Lecture 08. Molecular Motion.
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Martin, Rachel
 Principles of quantum mechanics with application to the elements of atomic structure and energy levels, diatomic molecular spectroscopy and structure determination, and chemical bonding in simple molecules. Slides: 0:
 Okay, so before we talk about, if 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? 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 seven, and rotational and vibrational spectroscopy. Thanks. And supposedly somebody is going to come fix this annoying blowing noise that's going on. Yes? Do you advise us to do work with regards to do problems from the book? So the question is, is it useful to do problems from 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 talk about in lecture. And if we talked 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 some things in 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 that I assign. The practice problems are a 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 emails 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. It, you know, it is what it is. It's from last year. 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? Is there a key up for it? No. You have to solve the problems yourself and you can, you can ask 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 post a 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 are lots of resources there. Anything else that we want to know about the exam? It's going to be 50 minutes. There will be a signed seating. So, please check the seating chart the night before. It'll be posted on the website. It really works a lot better if everybody knows your seat and comes in and can get seated right away so we can get started on time. Time will probably be an issue. There, you know, there are a lot 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, we won't let people start until everybody basically has it together. Question in the back. Okay. If you need a left-handed seat, don't worry about it. Just when the time comes, we'll switch. So, you can have one but I'm not going to put it into the seating 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. Okay. 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 them and, you know, shows up every time for them. But just in case, there's 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 Roland 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's going to be an assignment that you need to do that pertains to the seminar. That isn't posted yet. 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 to 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 to other universities and talking about our research. So the P-CEM 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 know, 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 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 some time 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 in to get the extra credit. Question? There's going to be an assignment, I haven't posted it yet, that asks 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 an 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 and runs away. Don't do that at the seminar. It's kind of, it's disruptive and the question and answer period is really part of it. If it goes over time and you have a class, that's a different story. If you have a class and it goes over time 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 opportunities that I can make to you there? Well, so that's an unfortunate thing. That's when 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 me or the TAs. But, you know, please don't punish me for this kindness by coming up with a million things that you want to go to that are at separate times. You know, try to just go to the PECEM seminar. Yes? Most of the classes that took they offered the lowest quiz to be dropped. The lowest quiz is dropped anyway. This is an additional opportunity. Yes? 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's more than one that wasn't so great for whatever reason it's just going to 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. Okay. 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 the schedule is. Okay. 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 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 were 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 write 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 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 9 because we have 9 objects in our basis and this case unit vectors. And then we started talking about what happens when you do a C2 rotation. Okay so remember this shortcut for the character which you can use as long as things map onto position previously occupied by something else in the basis. The way this shortcut works is if something changes places with another element it contributes 0 to the character. If it stays the same it contributes 1. If it changes sign it contributes minus 1 and you just 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 0 to the character. So we're only worried about the unit vectors on the oxygen. So x and y change sign, z stays the same and that adds up to minus 1. And so we can put this in the character table. Okay so now let's look at the reflections. So sigma at this point 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 y's 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 oxygen again. So or sorry I mean the hydrogens. That swaps the hydrogens so all the vectors on those contribute 0 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 an exam because it takes forever. So it's good to be able to just look at this and do it quickly. Yes? The sigma xz that's not negative 3. Sigma xz so all the x and z vectors stay the same so that's 6 and the y's change direction so that's positive 3. Yes? C2 why is it not negative 3? Why do you know negative 1? C2 so okay so all the vectors on the hydrogens change places so that's all 0 and x and y on the oxygen change sign but z stays the same because we're rotating about z. So it's negative 1. Okay so now we've done this. Yes? So y and z, y is not to be y and z goes to be 1. Because x contributes minus 1. X contributes minus 1 and then y and z contributes or would like to say right because it's 1 for y and z or did the hydrogens switch? The hydrogens just switch so they all contribute 0 so we're only talking about the ones on the oxygen so we have plus 2 minus 1. So this is one of these things where if you don't get it keep bugging the TAs in discussion, keep bugging me at office hours because once you get it it's really neat and you always will but it is challenging at first. Okay 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. Okay let's shut down the side 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 focused. Okay 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 than 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 in 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're 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. So now what do we do? So the idea is that we wanted to use this to tell us something about the motions of the molecule and in particular we're interested in vibrations. Yes? Sorry this might be a little behind but would you try this? What's your swing to the basis on the camera? Are we just going to swing on the ground? That's a good question. So the exam is going to be like a column. You know it's good 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 ramp up to you know here's some problem, solve it and people are going to get eluded 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 this 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 too but yes this is definitely something that you need to know how to set up on your own. Where do you find a good place to learn an effective way to use the basis? So chapter seven has some information about this but you know otherwise just do some practice problems and you know there really are 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 can just get out you know the general chemistry problems on Lewis structures and things like that and do those and you can check your answers 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 answer. So you can make up your own and do a whole bunch of them and that should be relatively straightforward. There aren't a lot of practice problems of this type in the book but it doesn't matter because you can make up your own and get the answers pretty readily. Okay 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 off the 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 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 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, 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. Okay 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 in each direction and you're going to have rotations about each of the three Cartesian axes and you have to take these 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 two A1 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 showed you what they were. We have a symmetric stretch and an 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 the math and trust that we get the right answer. OK. So 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 you the matrix for the polarizability tensor and it had terms that looked like x, x, x, y, x, z. 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 lower because the effect is weaker. But we're going to see three peaks. So the general idea is that for each irreducible representation that is active there is one peak. Right. So the idea is for every irreducible representation that we see 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 it's at 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 it's able to be polarized? If it's Raman active that means that that vibrational mode changes the polarizability. And the IR active means the vibrational mode changes the polarizability. That's right. Yes. For A1, can you have x squared, y squared and z squared? Would you get multiple peaks or is that all the quantities? That's a good question. So there's an x squared, 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's two A1 in the representation that you reduced. So there's two peaks not three. That's a good question. Okay. 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. Okay. So our basis is these four vectors. So that means that the identity operation has to have a character of four. 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 use the shortcut that we've been doing and just say, okay, we're holding it by that top hydrogen atom and rotating about the C3 axis. And so three of these things swap places and the one that we're 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. Okay, so there's the C3. Let's look at C2. So remember for methane the C2 axes 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 change positions. So now, you know, if we're holding the model so that, you know, we have two hydrogens here, one's coming out at you, one's coming toward me, if you turn it around they all change position. Yes? Can we bring molecular model kits? Alas, 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? I want to be able to use the flow chart and the biodegradable. Oh, that's a good question. Okay, so the things that I'm going to give you for the exam are, I'm going to give you the flow chart 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 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 give 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 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. And, you know, you can write as much stuff on that thing as you want to. If you want to print it out in one 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 cell phone is seen or heard, you're going to get kicked out of the exam. So if your primary calculator is your cell phone, find a different one. Borrow one from a friend and figure 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 in 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? Yeah, I have a question about the C3 operation. I'm sorry, could you repeat your question? Sorry, is this about the C3 rotation about the C? Yeah. What is the difference between the four operations or the three operations? But the C3 operation? Yes. So the question is why are there two different C3 operations? Why are there eight? So for some reason I was wondering if there are eight. Well, so you can hang on to each hydrogen and do it. Yeah, I vote. And then. You know what, why don't we talk about this after class? Because 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. Okay, 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 six 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 sense. 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.
 Okay, so before we talk about, if 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?  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 seven, and rotational  and vibrational spectroscopy.  Thanks. And supposedly somebody is going  to come fix this annoying blowing noise that's going on.  Yes?  Do you advise us to do work with regards to do problems  from the book?  So the question is, is it useful to do problems from 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 talk about in lecture.  And if we talked 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 some things  in 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 that I assign.  The practice problems are a 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 emails 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.  It, you know, it is what it is.  It's from last year.  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? Is there a key up for it?  No. You have to solve the problems yourself and you can,  you can ask 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 post a 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 are lots of resources there.  Anything else that we want to know about the exam?  It's going to be 50 minutes.  There will be a signed seating.  So, please check the seating chart the night before.  It'll be posted on the website.  It really works a lot better if everybody knows your seat  and comes in and can get seated right away  so we can get started on time.  Time will probably be an issue.  There, you know, there are a lot 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, we won't let people start  until everybody basically has it together.  Question in the back.  Okay. If you need a left-handed seat,  don't worry about it.  Just when the time comes, we'll switch.  So, you can have one but I'm not going to put it  into the seating 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.  Okay. 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 them and, you know,  shows up every time for them.  But just in case, there's 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 Roland 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's going to be an assignment that you need to do  that pertains to the seminar.  That isn't posted yet.  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 to 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 to other universities  and talking about our research.  So the P-CEM 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 know, 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 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 some time 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 in  to get the extra credit.  Question?  There's going to be an assignment, I haven't posted it yet,  that asks 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 an 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 and runs away.  Don't do that at the seminar.  It's kind of, it's disruptive  and the question and answer period is really part of it.  If it goes over time and you have a class,  that's a different story.  If you have a class and it goes over time 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 opportunities that I can make to you there?  Well, so that's an unfortunate thing.  That's when 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 me or the TAs.  But, you know, please don't punish me for this kindness by coming  up with a million things that you want to go to  that are at separate times.  You know, try to just go to the PECEM seminar.  Yes?  Most of the classes that took they offered the lowest quiz  to be dropped.  The lowest quiz is dropped anyway.  This is an additional opportunity.  Yes?  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's more than one  that wasn't so great for whatever reason it's just going  to 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.  Okay. 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 the schedule is.  Okay. 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 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 were 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 write  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 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 9  because we have 9 objects in our basis  and this case unit vectors.  And then we started talking about what happens  when you do a C2 rotation.  Okay so remember this shortcut for the character which you can use  as long as things map onto position previously occupied  by something else in the basis.  The way this shortcut works is if something changes places  with another element it contributes 0 to the character.  If it stays the same it contributes 1.  If it changes sign it contributes minus 1  and you just 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 0 to the character.  So we're only worried about the unit vectors on the oxygen.  So x and y change sign, z stays the same  and that adds up to minus 1.  And so we can put this in the character table.  Okay so now let's look at the reflections.  So sigma at this point 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 y's 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 oxygen again.  So or sorry I mean the hydrogens.  That swaps the hydrogens so all the vectors  on those contribute 0 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 an exam  because it takes forever.  So it's good to be able to just look at this  and do it quickly.  Yes?  The sigma xz that's not negative 3.  Sigma xz so all the x and z vectors stay the same so that's 6  and the y's change direction so that's positive 3.  Yes?  C2 why is it not negative 3?  Why do you know negative 1?  C2 so okay so all the vectors  on the hydrogens change places so that's all 0  and x and y on the oxygen change sign  but z stays the same because we're rotating about z.  So it's negative 1.  Okay so now we've done this.  Yes?  So y and z, y is not to be y and z goes to be 1.  Because x contributes minus 1.  X contributes minus 1 and then y and z contributes  or would like to say right because it's 1 for y and z  or did the hydrogens switch?  The hydrogens just switch so they all contribute 0  so we're only talking about the ones on the oxygen  so we have plus 2 minus 1.  So this is one of these things where if you don't get it keep  bugging the TAs in discussion, keep bugging me  at office hours because once you get it it's really neat  and you always will but it is challenging at first.  Okay 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.  Okay let's shut down the side 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 focused.  Okay 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 than 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 in 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're 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.  So now what do we do?  So the idea is that we wanted to use this to tell us something  about the motions of the molecule  and in particular we're interested in vibrations.  Yes?  Sorry this might be a little behind but would you try this?  What's your swing to the basis on the camera?  Are we just going to swing on the ground?  That's a good question.  So the exam is going to be like a column.  You know it's good 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 ramp up to you know here's some problem,  solve it and people are going to get eluded 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 this 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  too but yes this is definitely something that you need to know  how to set up on your own.  Where do you find a good place to learn an effective way  to use the basis?  So chapter seven has some information about this  but you know otherwise just do some practice problems  and you know there really are 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 can just get out you know the general chemistry problems  on Lewis structures and things like that and do those  and you can check your answers 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 answer.  So you can make up your own and do a whole bunch of them  and that should be relatively straightforward.  There aren't a lot of practice problems of this type in the book  but it doesn't matter because you can make up your own  and get the answers pretty readily.  Okay 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 off the 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 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 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, 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.  Okay 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 in each direction and you're going  to have rotations about each of the three Cartesian axes  and you have to take these 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 two A1 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 showed you what they were.  We have a symmetric stretch and an 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 the math  and trust that we get the right answer.  OK. So 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 you the matrix  for the polarizability tensor and it had terms  that looked like x, x, x, y, x, z.  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 lower because the effect is weaker.  But we're going to see three peaks.  So the general idea is that for each irreducible representation  that is active there is one peak.  Right. So the idea is for every irreducible representation  that we see 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 it's at 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 it's able to be polarized?  If it's Raman active that means  that that vibrational mode changes the polarizability.  And the IR active means the vibrational mode changes  the polarizability.  That's right.  Yes.  For A1, can you have x squared, y squared and z squared?  Would you get multiple peaks or is that all the quantities?  That's a good question.  So there's an x squared, 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's two A1 in the representation  that you reduced.  So there's two peaks not three.  That's a good question.  Okay. 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.  Okay. So our basis is these four vectors.  So that means that the identity operation has  to have a character of four.  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 use the shortcut  that we've been doing and just say, okay, we're holding it  by that top hydrogen atom and rotating about the C3 axis.  And so three of these things swap places and the one  that we're 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.  Okay, so there's the C3.  Let's look at C2.  So remember for methane the C2 axes 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 change positions.  So now, you know, if we're holding the model so that,  you know, we have two hydrogens here, one's coming  out at you, one's coming toward me,  if you turn it around they all change position.  Yes?  Can we bring molecular model kits?  Alas, 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?  I want to be able to use the flow chart  and the biodegradable.  Oh, that's a good question.  Okay, so the things that I'm going to give you for the exam are,  I'm going to give you the flow chart 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 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 give 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 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.  And, you know, you can write as much stuff  on that thing as you want to.  If you want to print it out in one 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 cell phone is seen or heard, you're going to get kicked  out of the exam.  So if your primary calculator is your cell phone,  find a different one.  Borrow one from a friend and figure  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 in 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?  Yeah, I have a question about the C3 operation.  I'm sorry, could you repeat your question?  Sorry, is this about the C3 rotation about the C?  Yeah.  What is the difference between the four operations  or the three operations?  But the C3 operation?  Yes.  So the question is why are there two different C3 operations?  Why are there eight?  So for some reason I was wondering if there are eight.  Well, so you can hang on to each hydrogen and do it.  Yeah, I vote.  And then.  You know what, why don't we talk about this after class?  Because 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.  Okay, 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 six 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 sense.  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.
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