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[ Silence ]
>> OK. So, before we talk about we finish up our discussion
on molecular vibration,
we should probably talk about some logistics.
So first of all, exam logistics.
Is there anything that anyone wants to know about it?
>> Yeah.
>> Yes.
>> What are we covering up to?
>> What are we covering up to?
Basically everything that we do in lecture before the exam
so all the symmetry stuff, chapter 7 and rotational
and vibrational spectroscopy.
[ Inaudible Remark ]
>> Yes. And supposedly, somebody is going
to come fix this annoying blowing noise that's going on.
Yes?
>> Do [inaudible] I'm sorry, do problems on the book?
>> So, the question is it useful do to problems on the book.
Yeah, if you want extra problems to do.
So, if you understand-- so the main things that are going to be
on the exam are things that we talked about in lecture.
And if we talk about something
in lecture a whole lot then it's really, really likely
that that's going to be on the exam.
Things that you do in discussion are also important
so the TAs are, you know, trying to cover something
at a little bit more depth that maybe we went through quickly
and that's important too, and anything that's in the book
that you need to do the practice problems I that assigned.
The practice problems are really big part of it.
So, sitting there working out these things are, you know,
that's a major part of how you really get the material.
So, if you've done all of that
and you still want extra practice,
problems in the book are a fine thing to do too.
I've also posted last year's exam just
in case people want it.
So, here's the caveat for that.
The class is not identical.
I've changed up the order of things.
We're skipping some stuff that we did last year, you know,
we're doing some other things.
And, so there are things on last year's exam
that we haven't covered at all in class.
I really, really don't want 50 e-mails asking if that thing
that we haven't covered this year is on the exam.
It's not. So, you know, it's there as a resource.
Everybody has it if they want it.
You know, it is what it is.
It's from year last, it's not intended to be a perfect replica
of what's going to be on this year's exam but, you know,
there it is and everyone has access to it.
Yes?
>> What--
>> Is there a key up for it?
No, you have to solve the problems yourself
and you can your TAs.
That sounds like a fine thing to do in discussion.
I have tons and tons of office hours.
You can try to work out the problems and come ask me there.
But no I'm not going to [inaudible] key.
The other thing is you can also use the Facebook page.
There's absolutely no rule against, you know,
posting what you got for the answers
and everybody discussing it, and in fact I encourage that
and the TAs and I will weigh in on, you know,
what we think about what you did.
So, there're lots of resources there.
Anything else that we want to know about the exam?
It's going to be 50 minutes.
There will be assigned sitting
so please check the sitting chart the night before.
It will be posted on the website.
It really works a lot better if everybody knows your sit
and comes in and can and get seated right way
so we can get started on time.
Time will probably be an issue.
You know, there are lots of problems and it might be hard
to finish so it's good
if everybody knows what they're doing and gets seated on time.
You know, we won't let people start
until everybody basically has it together.
Question in the back?
[ Inaudible Remark ]
OK. If you need a left-handed seat, don't worry about it.
Just when it's-- when the time times comes we'll switch.
So, you can have one but I'm not going to put it
into the sitting chart beforehand.
And we are going to check IDs so make sure you bring your ID.
It's a big class so we need to do this stuff.
OK. So one more logistical thing that I want to talk
about before we move on is, I have an extra credit opportunity
for you in the, you know,
off-chance that somebody didn't do well on some of the quizzes.
Probably that's not true.
Probably everyone is doing great on the--
you know, shows up every time for them.
But just in case, there is an extra credit opportunity.
And that is, what you need to do is go
to the physical chemistry seminar
which is say it's something offered
by the chemistry department, they're usually on Tuesdays.
They're at 3:30 to 4:30 in Rowland Hall.
And all of this information is it's
on the UCI chemistry website and it's linked to our class website
and you can look at it.
There is going to be an assignment that you need to do
that pertains to the seminar.
That isn't [inaudible] I'll try to do it on--
I'll try to do it this weekend so that if anybody wants to go
to the one on Tuesday, you can go.
So, when you go the seminar, what this is about is--
you know, of course as you know, professors teach
but we also do research
like that's a large part of what we do.
And part of it is going around other universities
and talking about our research.
So, the PChem seminar is professors working
in physical chemistry from other universities who are coming
to talk about their latest research results.
And when you go to this, you might not understand everything.
It's going to be hard.
I mean, this is for graduate students and professors.
And so, what you really want to try to do is, you know,
at least the first part of it when they're talking
about the background and the motivation
for what they're doing, you try
to really see how much you can get out of that but,
you know, I am warning you.
It's hard to jump in.
And this is an important part of learning how to be a scientist
in a particular field.
So, you know, if you want to be become a physical chemist and go
to grad school in this area, this is something
that you have to ramp up on.
And it's difficult because it's
like the bus is going 30 miles an hour and you have to jump on,
and it takes sometime to get going.
So, don't be discouraged
if you don't understand everything that's
at the seminar, you know, just try to pick up what you can.
And there will be some basic questions that you have
to answer about the seminar and turn it to get the extra credit.
Question?
[ Inaudible Remark ]
There's going to be an assignment.
I haven't posted it yet, that ask you some general things
about the seminar and you're going to sign a statement saying
that you actually went to the seminar
and answered the questions yourself and, you know,
not doing that is academic dishonesty.
I'm sure nobody would do that in upper division class but,
you know, it's there just to be sure.
The other thing that I want to say is
that the way this works is, you know, there's a whole seminar
and then at the end there's a question and answer period.
The question and answer period is part of the seminar,
like that's part of the thing.
So, please do not do what often happens in class
where the PowerPoint slides have some magical property
that when they stop everyone gets up runs away.
Don't do that at the seminar, it's kind--
it's disruptive and the question
and answer period is really part of it.
If it goes overtime and you have a class,
that's a different story.
If you have a class and it goes overtime, you can run away.
That's their fault for not staying on the time,
but otherwise please stay for the question and answer period.
That's part of it.
Question?
>> Will there be any other activities [inaudible]?
>> Well, so that's-- that's an unfortunate thing.
That's what it is.
And, you know, otherwise you just have
to come to the quizzes.
So, here's another thing you can do.
You can find other seminars offered
by the chemistry department and make a case that it has to do
with physical chemistry and run it by near the TAs.
But, you know, please don't punish me for this kind
by coming up with a million things that you want to go
that are at separate times.
Try to just go to the PChem seminar.
Yes?
>> Most of the classes [inaudible] they offer the
lowest quiz to be dropped [inaudible].
>> The lowest quizzes dropped anyway.
This is an additional opportunity.
[ Inaudible Remark ]
Yes.
>> It's part of the quiz grade.
>> It's part of the quiz grade.
So, if you do this and you get credit for it, it's just going
to be averaged in with the rest
of your quiz grade as an extra thing.
And so, if there-- you know, if there is more than one
that wasn't so great for whatever reason it's just going
to be bring-up that average.
So, that's how it works.
And, it's completely optional.
You don't have to do it.
So, you know, if you can't go then, you know,
I hope you can make it for all the quizzes.
OK. Yes? Another question?
>> When and where is the seminar?
>> It's Tuesdays at 3:30, but you have to go look
at the schedule and see, you know, on the website
because it's not every Tuesday and you just have
to check out what schedule is.
OK. So, last time, we left off talking about molecular motions.
And, now we're learning how to use the character table
and the information contained there to find--
to try to predict some things about IR
and Raman spectra of molecules.
So, in this case our basis is a set
of little unit vectors attached to each atom.
And of course, the reason for that is that we're talking
about the displacement of these atoms.
So, when we do these problems the basis always has something
to do with the symmetry of the actual problem
that we're concerned about.
So, when we're talking about bonding, they pointed
in the direction of the bonds.
Now we're talking about motion so we have these things
that have to do with the displacement of the atoms.
And of course, to do this problem, we could right
down a full matrix for each operation but it's a 9
by 9 matrix and I don't want to,
I make enough typos those anyway.
So, instead what we started doing last time is using this
shortcut to just figure out the character of the matrix.
And so for the identity, we just get nine,
because we have nine objects in our basis
in this case unit vectors.
And, then we started talking about what happens
when you do a C2 rotation.
OK. So, remember the shortcut for the character
which you can use as long as things map on to, you know,
position previously occupied by something else in the basis,
the way the shortcut works is if something changes places
with another element it contribute zero
to the character, if it stays the same it contributes one,
if it changes the sign it contributes minus 1
and you just to add them all up.
So, for-- if we do a C2 rotation and, you know,
number the atoms 1, 2, and 3,
the ones on the hydrogens all switch places.
So, they all contribute zero to the character.
So, we're only worried about the one--
the unit vectors on the oxygen.
So, X and Y changed sign, Z stays the same and that's adds
up to minus 1, and so we can put this in the character table.
OK. So now let's look at the reflections.
So, sigma at this point is described-- is defined as XZ,
so it's in the XZ plane.
And so, what that means is all the Y axes are going
to change sign and everything else stays the same.
So, X and Z each contribute 1.
All the Ys contribute minus 1.
So, we get a total of 3 for the character.
In sigma prime, so that's the one cutting
through the molecule, that swaps the oxygens again so--
or sorry, I mean the hydrogens.
That's swaps the hydrogens so all of the vectors
on those contribute zero
and we're just worried about the oxygen.
And so in that case, the Y and Z unit vectors stay the same,
X switches sign and we end up with 1.
So again, you can write down the whole 9 by 9 matrix
for this and look at it.
It's probably worth doing once just to prove to yourself
that that's how it works and that you can use the shortcut.
I really don't recommend trying to do that on the exam
because it takes forever.
So, it's good to be able to just look at this and do it quickly.
>> Question.
>> Yes.
>> The sigma XZ that's not the [inaudible]?
>> Sigma XZ, so all the X and Z vectors stayed the same
so that's six, and the Ys changed direction
so that's positive 3.
Yes?
[ Inaudible Remark ]
C2? OK, so all the vectors on the hydrogens change places
so that's all zero, and X and Y on the oxygen changed sign
but Z stays the same because we're rotating
about Z. So, it's negative 1.
OK. So, now we've done this.
Yes?
>> So Y and Z, Y is that one not the [inaudible] Y
and Z both negative 1?
>> Because X contributes minus 1.
>> X contributes minus 1 and then Y
and Z contribute [inaudible] 2, right,
because it's 1/3 Y [inaudible]
or did the hydrogens switched and--
>> The hydrogens switched so they all contribute 0.
So we're only talking about the 1s on the oxygen.
So we have plus 2 and minus 1.
>> All right.
>> So, this is one of these things
where if you don't get it, keep bugging the TAs in discussion,
keep bugging at office hours because once you get it,
it's really neat and, you know, you always will it's--
but it is challenging at first.
OK. So now we have this, right?
We have our reducible representation that is going
to tell us something about the displacement for the molecule.
And so, now we need to reduce it and try to learn something.
OK. Let's shut down the slide conversations, I'm really happy
to answer questions but with this thing going
on it's already really hard to talk over it and keep focus.
OK. So we have our reducible representation
and then we're going to use the reduction formula
which I'm not going to do because it takes too long
but I know everybody knows how to do it.
And, here's the answer we get.
So, we have more symmetry species that we did in some
of these other things because our basis is more complex.
So one thing that you should notice is the number
of symmetry species that we get should be the same as the number
of elements that were on our basis in the first place.
So, we had nine vectors
and so we should get nine symmetry species
in the reduced answer.
And this is worth knowing, because when you are trying
to do these problems that's a good checkpoint
to check your answer.
So, if you get fractions you know that's not good and also
if you get something that doesn't add
up to the original number of things
in the basis that's a sign that you should go check your answer.
All right.
So, now what do we do?
So, the ideas that we wanted to use this to tell us something
about the motions of the molecule.
In particular, we're interested in vibrations.
Yes?
[ Inaudible Remark ]
That's a good question.
So, the exam is going to be like a column.
You know, it's like you're going to start with problems
that are kind of easy where I do tell you the basis
and you just have to come up with something
and then they're going to get harder and ramped up to,
you know, here's some problem, solve it, and people are going
to get alluded off in order of how much they know
and hopefully everybody will be with it at the end.
So, there are going to be problems exactly like this,
where the question is here's some molecule,
tell me which vibrations are IR and Raman active
and you're going to need to know how to set
up all the stuff to do it.
Those aren't the only kinds of questions.
There are going to be some things
where you have some more guidance to.
But, yes, this is definitely something that you need
to know how to set up on your own.
[ Inaudible Remark ]
So, chapter 7 has some information about this but,
you know, otherwise just do some practice problems.
And, you know, there really--
for the kind of problems that we've been talking about,
we have sort of two things, one is we've talked about bonding.
And so those are good practice problems
because you know the answers.
You could just get out, you know,
the general chemistry problems on Lewis structure and things
like that and do those, and you can check your answer really
easily because you know them.
The other thing that we've been talking about where you have
to set up your basis is molecular motions,
and that's problems like this.
You can also check your answers with that
because you can Google the IR and Raman spectra
of these molecules and see if you came
up with the right answers.
So, you can make up your own and do a whole bunch of them,
and that should be relatively straightforward.
There are a lot of practice problems of this type
in the book, but it doesn't matter 'cause you can make
up your own and get the answers pretty readily.
OK. So, we're talking about molecular motions, right?
But, the ones we care about are vibrations
because that's what we measure when we do infrared
or Raman spectroscopy, so either absorption
or scattering of a molecule.
And, so what we have to do before we can figure out which
of these things are vibrations is we have to subtract
out the symmetry species that belong
to translations and rotations.
So, remember, we reduced this basis that has to do with the--
just displacements of all the atoms.
So, that doesn't distinguish among what kinds
of motions that there are.
So, you'll see what I mean in a minute.
So we have-- if we have some molecule and it can move around,
we have to deal with just the symmetry
of displacements in space.
So, it's moving, you know, along the X direction
or along the Y direction or along the Z direction.
And so, we do that by looking at where these translations are
in terms of the symmetry species.
So, if you look at the character table for C2v, you find that X,
Y, and Z belong to the B1 and B2
and A1 symmetry species respectively.
And so the translations remove one of each of those
from the representation.
So, those get taken out
and they're not available for vibrations.
OK. So then the next thing we have
to worry about is rotations.
And if you look at your character table, there are RX,
RY and RZ that are assigned to symmetry species.
Those are rotations about that axis.
And so, for those of you who have been wondering what we use
that for now you know.
And so we look at what symmetry species those belong to
and then we take those out.
And so, for any molecule that we're talking about,
you are going to have translations of each direction
and you're going to have rotations about each
of the three Cartesian axes, and you have to take this
into account before we talk about what's going
on with the vibrations.
So, we remove these from our reduced representation
because they're accounted for,
and then what's left is the vibrations.
And so, what we have left are 2A1 because one
of them got taken out for a translation,
and we also have a B1 left, and that's it.
So the water molecule has three vibrational modes
that we can pick up in the spectra.
And, you know, remember when we first started talking
about this, I've showed you what they were.
We have a symmetric stretch and asymmetric stretch and a bend.
So, I like to do water first
because we can visualize really easily what all the vibrational
modes are.
For some more complicated molecules it's going
to be hard and, you know, we're just going to have
to use [inaudible] that we get to the right answer.
OK. So we've got two-- we've got three vibrational modes.
And remember, our gross selection rules.
So, for something to be infrared active it has
to change the dipole moment.
And so that means that it has to belong
to the same symmetry species
as a component of the dipole moment.
That means X, Y, or Z. So, how do we figure this out?
We just look at the character table.
So, we have a B1, and that belongs
to the same irreducible representation as X,
and then A1 has Z. And so that means that all three
of these vibrational modes are IR active.
So, if we take an IR spectrum of water,
we're going to see three peaks.
All right, so now what happens if we take a Raman spectrum?
So, remember the rule for that is that it has
to change the polarizability.
There has to be an anisotropic polarizability
when we put the molecule in an electric field,
the electron cloud distorts more along one direction
than the other, depending
on whether it's parallel or perpendicular.
And so that means that your vibrations have to belong
to a component of the polarizability.
So remember, I showed the matrix for the polarizability tensor,
and it had terms that look like XX, XY, XZ.
So, if you have something that looks like that
in that symmetry species then your vibrations are
Raman active.
And be careful, because if you find
out that they're all IR active
that doesn't mean they're not Raman active too.
They can be one or the other, they can be both,
they can be neither, it just depends you have to look.
So, B1 has an XZ and A1 has X squared,
Y squared and Z squared.
So, they're all Raman active too.
So, if we take a Raman spectrum of water,
if we have the same amount
of sample the intensity will be a lot a lower
because the effect is weaker but we're going to see three peaks.
Yes?
>> So, the general idea is
that for each irreducible representation
that is active [inaudible]?
>> Right. So, the idea is every--
for every irreducible representation that we see,
you know, that is predicted by symmetry to show
up in the spectrum, there's going to be a peak.
So we have 2A1, there are two different peaks.
So, that brings us to a good point
about what symmetry does and doesn't tell us.
So, it tells us that there is a peak somewhere.
It doesn't tell us what energy is that, for example.
It doesn't tell us how strong it is.
It's just a yes or no answer.
So, this is really powerful as far as predicting some things
about the spectrum but it doesn't tell us everything.
It doesn't tell us where that line is going to be located
and it doesn't tell us how strong it is.
There are other ways that we can do that and we're going
to learn about some of them.
But it is really powerful that we can at least figure
out what's in the spectrum.
Yes?
>> So, the Raman active means [inaudible] to be polarized?
>> If it's Raman active that means
that that vibrational mode changes the polarizability.
>> OK. And the IR active [inaudible] the vibrational mode
change [inaudible]?
>> That's right.
Yes?
>> A1 [inaudible] X squared, Y squared and Z squared,
would you get [inaudible] or is
that still-- is that [inaudible]?
>> That's a good question.
So, for-- so there's X squared and Y squared and Z squared
in the representation.
That's not what tells you how many peaks you have.
It's the fact that there is 2A1
in the representation that you reduced.
So, there's a two peaks not three.
That's a good question.
OK. So, we're going to do another example.
And we're going to go through bonding and we're going to go
through the rotations, translations and vibrations,
for an example that's harder than what you're going
to be asked to do on the exam.
So, if you know how to do this, you're in good shape.
Let's talk about methane.
So, methane is hard because it has a lot
of different operations that we can do.
It belongs to a high symmetry group.
So, first let's talk about bonding.
So, if we want to know which orbitals make up the sigma bonds
in this tetrahedral molecule our basis has
to be little vectors pointing along the bonds,
because of course we want to start with something
that has the same symmetry as the object that we're interested
in and then we want to find that out in terms
of the actual atomic orbitals.
OK. So, our basis is these four vectors, so that means
that the identity operation has to have a character of 4.
Now, let's talk about some other stuff.
So, let's think about C3 first.
So, if we write down our basis elements as a vector just
in the order, 1, 2, 3, 4 and then we do a rotation,
we can write down the matrix that it takes to represent that,
oops, and so that's one way to do it.
The other thing you can do is, is use the shortcut
that we've been doing and just say, OK, we're holding it
by that top hydrogen atom and rotating about the C3 axis.
And so three of these things swapped places and the one
that were rotating about stays the same so the character is 1.
That's a totally fine way to do it too.
And on the exam, we don't really care how you do any
of this stuff as long as you get to the right answer.
So, if it's right it's just right as long
as there's some reasonable work.
If it's wrong, you know, try to write down as much as you can
so that we can see what you're thinking.
OK, so there's the C3.
Let's look at C2.
So, remember for methane the C2 axis go
between the hydrogen atoms like this, and if that's hard
to visualize play with your models.
And so, if you remember where the axis goes, it's easy to see
that all your vectors changed position.
So now, you know, if we're holding the model so that,
you know, we have two hydrogens here and ones coming
out at you ones coming toward me, if you turn it
around they all change position.
Yes?
>> Can we bring molecular model?
>> Last, no.
I don't think you can use molecular model kits just
because it's going to be too much going on.
So, practice and learn how to visualize them.
Yes?
[ Inaudible Remark ]
Oh, that's a good question.
OK. So the things that I'm going to give your for the exam are--
I'm going to give you the flowchart that has--
that tells you how to put things in a point group.
I'm going to give you the character table.
I'm not going to make a copy of the whole thing.
I'm going to copy, you know, particular point groups
that you need and some that you don't need.
So, just because it's in there it doesn't mean
that you should feel compelled to use it, but you are going
to have all the point group tables that you need.
What else am I going to give you?
I'm going to you a periodic table to help
with drawing Lewis structures.
And, that is all I'm going to give you.
You may bring a calculator, which should only be used
for doing numerical calculations like--
please don't store a bunch of stuff in there.
And then you can also bring a cheat sheet, which is one 8 1/2
by 11 piece of paper with stuff written on it.
>> Both sides?
>> Both sides.
And you know, you can write as much stuff
on that thing as you want too.
If you want to print it out in 1 point font and you can read it,
you know, good for you.
You can't bring a magnifying glass though.
No microscopes.
So the rules for the exam, you can use a calculator.
You can use this cheat sheet.
I'm going to give you the information I said.
If your cellphone is seen or heard you're going
to get kick out of the exam.
So, if your primary calculator is your cellphone find a
different one.
Borrow one from a friend and figure it out how
to use it before then.
Yes?
>> No textbook and no notes?
>> No textbook and no notes, well,
other than your one page cheat sheet.
I like the cheat sheet because you would get all the benefit
out of it even if I made you throw it on the trash on the way
in the door because you have to study and figure out, you know,
what's important that you're going to write on that thing.
And then as we go through the class, you still only have one
so you have to remember more stuff to put it on there.
I'm not going to make you throw it away, but it would do just
as much good if I did.
Question?
[ Inaudible Remark ]
>> I'm sorry.
Could you repeat your question?
[ Inaudible Remark ]
Yeah.
[ Inaudible Remark ]
>> The C3 operation?
>> Yeah.
>> So, the question is why are there--
why are there two different C3 operations?
[ Inaudible Remark ]
Well, so you can-- you can hang on to each--
you know, you can hang on to each hydrogen and do it.
>> Yeah.
>> And then--
[ Inaudible Remark ]
You know what, why don't we talk about this
after class 'cause I think it might--
it's hard to do with this much distance and we should get
through a little bit more of this, but we'll talk about it.
OK. So, for C2-- all right, I do want to try to get
through this example, at least the bonding.
All right, so for C2 everything changes position,
for S4 everything also changes position.
So, remember what S4 is, that means rotate 90 degrees
and then reflect about a plane that's parallel to that axis.
So, everything changes position.
And then we have 6 sigma D. And for that we have two vectors
that stay the same because they're in the plane, you know,
we're cutting through those bonds, and then we have two
of them that get swapped.
So, that is our representation for bonding.
Then we need to reduce it.
And again, everybody knows how to do
that so I'm not going to show you.
And here's what we get.
And what we learn is that A1 is the S orbital.
So, remember the symmetry species that has ones
under every operation is invariant.
That's the symmetry of a sphere so that's an S-orbital.
And then we also get T2.
And remember I told you that something that has a T
in the character name is triply degenerate.
And if we look at that, that has X, Y and Z, so those correspond
to the three P orbitals on carbon.
And of course, you have to know some chemistry
because you can also get an answer involving D orbitals.
And if we were talking about permanganate
that might make some since but we know
that for methane they're not involved.
So again, you know, when you're doing these things check your
answer and make sure that it makes sense.
Next time, we're going to start back up with this example
and talk about its vibrations and then we're going to move
on to diatomic molecules and how
to predict some more numerical things.
See you next time. ------------------------------84d143da4d29--