Lecture 08. Molecular Motion.


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Lecture 08. Molecular Motion.
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Martin, Rachel
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UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 08. Molecular Structure & Statistical Mechanics -- Molecular Motion. Instructor: Rachel Martin, Ph.D. Description: 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: 0:00:08 Molecular Motion 0:26:37 Methane Bonding
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OK so before we talk about the fairness of our discussion molecular vibration we on we should probably talk about them logistics so 1st of all I think exam logistics Is there anything they want to know about yes but the watery covering up to basically everything that we do in lecture before the exams all the cemetery stop Chapter 7 and rotational and vibrational spectroscopy and supposedly somebody's going to conflicts this annoying blowing ways that that's going on yes so the question is is it useful to new problems with vote yet you want extra problems to do so if you if you understand to the main things that are going to be on the exam are the things that we talk about in lecture and if we talk about something and lecturer whole lot then it's really really likely that in the end the exam on things that you and discussions are also important so that so that users you know trying to cover something a little bit more debt that may be movement through quickly and that's important to and anything that's in the book that you need to do the practice problems that I signed the practice problems really part of was sitting there working out these things for you know that that's a major part of heightened really get material so if you've done all that and you still want extra practice problems in the Booker finding to too but I also posted last year's examines just in case people wanted so here's the caveat that the class is not identical exchanged at the order of things were skipping some stuff that we did last year you know we're doing some other frames and so there are things on last year's exam that we haven't covered it all in class I really really don't want to be e-mails asking if that thing that we haven't covered this year is on the map it's not so you know it's there as a resource everybody has it if they wanted it get you know it is what it is it's it's from last year it's not intended to be a perfect replica of what's going to be this exam but if you there it is and everyone has access to it yes it is there to be up for it no you have to solve problems yourself and you can you can ask your CA that sounds like a fine thing to do and discussions of I have tons and tons of office hours you can try to work out the problems and some nasty there's no not following the other thing is you can also use the Facebook page there is there's absolutely no rule against you know hosting what you got for the answers and everybody discussing it and in fact I encourage that and years and I will weigh in on you know what we think about what to do there are lots of resources there on anything else that we want to know about the exam it's going to be 15 minutes there will be assigned seating so please check the seating chart connecting for post on the website it really works a lot better everybody knows 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 better for everybody knows what they're doing and gets seated on time more we won't let people start and told everybody basically has it together ?question mark I'm OK tendency I don't worry about it just when it's when the time comes we will switch so you can have 1 but but I'm not going to put it into the seating chart beforehand and then we are going to check ID so make sure you bring your idea it's a big laugh so to lead to the south OK so when the logistical things that I want to talk about before we move on it is I have an extra credit opportunity for you the media on the off chance that somebody didn't do well and 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 I just think case there is a sex offender opportunity and that is well what we need to do is go to the physical chemistry seminar which is 1 of 6 something offered by the chemistry department there are usually on Tuesday as the 330 to 430 enrolled Hall and all this information is From the UCI chemistry website and it's linked to our past website you can look at it if there's going to be an assignment that you need to do that pertains to the seminar that isn't host Seattle 20 on all tied to do it this weekend so that if anybody wants to go to the 1 on Tuesday you can go so we got a seminar about what this is about is he of course as as you know professors teach but we also do research like that a lot of large part of what we do and part of it is going other universities and talking about research so that he can summon is professors working in
physical chemistry from other universities who were coming to talk about the latest research results and when you this you might not understand everything it's going to be hot ministers for graduate students and professors and so what you really want trying to do is not least the 1st part of it when they're talking about the background and the motivation for what they're doing you try to really the way how much you can get out of that but you know I am I am warning you it's hard to jump in and this is an important part of learning how to be a scientist in particular field so you know if you want to become a physical chemist to go to grad school in this area this is something that you have to ramp up on it's difficult because it's like busses going 30 miles an hour and 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 of the the summer you just see kind of pick up what you can and will be some basic questions that you have to answer about the seminar and turn in to get the extra credit question we there is there's a there's going to be an assignment have posted that there are still some general things about something and you're going to sign a statement saying that you actually went to the seminary answered the questions yourself and you know not doing that is his academic dishonesty and sure nobody would do that in a provision class but you know it's it's there just to just to be sure parliament the other thing that I want to say is that the way this works is you there's a whole seminars and then at the end there is a question and answer period the question-and-answer period as part of a seminar on that part of the thing so please do not do what often happens in class during the PowerPoint slides have some medical property that when they stop everyone gets up and runs away don't do that the seminar extended its destructive and the question-and-answer period is really part of it he it goes if it goes over time and you have a class that's a different story if you have a class goes over time you can run away that's their fault for not staying on time but otherwise please stay for the question-and-answer period that occurred question 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 is 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 by nearly 2 years by you know please don't punish me for this kindness despite coming up with a million things that they want to go to the bar at separate times to try to just go to the consumer gets on top of the of each the lowest quizzes dropped anyway this is an additional opportunity yes that's part of it was great so if you do this and you get credit for it it's just going to be operated in with the rest of your quiz grade as an extra thing and so if there were you know if there's more than 1 that wasn't so great for release and it's just gonna bring up that average that's not how it works and it's completely optional you don't have to do it so you know if you can if you can't go there and you know what I hope you can make it for was OK yes no question it's Tuesday's at 330 but you have to go look at the scandal and see the on the Web site because it's not every Tuesday and just have to check out the scandalous 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 fight to try to predict some things about R Rahman spectrum molecules so in this case are basis is a set of little unit vectors attached to each Adams and of course the reason for that is that work were talking about the displacement of these adults so when we do these problems the bases always has something to do with the symmetry of the actual problem there were concerned about so we're talking about wanting they pointed in the direction of what's 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 then I might it's the mind matrix and I don't want make enough Tyco's anyway so instead what we started by doing last time is using this shortcut to just figure out the the character of the matrix and so for the identity we just get 9 because we have 19 objects in a basis in this case unit vectors and then we started talking about what happens when you do see 2 workstation OK so remember this this shortcut for the character which you can use as long as things now want to the opposition previously occupied by something else in the basis when a shortcut works as if something changes places with another element it contribute 0 the the character if it stays the same it contributes 1 if the changes sign it contributes minus 1 just animal lot so for if we do see each irritation and you number the Adams 1 2 and 3 the ones on the hydrogen this all switch places so they all contribute 0 2 character so we're only worry about 1 the union vectors on the so X and Y change signed these days the same and that adds up to minus 1 and so we can put this India but the character table a case announced that the reflections SOS signal at this point is described as defined as X The Sowetan the EXE plane and so what that means is all the y Accies gonna change signs and everything else is the same so Excellency each contribute 1 otherwise contribute minus 1 so we get a total of 3 for the character In a single crime so that's the 1 cutting through the molecule that swaps the oxygen is again so er sorry mean hybrid that's what's hydrogen sold the vectors on those contributed 0 and we're just worried about the oxygen and so in that case the widens the unit vector stay the same X which is signed and we end up with 1 so again you can write down the whole line by matrix for this and look at it it's probably worth doing once just to prove to yourself that but that's how it works and that this they can use the shortcut I really don't recommend remedial unexamined takes so it's it's going to be able to to just look at this and you quickly yes Sigma X z so all Excellency vectors status since about sex and the wise change direction so that positive 3 yes I think c to so peso so that all the vectors on hydrogen strange places so that's all 0 and X and Y on the oxygen change signed busy stays the same because we're repeating about the social and OK so now we've done this yes I think that what you want to do this because X contributes minus 1 you know what you don't like it was the end the hydrogen is switch so they contribute 0 so we're only talking about the ones on the accident so we must you minus 1 so this is 1 of these things work if you don't if you don't get it keep bugging me ETA in discussions keep bugging the office hours because once you get it it's really need you knew what you always well it's so but it but it is challenging 1st OK so now we have this great we really we have our irreducible 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 became a center on the site conversations I'm really happy to answer questions but with this thing going on it's already really hard to talk program the focus
OK so we have a really small 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 sedentary species than we did in some of these other things and because our basis is more complex so 1 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 the basis in the 1st place so we had 9 vectors and so we should get 9 symmetry species and be a reduced cancer N 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 on the basis that's a sign that he should go tractor answer all right so now what are we doing so the idea is that we wanted to use this to tell us something about the motions of molecule and 4 in particular were interested in vibrations yes and what about you the that's a good question so the exam is going to be like like a column notes good like you're going to start with problems that are kind of easy where do tell you the basis you just have to come up with something and then they're going to get harder and ramp up to you hear some problem and people are going to get eluded often were how much they know and hopefully everybody will be with it at the end so there are going to problems exactly like this where the question is here some molecule tell me which vibrations are higher on active and you need to know how to set up all the stuff to do it those are the only kinds of questions there are already some things really helps more guidance to but yes this is definitely something we need to know how to set up on own following subchapter 7 has some information about this by you know otherwise just do some practice problems and being you know they're they're really are further the part of the kind of problems that we've been talking about we have sort of 2 things 1 is we talk about bonding and so those are good practice problems because you know the answers you could just get out the general chemistry problems on Lewis structures and things like that and do those and you can check eventually easily because you know that the other thing that we've been talking about where you have to say that the basis molecular motions and that's problems like this you can also check your answers with that because you can Google the IRA enrollment spectra of these molecules and see if you came up with the right answer she can make up your own and you will want to and that that should be relatively straightforward there are a lot of practice problems of this type in the book but it doesn't matter because you can make up your mind and get the answers pretty well OK so we're talking about molecular motions raised by the ones we care about the vibrations because that's what we measure what we do infrared Rollins cost city the absorption and scattering of molecule and so what we have to do before we can figure out which of these things our vibrations as we have to subtract out the cemetery species that belonged to translations and rotations so remember we reduced this basis that has to do with the just displacements of all the adults so that doesn't distinguish among what kinds of of motions of so you'll see what I mean and met so we have if we had some molecule that can move around we have to deal with just this the symmetry of displacements in space so it's it's moving along the extraction along the Huai direction along the direction and so we do that by looking at where were these translations are in terms of the cemetery species if you look at the character table 4 c to see you find that x y and z belonged to the B-1 B-2 and 81 symmetry species respectively and so the translations to remove 1 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 forex are Ozzie their assigned a cemetery species those rotations about that access and so for those of you who've been wondering what we use that for 19 0 and so we look at what cemetery species those belong to you and then we take those yeah and sofa for any molecule that there were talking about you are going to have translations in each direction and you're going to have rotations about each of the 3 parties in taxis 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 readers representation because there are accounted for and what's left is the vibrations and so what we have left our to 281 it is 1 of the taken out for a translation and we also have a new 1 left and that's it so the water molecule has 3 vibrational modes that we can pick up inspector and they don't remember when we 1st started talking about this I should do with their work we have an asthmatic stretch and an asymmetric stretch and then so I like to do Water 1st because we can visualize really easily won all the vibrational modes are for some more complicated molecules it's going to be hot and you know we were just going to have to to use the mountain and trust that we get the right answer OK so we've got to we've got 3 vibrational modes and
remember our selection rules so for something to be infrared active it has to change the Bible moment and so that means that it has to belong to the same cemetery species as a component of the dipole moment that means wires eh so and we figured this out we just look at the character table so we have a 1 and that belongs to the same irreducible representation as X and then a 1 has cuisine and so that means that all 3 of these vibrational modes are IRA active so if we take an I spectrum of water worthiness he repeats Eriksson now what happens if we take a Roman spectrum so remember the role for that is that it has to change the polarize ability there has to be an isotropic always ability when we put the molecule in electric fields the electron distorts along 1 direction and the other UN depending whether it's Carol perpendicular and so that means that you're vibrations have to belong to a component of the plausibility to ratio to the matrix for the portability tenser it had terms that looked like X X X Y. X so if you have something that looks like that in that cemetery species then your vibrations a Roman active and be careful because if you find out that they're all IRA active that doesn't mean they're not Roman active to they can be 1 or the other they can be both can neither it just depends on the what's so the 1 has an ecstasy anyone has expert the square so the overall enacted too so if we take a Roman spectrum of water if we have the same amount of sample the intensity will be a lot lower because the effect is weaker going 3 peaks yes the general of the European tour right so the ideas every for every irreducible representation that we see no predicted by symmetry 2 hours to show up in the spectrum there's going to be there's going to be so we have to to anyone there are 2 different things so that give brings us to the point about what symmetry doesn't doesn't tell us so it tells us that there is a peak somewhere it doesn't tell us what energy attack for example it doesn't tell us how strong it is it's just a
yes-or-no answer so this is really powerful Spurs predicting some things about the spectrum but it doesn't tell us everything doesn't tell us where that line is going to be located and it doesn't tell us how strong this there are other ways that we can do that and Morgan learned about some of them but it is really powerful that we can at least figure out what's in the spectrum yes and if
it it's wrong enacted that means that that operational mode changes the plausibility ability the that's right yes it was you don't want to be around the world that's a good question so before so there's an extra points for disease word in the representation that's not what tells you how many peaks you have it's the fact that there's 281 in the representation that you reduced so there's 2 peaks not free but the good question OK so soaring and you another example and we're going to go through bonding and we're going to go through the rotations translations of vibrations for an example that's harder than waiting to be asked to do an so if
you during the check .period about methane so nothing is hard because it has a lot of different operations that we can do it belongs to a high symmetry group so firstly to talk about bonding so if we want to know which orbitals make up the single bonds in this technical molecule Our basis has to be a little vectors pointing won the bonds because of course we want to start with something that has the same cemetery is the article were interested in and we want to find that out in terms of the the the actual atomic orbitals OK so basis is these 4 records so that means that the identity operation has to have a character of now let's talk about some other stuff so what I think about C 3 1st so if we right our basis elements as a factor just in Europe 1 2 3 4 and then we do rotation we can write on them that the matrix that it takes 2 represent that troops and so that's 1 way to do
it the other thing you can do is use the shortcut that we've been doing just say OK holding it by that talk of a hydrogen atom and retaining about the C 3 axis and so 3 of these things swap places on the 1 that were rotating about stays the same so the characters 1 that the totally fine way to do it too yeah and on the exam we don't really care how we do any of this stuff as long as you get to the right answers so that's right it's just it's just right as long as there's some reasonable work if it's wrong you know I try to write down as much as you can so that we can see what you're thinking OK so there's a C 3 what's
look at sea to so remember for methane the beseech you taxis go between the hydrogen atoms like this and if that's so if that target is always play with your models and so if you if you're ready access those it's easy to see that all your actors change positions so so now know for working for holding that the model so that you into hydrogen Surat ones coming out of you ones coming toward me if you turn around they'll change position yes a no I don't like it I don't think so you can use like the model just because of it's going to be too much going on so practice and and 100 had visualized guessed it with all that's a good question OK so the the things that I'm going to give you for the exams are I'm going to give you the flow chart that has that tells you how to put things in a pointer I'm going to give you the character table I'm not going to make a copy of the whole thing and then a copy no 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 of the pointer tables that we need what else might give you an many give a periodic table to help with the driver Lewis structures and so that is all I mean giving 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 1 8 half by 11 piece of paper With stuff written on it "quotation mark and you know you can write as much stuff on that thing is you want to European you want printed out 1 point font and you can read it no good for you you can bring a magnifying glass that no microscopes so so the rules for example you can use a calculator you can use this cheat sheet I'm going to give you the information I said if your cellphone Encina herded many get kicked out of the exam so if your primary calculator is your cellphone find a different 1 borrower borrowed 1 from a friend and figure out how use it before then yes no textbook no notes while other than Europe .period page cheat sheet I like a cheat sheet because you would get all the benefit out of it even if a major thrown in the trash on the way in the door because you have to study and figure out you you know what's important you then right on that thing and then as we go through the class you still only have once you have to remember more started to put it on there I'm not going to make a further away but it would do just as much of it if I didn't question and while the of yeah and I'm sorry I couldn't hear question yeah but the C 3 operation so that the question is wired the wider 2 different C 3 operations also you can you can hang onto each shot you can have its hydrogen and do it the you know what would we talk about the separate classes I think it might it's it's it's hard to do With there is much distance and we should get a little bit more this will talk about it OK so for seat you alright and I do want to trading through this this example is the bonding rights sofa see to everything changes position for asked for everything also changes positions to remember what s for years that means rotate 90 degrees and then reflect about a plane that heralds that access to everything changes position and then we have 6 segment and for that we have 2 vectors that status same because there were In the playing there were coming through those bonds and then we have to them they get swapped so that is a representation for bonding then we need to review said and again everybody knows how to do that some market share and here's what we get and what we learned is that anyone is the assault also remember the cemetery species that has ones under every operation is invariant that's the symmetry of a sphere so that the Nassau Vermont and then we also get T 2 and underwrite told you that something that has a team in their character name is I'm terribly degenerate and if we look at that has x y and z so those correspond to the 3 fewer rules on permanent and of course you have to know some chemistry because you can also get an extra involving the orbitals and if we were talking about Khamenei made 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 make sure that it makes us next time Morgan start back up with this example and talk about it vibrations and then we're going to move on to the diatonic molecules and protect somewhat numerical things next


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