.911
Right?

34:21.909 --> 34:24.179
It's unfavorable.

34:24.179 --> 34:26.109
So it's better for them to come
apart.

34:26.110 --> 34:28.370
But if they come apart,
you don't do anything with the

34:28.367 --> 34:28.877
blue node.

34:28.880 --> 34:32.130
It's still there,
it's part of the atom.

34:32.130 --> 34:32.970
Okay?

34:32.969 --> 34:36.179
So you have to recognize that
there are two kinds of nodes.

34:36.179 --> 34:38.169
There are nodes that were there
already,

34:38.170 --> 34:40.860
atomic orbital nodes,
and there are ones that are

34:40.862 --> 34:43.052
associated with the coming
together,

34:43.050 --> 34:45.090
and that's what makes something
bonding,

34:45.090 --> 34:48.910
or antibonding;
in this particular case it's

34:48.905 --> 34:49.935
antibonding.

34:49.940 --> 34:53.840
Okay now let's look,
instead of H-F,

34:53.838 --> 34:56.398
let's look at CH_3-F.

34:56.400 --> 34:57.620
Sam?

34:57.619 --> 34:59.799
Student:  Why is it
called a frontier?

34:59.800 --> 35:02.990
Prof: Because you have
occupied orbitals,

35:02.989 --> 35:05.759
and then you have vacant
orbitals, and the ones you're

35:05.760 --> 35:08.900
interested in are the lowest of
the vacant and the highest of

35:08.898 --> 35:13.668
the occupied,
at this border between occupied

35:13.672 --> 35:16.272
and vacant orbitals.

35:16.268 --> 35:19.848
Okay, so this one has seven
valence pairs of electrons.

35:19.849 --> 35:21.889
So you're going to occupy seven
orbitals.

35:21.889 --> 35:24.959
And here's what they look like,
the seven that are occupied.

35:24.960 --> 35:28.480
What's the very lowest one,
mostly?

35:28.480 --> 35:30.130
<<Students speak over one
another>>

35:30.130 --> 35:32.370
Prof: It's the 2s
of fluorine.

35:32.371 --> 35:32.791
Right?

35:32.789 --> 35:36.449
And what's the next one?

35:36.449 --> 35:40.469
Well it's C-H bonds,
all mixed together.

35:40.474 --> 35:41.304
Right?

35:41.300 --> 35:45.210
But also a little bit of a
p orbital on fluorine.

35:45.210 --> 35:47.320
It has the blue,
sort of, toward the front,

35:47.315 --> 35:50.275
and a little bit of that red
behind, as part of the p

35:50.275 --> 35:51.475
orbital on fluorine.

35:51.480 --> 35:56.050
So it's a mixture of the C-H
bonds and of the p

35:56.045 --> 35:58.465
orbital on fluorine.

35:58.469 --> 36:02.029
And then we have these others,
some of them coming in pairs,

36:02.025 --> 36:05.515
and those are the HOMOs,
because we have seven occupied.

36:05.518 --> 36:09.168
And let's look at them a little
more closely and compare them,

36:09.172 --> 36:11.332
each one, with the one beneath
it.

36:11.329 --> 36:15.979
And I'll draw another picture
too, of that older kind,

36:15.983 --> 36:18.533
for making this comparison.

36:18.530 --> 36:22.310
And we're interested in what is
it that went together,

36:22.311 --> 36:26.161
to make these orbitals,
and why is one lower in energy,

36:26.164 --> 36:27.954
and the other higher?

36:27.949 --> 36:32.539
So what do you see on the top
orbital, say this one here,

36:32.539 --> 36:35.459
the top left;
what's that made up of?

36:35.460 --> 36:38.020
What is it on the left side?

36:38.018 --> 36:41.868
Sophie, what would you say the
orbital is on the left side of

36:41.869 --> 36:42.319
that?

36:42.320 --> 36:43.410
Student:  I think it's
2p over there.

36:43.409 --> 36:44.009
Prof: Right.

36:44.010 --> 36:48.950
This part here is a 2p
π orbital of fluorine.

36:48.949 --> 36:55.269
Now what's this thing on the
right here, the dash bit down

36:55.273 --> 36:56.053
here?

36:56.050 --> 36:58.590
If you just saw that,
without any of the rest of it,

36:58.586 --> 37:00.076
what would you say that was?

37:00.079 --> 37:01.979
Students:  1s.

37:01.980 --> 37:03.860
Prof: It's more than a
1s on hydrogen;

37:03.860 --> 37:06.430
that would be spherical.

37:06.429 --> 37:12.529
It's, at a certain contour,
the C-H bond.

37:12.530 --> 37:14.500
Do you see that?

37:14.500 --> 37:19.280
So this is electron density in
here, bonding between C and H.

37:19.280 --> 37:23.550
And these two on the top are
little bits of C-H bonds as

37:23.552 --> 37:25.342
well, mixed together.

37:25.340 --> 37:29.220
So what this orbital is,
is a mixture between some

37:29.224 --> 37:34.144
combination of C-H bonds on the
right, and the p orbital

37:34.139 --> 37:36.359
of fluorine on the left.

37:36.360 --> 37:42.180
Now is it a favorable,
or an unfavorable combination,

37:42.184 --> 37:47.564
of the fluorine orbital with
the C-H orbitals?

37:47.559 --> 37:48.969
This one up here.

37:48.969 --> 37:53.039
Is the interaction between the
fluorine orbital and the C-H

37:53.041 --> 37:55.431
orbitals bonding or antibonding?

37:55.429 --> 37:55.989
Students:  Antibonding.

37:55.989 --> 37:59.939
Prof: Becky,
do you have an idea?

37:59.940 --> 38:02.990
Are they building up electron
density in between,

38:02.985 --> 38:04.885
or having a node in between?

38:04.889 --> 38:05.659
Student:  A node.

38:05.659 --> 38:06.869
Prof: There's a node in
between.

38:06.869 --> 38:08.819
So that's antibonding.

38:08.820 --> 38:12.680
What's the orbital on the
bottom, this one?

38:12.679 --> 38:15.349
Student:  Bonding.

38:15.349 --> 38:19.439
Prof: That's the same
components, but it's the bonding

38:19.443 --> 38:20.403
combination.

38:20.400 --> 38:23.600
So this is the favorable
combination of those,

38:23.599 --> 38:26.729
and this is their unfavorable
combination.

38:26.730 --> 38:30.640
So this lower-energy one is
favorable, and the upper energy

38:30.643 --> 38:32.603
is unfavorable combination.

38:32.599 --> 38:34.969
How about here and here?

38:34.969 --> 38:37.459
Can you see what that is?

38:37.460 --> 38:45.020
What's on the left,
here, that lump of red and this

38:45.021 --> 38:47.291
lump of blue?

38:47.289 --> 38:50.009
Eric?

38:50.010 --> 38:52.920
Here, this thing,
it's very complicated.

38:52.920 --> 38:55.440
Okay, will you agree on that?

38:55.440 --> 38:56.280
Student:  Okay.

38:56.280 --> 38:59.390
Prof: But part of it,
this part on the left,

38:59.393 --> 39:02.883
there's a red lump in behind
and a blue lump in front.

39:02.880 --> 39:05.090
You can see it maybe more
clearly here.

39:05.090 --> 39:09.420
Red behind, and blue in front,
surrounding the green fluorine

39:09.423 --> 39:09.933
atom.

39:09.929 --> 39:14.509
What is that orbital,
that atomic orbital?

39:14.510 --> 39:15.450
Student:  Probably the
p orbital.

39:15.449 --> 39:16.609
Prof: Can't hear very
well.

39:16.610 --> 39:17.520
Student:  Probably the
p orbital,

39:17.523 --> 39:18.043
a different orientation.

39:18.039 --> 39:20.609
Prof: It's the p
orbital on fluorine that's

39:20.606 --> 39:22.206
pointing more or less toward
you.

39:22.210 --> 39:23.090
Okay?

39:23.090 --> 39:27.410
So this is the p orbital
of fluorine, that's mixing with

39:27.407 --> 39:28.447
C-H bonds here.

39:28.452 --> 39:29.082
Right?

39:29.079 --> 39:33.789
In fact, it's the same thing as
this, turned on its side.

39:33.789 --> 39:36.609
Okay?

39:36.610 --> 39:39.960
So this is the bonding
combination, built up between

39:39.956 --> 39:41.856
the fluorine and the C-H's.

39:41.860 --> 39:44.870
This is the antibonding one,
with a node between the

39:44.865 --> 39:46.335
fluorine and the C-H's.

39:46.340 --> 39:50.380
So here we have a node,
in this bottom one,

39:50.376 --> 39:54.796
but that node came from the
atomic orbitals.

39:54.800 --> 39:57.380
That's what made it a p
orbital here,

39:57.380 --> 39:58.220
on fluorine.

39:58.219 --> 40:02.949
That one, you don't get rid of,
if you pull the fluorine away.

40:02.949 --> 40:05.639
That doesn't have anything to
do with the bonding,

40:05.641 --> 40:07.511
that's just an atomic orbital
node.

40:07.510 --> 40:08.060
Right?

40:08.059 --> 40:11.389
On the top, you again have the
same atomic orbital node,

40:11.389 --> 40:14.839
because it's the same p
orbital that's involved.

40:14.840 --> 40:17.070
But what about the top?

40:17.070 --> 40:17.930
Sam?

40:17.929 --> 40:19.089
Student:  You have
another node but --

40:19.090 --> 40:22.140
Prof: There's another
node, that one,

40:22.135 --> 40:24.325
and that's an antibonding node.

40:24.331 --> 40:24.971
Right?

40:24.969 --> 40:29.519
The electrons in that orbital
would get lower in energy if you

40:29.518 --> 40:32.798
broke the bond,
if the fluorine came away.

40:32.800 --> 40:35.080
So the pink nodes are the ones
we're interested in;

40:35.079 --> 40:39.059
the antibonding nodes,
not the ones that are just part

40:39.057 --> 40:40.857
of the atomic orbital.

40:40.860 --> 40:41.640
Okay.

40:41.639 --> 40:45.049
Now, we're getting to Lucas's
question.

40:45.050 --> 40:52.670
So this thing down here is made
up of fluorine and C-H.

40:52.670 --> 40:56.230
The one here is made up of
fluorine and C-H.

40:56.228 --> 40:56.888
Right?

40:56.889 --> 41:01.869
This is the favorable
combination, and this is the

41:01.873 --> 41:04.523
unfavorable combination.

41:04.519 --> 41:05.359
So get it right.

41:05.360 --> 41:07.880
So here are the two of them.

41:07.880 --> 41:11.460
They come together when the F
comes up to the methyl.

41:11.458 --> 41:12.008
Right?

41:12.010 --> 41:15.490
And you get a favorable one and
an unfavorable one.

41:15.489 --> 41:22.969
But the fluorine and the C-H's
may not be at the same energy.

41:22.969 --> 41:24.809
How do you know which one's
lower?

41:24.809 --> 41:27.589
That's your question.

41:27.590 --> 41:31.990
Is the fluorine lower,
or is the C-H lower,

41:31.990 --> 41:35.030
or are they about the same?

41:35.030 --> 41:38.270
Now how are we going to tell?

41:38.268 --> 41:41.528
If the fluorine is lower,
and they come together,

41:41.525 --> 41:44.505
what does the lower one look
like, mostly?

41:44.510 --> 41:45.080
Student:  Fluorine.

41:45.079 --> 41:46.129
Prof: Fluorine.

41:46.130 --> 41:49.200
If the fluorine's higher,
and they come together,

41:49.197 --> 41:51.367
what does the low one look
like?

41:51.369 --> 41:51.989
Student:  C-H.

41:51.989 --> 41:53.889
Prof: Mostly C-H, right?

41:53.889 --> 41:58.129
So by looking at how big these
are, we can tell which one is

41:58.134 --> 41:58.714
lower.

41:58.710 --> 42:03.980
So when we look here,
we see that here I would say

42:03.978 --> 42:08.278
they're pretty similar,
left to right.

42:08.280 --> 42:11.530
There's not much difference
between a 2p orbital on

42:11.525 --> 42:14.995
fluorine and C-H σ
bonds; not much difference.

42:15.000 --> 42:17.480
But to the extent they're
different I would say,

42:17.478 --> 42:19.958
looking at this,
that the C-H is a little bigger

42:19.958 --> 42:22.648
here, and the fluorine is a
little bigger here.

42:22.650 --> 42:24.630
Would you say that?

42:24.630 --> 42:27.620
So which is lower,
a C-H σ bond or

42:27.617 --> 42:29.887
the p orbital of
fluorine?

42:29.889 --> 42:30.959
Students:  C-H.

42:30.960 --> 42:33.080
Prof: C-H σ
bond would be a little lower

42:33.076 --> 42:35.656
than fluorine;
not much though, pretty similar.

42:35.659 --> 42:39.189
So they're about the same,
as we say.

42:39.190 --> 42:42.900
But if you have to make a
choice, the C-H is a little bit

42:42.898 --> 42:46.438
lower in energy;
the fluorine's a little higher.

42:46.440 --> 42:48.200
Okay.

42:48.199 --> 42:51.179
Now there's also a vacant
orbital, made up with the

42:51.182 --> 42:53.572
leftovers here,
some of the leftovers.

42:53.570 --> 42:54.570
And what's that?

42:54.570 --> 42:57.050
Let's look at a different
picture of it.

42:57.050 --> 43:00.740
So this has three nodes that
are obvious.

43:00.739 --> 43:03.629
There's one that's near the
fluorine atom,

43:03.632 --> 43:05.892
a node, plane,
that goes back.

43:05.889 --> 43:07.079
The furthest to the left.

43:07.079 --> 43:09.169
Everyone see that?

43:09.170 --> 43:13.880
Is that an antibonding node,
or is that an atomic orbital

43:13.880 --> 43:14.470
node?

43:14.469 --> 43:15.759
Student:  Atomic orbital.

43:15.760 --> 43:18.630
Prof: That's part of the
fluorine atomic orbital of some

43:18.632 --> 43:19.512
hybrid on fluorine.

43:19.512 --> 43:19.932
Right?

43:19.929 --> 43:22.389
And the same is true at the C-H
end.

43:22.389 --> 43:25.619
There's a node that's an atomic
orbital node of the carbon.

43:25.623 --> 43:26.073
Right?

43:26.070 --> 43:29.760
But what's important?

43:29.760 --> 43:33.110
Between those other two is
what's between the fluorine and

43:33.114 --> 43:35.004
the carbon, and the CH_3_.

43:35.000 --> 43:36.660
And that's antibonding.

43:36.659 --> 43:42.579
So that, the LUMO is a
σ* antibond,

43:42.581 --> 43:45.481
between C and methyl.

43:45.480 --> 43:49.270
And why is it unusually low?

43:49.268 --> 43:52.738
The question is whether the
LUMO should be unusually low.

43:52.739 --> 43:54.889
Why is it unusually low?

43:54.889 --> 43:57.159
Is the overlap bad?

43:57.159 --> 43:58.619
Student:  It's fine.

43:58.619 --> 43:59.719
Prof: No,
the overlap's good;

43:59.719 --> 44:02.909
the hybrids are pointing right
toward one another.

44:02.909 --> 44:09.119
But what makes it low in energy?

44:09.119 --> 44:12.999
So I'm not giving you specific
problems on this,

44:13.000 --> 44:16.620
but look over those things and
run your brain as to those four

44:16.617 --> 44:19.697
different things that make
orbitals unusually high or

44:19.702 --> 44:20.772
unusually low.

44:20.768 --> 44:23.498
Because that's what you'll be
doing next week when you're

44:23.500 --> 44:24.960
doing these Wikis,
each of you,

44:24.961 --> 44:27.791
to decide some functional
group, why is it functional?

44:27.789 --> 44:31.279
What makes it unusually high or
unusually low;

44:31.280 --> 44:33.220
or maybe neither? Right?

44:33.219 --> 44:38.559
Why is the C-F bond,
more properly the C-F

44:38.563 --> 44:44.823
σ* orbital,
the antibonding orbital,

44:44.820 --> 44:48.470
why is it unusually low?

44:48.469 --> 44:51.539
Compared to what?

44:51.539 --> 44:53.449
What do you compare it to?

44:53.449 --> 44:54.669
Student:  C-H.

44:54.670 --> 44:56.490
Prof: A C-H bond.

44:56.489 --> 45:01.219
How come C-F is lower,
for the σ*?

45:01.219 --> 45:01.989
Alex?

45:01.989 --> 45:02.849
Student:  Energy
mismatch.

45:02.849 --> 45:03.369
Prof: Pardon me?

45:03.369 --> 45:03.969
Student:  Energy
mismatch.

45:03.969 --> 45:06.269
Prof: Yes,
the fluorine is really low,

45:06.273 --> 45:07.743
their average is very low.

45:07.739 --> 45:09.789
So the vacant orbital is
unusually low.

45:09.789 --> 45:11.719
It didn't go up much. Right?

45:11.719 --> 45:15.669
Where have you seen that before?

45:15.670 --> 45:18.250
H-F.

45:18.250 --> 45:20.760
The previous slide,
H-F, was exactly the same.

45:20.760 --> 45:22.590
It's an acid.

45:22.590 --> 45:24.010
Remember Kate,
you helped us with that.

45:24.010 --> 45:28.140
It's an acid because of the bad
energy match between fluorine

45:28.137 --> 45:29.167
and hydrogen.

45:29.170 --> 45:32.410
This is the same thing,
but it's the bad energy match

45:32.409 --> 45:34.279
between fluorine and carbon.

45:34.280 --> 45:34.790
Okay.

45:34.789 --> 45:44.719
So CH_3-F is an acid for the
same reason that H-F is an acid.

45:44.724 --> 45:46.054
Right?

45:46.050 --> 45:48.340
There's the low LUMO of H-F.

45:48.338 --> 45:48.908
Right?

45:48.909 --> 45:52.589
It's got that same antibonding
node.

45:52.590 --> 45:53.410
Shai?

45:53.409 --> 45:58.289
Student:  Why is there
no energy mismatch between

45:58.288 --> 46:00.238
carbon and hydrogen?

46:00.239 --> 46:03.439
Prof: It just happens
that it worked out that way.

46:03.440 --> 46:05.010
But it's true.

46:05.010 --> 46:06.490
Hydrogen is 1s.

46:06.489 --> 46:07.719
That makes it unusually low.

46:07.719 --> 46:09.889
But it doesn't have a very big
nuclear charge.

46:09.889 --> 46:12.919
Carbon has a higher nuclear
charge, but you're talking

46:12.922 --> 46:14.412
2s and 2p.

46:14.409 --> 46:17.169
And it turns out those just
cancel out.

46:17.170 --> 46:20.000
If that hadn't been the case,
organic chemists --

46:20.000 --> 46:24.190
like if boron happened to match
hydrogen,

46:24.190 --> 46:27.350
then maybe our organic
chemistry would be

46:27.347 --> 46:29.957
boron-hydrogen,
not -- there would be

46:29.960 --> 46:33.060
borohydrates,
not carbohydrates. Right?

46:33.059 --> 46:35.249
But that's the way things are.

46:35.250 --> 46:36.950
Student:  So in this
picture we can tell that --

46:36.949 --> 46:38.629
Prof: Actually there are
other reasons it wouldn't be

46:38.632 --> 46:40.572
boron,
because boron has these vacant

46:40.570 --> 46:43.260
orbitals and forms B_2H_6_
and so on.

46:43.260 --> 46:46.570
But it just happens that that
cancellation works that way.

46:46.570 --> 46:47.090
Lucas?

46:47.090 --> 46:50.310
Student:  Just by
looking at this picture we can

46:50.313 --> 46:52.963
say that CH_3,
that there's poor energy match

46:52.963 --> 46:56.073
because the orbitals around
fluorine are much smaller than

46:56.065 --> 46:57.205
those around CH_3.

46:57.210 --> 46:59.940
Prof: Let's look at the
next slide here.

46:59.940 --> 47:01.110
Is it this one? No.

47:01.110 --> 47:01.860
We're going to get to that.

47:01.860 --> 47:04.820
If you looked at ones that were
very badly mismatched,

47:04.824 --> 47:07.744
then the favorable and
unfavorable combinations would

47:07.735 --> 47:08.905
be very dramatic.

47:08.909 --> 47:12.389
Actually, you've already seen
that in H-F.

47:12.389 --> 47:15.519
Okay, we have one minute to
start this.

47:15.518 --> 47:22.148
Okay, so we're going to look at
how CH_3-F behaves like H-F.

47:22.150 --> 47:23.050
Right?

47:23.050 --> 47:24.110
Both of them are acids.

47:24.110 --> 47:26.680
So first we'll look at H-F,
and next time we'll go on to

47:26.679 --> 47:27.099
CH_3-F.

47:27.099 --> 47:28.929
So here's H-F.

47:28.929 --> 47:32.259
So you have to bring -- here's
a low vacant orbital.

47:32.260 --> 47:34.530
We've talked about that ad
nauseam.

47:34.530 --> 47:35.130
Okay?

47:35.130 --> 47:37.820
Now you want to get good
overlap.

47:37.820 --> 47:40.460
From what direction will
another orbital come,

47:40.460 --> 47:43.920
in order to get good overlap,
without the nuclei getting too

47:43.923 --> 47:45.043
close together?

47:45.039 --> 47:47.589
Obviously it'll come from off
in the right,

47:47.588 --> 47:50.748
where this orbital is big,
where you can get a lot of

47:50.746 --> 47:53.656
overlap without getting close to
the nuclei.

47:53.659 --> 47:56.679
So if you had something with a
high-energy pair of electrons,

47:56.675 --> 47:59.335
it would come and it would
overlap, from the right;

47:59.340 --> 48:02.510
something like OH^-.

48:02.510 --> 48:05.890
And you'd draw a curved arrow,
to show those electrons;

48:05.889 --> 48:10.029
the high HOMO of OH^-,
being stabilized by the vacant

48:10.027 --> 48:11.377
orbital of H-F.

48:11.380 --> 48:13.440
And how would you draw the
curved arrow?

48:13.440 --> 48:18.020
Where would it start,
where would it end?

48:18.018 --> 48:24.508
To show the electrons of OH^-
forming a bond with -- OH bond?

48:24.510 --> 48:27.080
<<Students speak over one
another>>

48:27.079 --> 48:30.009
Prof: You'd start from
the pair of electrons that

48:30.010 --> 48:32.570
you're talking about,
and you'd end between H and

48:32.570 --> 48:33.370
O.***Right?

48:33.369 --> 48:37.429
But that means -- this is
really important -- that means

48:37.432 --> 48:41.132
you're putting electrons,
putting electron density,

48:41.126 --> 48:42.456
into this orbital.

48:42.456 --> 48:43.266
Right?

48:43.268 --> 48:50.338
What effect does putting
electrons in that orbital have

48:50.335 --> 48:52.685
on the H-F bond?

48:52.690 --> 48:54.320
Okay, the curved arrows,
blah-blah;

48:54.320 --> 48:57.760
we did that.

48:57.760 --> 48:58.860
Sherwin?

48:58.860 --> 49:01.280
Student:  It's like it
pushes them out.

49:01.280 --> 49:02.030
Prof: It's what?

49:02.030 --> 49:05.260
What do you call that orbital?

49:05.260 --> 49:08.660
What's the name of the orbital,
that we're putting electrons

49:08.655 --> 49:09.055
into?

49:09.059 --> 49:09.969
Student:  1s for
--

49:09.969 --> 49:11.199
Prof: It's
σ*.

49:11.199 --> 49:13.309
It's mostly 1s on
Hydrogen, but it's

49:13.306 --> 49:14.206
σ*.

49:14.210 --> 49:15.780
What does * mean?

49:15.780 --> 49:16.610
Students:  Antibonding.

49:16.610 --> 49:18.820
Prof: What does it mean
if you put electrons in?

49:18.820 --> 49:19.800
Student:  The bond
breaks.

49:19.800 --> 49:21.190
Prof: The bond will
break.

49:21.192 --> 49:21.542
Right?

49:21.539 --> 49:24.159
It has that antibonding node.

49:24.159 --> 49:29.489
So electrons that go into that
will get more stable if the bond

49:29.494 --> 49:30.274
breaks.

49:30.268 --> 49:35.718
So we're going to draw another
curved arrow,

49:35.719 --> 49:37.239
like that.

49:37.239 --> 49:41.889
So we make a new bond between H
and O, but we lose the bond

49:41.887 --> 49:43.327
between H and F.

49:43.329 --> 49:44.639
So there's our product.

49:44.639 --> 49:50.089
That's an acid-base reaction,
and it showed H-F acting as an

49:50.092 --> 49:52.282
acid;
not because it gave H^+.

49:52.280 --> 49:55.380
H^+ never appears in here.

49:55.376 --> 49:56.206
Right?

49:56.210 --> 49:59.590
What happened is you make a
bond and break a bond to the

49:59.592 --> 50:00.272
hydrogen.

50:00.269 --> 50:02.159
So it's an acid-base reaction.

50:02.159 --> 50:05.239
And the same thing,
we'll show next time,

50:05.244 --> 50:07.024
happens with CH _3-F.

50:07.019 --> 50:07.899
Okay.

50:07.900 --> 50:13.000