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Lecture 15. Electronic Spectroscopy (Pt. IV)


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Title Lecture 15. Electronic Spectroscopy (Pt. IV)
Title of Series Chem 131B: Molecular Structure & Statistical Mechanics
Part Number 15
Number of Parts 26
Author Martin, Rachel
License CC Attribution - ShareAlike 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor and the work or content is shared also in adapted form only under the conditions of this license.
DOI 10.5446/18923
Publisher University of California Irvine (UCI)
Release Date 2013
Language English

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Subject Area Chemistry
Abstract UCI Chem 131B Molecular Structure & Statistical Mechanics (Winter 2013) Lec 15. Molecular Structure & Statistical Mechanics -- Electronic Spectroscopy -- Part 4. 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. Index of Topics: 0:01:42 Quiz 3: Electronic Transition 0:09:25 Diatomic Molecular Term Symbols 0:15:19 Frank-Condon Factors: Diagram 0:17:40 Dissociation Energies 0:20:57 Photoelectron Spectroscopy 0:27:38 X-Ray Crystallography
good morning today the plan is to finish up talking about electron spectroscopy and to start moving toward talking about mastering have a little detour where we look at 48 transformers and talk about crystallography really briefly just because it's neat and it ties into a lot of other things that we that we've been doing it uses for it transforms it involves the interactions between protons and and matter it's not spectroscopy for and talk about it not many great have it's neat involves symmetry I mean does anybody have any questions about electronic spectroscopy for anything from last guess it's hard to hear me Academy seafaring that because of the character any other questions about electronic spectroscopy it Franklin factors or anything like that OK good everybody's ready to take a quiz on instant you I remind you what they knew that I would be happy to stand here as the answering questions as much as you want but you use it during the day because of the it his enemy dropped anyway no matter what and the way that the way the seminars work is you get points if you answer the questions and then giving 5 points France when questions you have to answer every question and raise a reasonable amount for each thing to to get all the points so seminars on In general worth a little more than the average and how it works as they just get averaging acute respiratory so you can go to as many as you want as long as the actual key camp seminars are things that I've approved as far as being related to keep count and there's no limit so you know I'm sure this would never happen but if you mess up the quiz a retirement but a lot of summaries you can pretty much make it go away and not that not that anyone is worried about that today but there is also talk about this a little bit so it's it's not actually that difficult but I think it's a little tricky because it may worded in a different way than you're used to seeing have to pull up pull together a lot of stuff from the 2 blocks from different places in the class and that is kind of hard so that's all that's 1 of the things that I'd really like to get out of it so 1 of the problems with the with the Kennedys starting out is a lot of things that that people actually do in our research labs is so involves computationally that we can't really do more realistic example on Class B and so what I'd like to get out of it is an understanding of how we sort work through these problems here with the concepts are the cases where symmetry helps us and to really understand the fundamentals of some basic problems and many of the become the physical chemist new electronic spectroscopy a more complicated molecules then you can learn all the tools that you need to to understand these things application of its artist human time on this but I just wanted to briefly talk about 100 do a for the 1st 1 is an electronic transition from a signal plus state to a signal minus state induced by the polarized radiation allowed in HCl OK so what do you need no here you need you remember that each Cl belongs to the sea infinity the pointer which hopefully everyone figured out from having the pointer people there if nothing else on the other important thing about this question is that if you just remember Laporte's rule you got wrong answer because that only works for environments where there's an inversion center and of course the Cheltenham in Britain said so how do you actually do this is you take your character table and look at the cemeteries for the role of the relevant species so Sigma Plus is a 1 we have the for the dipole moment operator in the direction that's also a 1 and then Sigma minus is 82 and you multiply the coefficients for those things together and of course what you end up with belongs to the 8 2 symmetry species which is not everyone can see you can say the transition is not allowed so that's how you get so again it's really easy if you remember how to do it and if you don't it's confusing you know what want what I want to take a message is the Mentawai wanted to take a message to the it's just you know think about the the problem and the information that you're given and you figure out how to do it yes the good thing is that all of the money I do not think it would be a lot but now so it's Susie polarized radiation is telling us that you know it's only along the so so that the idea is is kind of a but that you got confused about the details OK I guess not at I'm To like the transition from minuses forbidden in what cases right so we we talk about various specific cases on you know as far as getting credit if you get the right answer when he wrote some reasonable rationale you get the right answer but I guess what I worry about the other on exams is that if you get the wrong answer but you had a reasonable thought process please make sure you write down enough that so that we can give you perfectly OK so that's the 1st 1 the 2nd 1 basically I just wanted you to draw up a potential diagram foreign these electronic status it only has to make it relatively simple and the business about the upper stage being shifted in the direction by a new 1 . 5 times the equilibrium bond distance is just to show that the apostate is viewership during the extraction as far as where its minimum and so if you drew something that looks kind of like that and you know drew in some vibrational energy levels than that but it's useful to deal with visualize these things and then for the expression for the amplitude of the transition basically what immediately is recognized there that the electronic part of it doesn't really enter and we're talking about the the franc common factor between these vibrational states so new double prime equals 0 means that this 1st permeate polynomial represents your initial state and then on to new prime equals 3 so your final state is represented by this other relief on a the and then you have to stick the X operator in between them because that's your that's a dipole moment operator and integrate that with respect to the axis and that's your that's Europe transition dipole and then the Francona factors related to that support so that's basically which you yes you of the to it's it's a whole wave function but for this example its units are related to these Herman on us so anyway he did need to evaluate it that wasn't part of the assurance was at yes no if you put this proportional to the overlap in the 2 states that is also fine yet OK so long
annoying OK technical difficulties sorry let's finish
up a discussion of electronic spectroscopy so the term symbols necessary for describing the states these molecules that I just wanna to talk about this in a little bit more detail for diatonic molecules because I think some people are confused about it I think everyone gets the atomic apart from last quarter and the people of parties seem to have a really good handle on that but I think for where this comes from 4 diatonic molecules is a little bit confusing and at this point like before I don't spend a lot of time learning how to generate these for complex molecules was just worry about the diatonic case and mostly I want to understand what they mean so we have our diatonic molecule we have the values of Ellen for the whole thing and our terms symbol looks like this we've got the the superscript is spin multiplicity which is 2 plus 1 and here as is the total spin quantum number for the molecule so to get you know to get this we have to some over all the electrons in the molecule and then this thing which is going to be Sigma Pi Delta etc. just like its STB for the honor atomic case that just tells you about the value of land for the molecule again some overall electrons and then this thing the subscript which was Jay the atomic case here it's called and same thing you're adding up the on busy projections of Ellen and here's little diagram of that for the molecule I also posted PDF of the tutorial on this stuff that I found online on that I think might be helpful so you can check that out a few if you want to work he still feeling the need to review of the stuff OK and again just terminology and in this particular thing signals the projection of at on the Internet clear axis so the same thing as what was when we're talking about me the atomic case we had like the total angular momentum and busy component of the England momentum here were projecting everything on the Internet where access but the idea is the same so that's where these things are coming from and what they're about OK so let's look at some specific examples of how to build the stuff so if we have our General Chemistry level of molecular orbital diagram we start with simply orbitals in here we're going to define Zia's the inner nuclear access and say This is what we get 1 hour when our PC orbitals overlap so we know that we get to molecular orbitals begin a bonding and anti bonding orbital and now we know that we can describe these as having GNU cemetery based on whether there even ride with respect to inversion and since we started out with the total value of em said all equal 0 and added that up that's going to give us a sick that's going to give a signature terms so we're going to get signal orbitals enforcing the terms we have an additional cemetery descriptor that we need to worry about said Gene you refer to what happens when you go through an inversion does a change sign or stay the same and then we also have a plus and minus and plus and minus refers to what happens when you reflect through a plane containing the Internet where access and there's a picture that it's a that is the Sigma minus terms because when reflected that plane changes sign whereas something that looks like this was bonding molecular orbital that's be signal plus because it stays the same when you're reflected through that plane so those are the cemetery descriptors for signatures when we get into things that have come larger values of blander than some of these things disappear so we don't have the the plus and minus a descriptor anymore but we can still write term symbols for these things so now let's say we have PX PY orbitals and they're going to be the same so we can just look at the the PX working the same thing these can overlap constructively or destructively we started with 2 atomic orbitals so we need to get to molecular orbitals at the end and we get a pie and pies start molecular orbital but now we have and being plus or minus 1 for the PX antivirals and again we can describe our client star molecular orbitals as having year you symmetry With respect to In version and these things up give us pipe terms and we need this summer over all electrons to to get that and it's plus remains 1 so hopefully that helps seeing some concrete examples as to what these things mean what talk about Frank Condon factors a little bit more so we have look at this mathematically and we've seen her radon expressions for them let's just look at some pictures and see what that looks like a graphically so basically if we have the bonding character to states being pretty similar so in this case both these wave functions look like there's a lot of fun electron density between the Adams there they have a lot of bonding character In that case the there's going to be a lot of overlap right at the .period were the into clear separation is that people are distress and were not a lot of fun different vibrational lines going on there because there is no reason for the nuclei to interchange position very much as a result of the electron coughing up to that excited states Strawberry said that the mechanism for that is that the electrons change state and then suddenly the nuclear feeling all kinds of different cell electronic potentials than they were before because the electron habits change shape and then they start to move around and we see these of original directions if the world pretty similar bonding character to begin with but there's not really much change and we'll see Of all winter of lines and spectrum whereas if the bonding character of the 2 states is really different so in this case we got the electronic ground state you know doesn't have a node in the middle of it and then it pops up to this excited states where there's a lot of new roads it does it does not have a there it does not have a rematch binding character in the middle of a molecule that causes a big change in the shape of the electron clouds and so we see this progression that has a lot of pizza and also the potential is shifted x-direction relative to that of the ransom a so we can also look at these things and learn something about dissociation energies so the In some cases we can estimate this really directly so again G U Nu was the year the energy of this electronic transition expressed in wave numbers and new is that is the point number here so we can write this down in terms of the the frequency of the transition and their access correction today the potential for a Morse oscillator which I know we did something some practice problems like that in the homework and so we can look at what happened at new Macs so when when you
is is maximized here that means were at the dissociation limit and so if we maximize this and and look at what happens when people 0 that gives us an expression for new match and the value for the energy of the transition when that condition is satisfied tells us about the dissociation at and so sometimes accumulating estimated directly another thing you can do is on use something like the birds from the plot which we talked about that there were some practice problems on that that's on where you plot that frequency versus the separation and take the uniformly should take area under a lot of times you have to exactly because you don't see lines going all the way up to the the dissociation limit here and so these are the kinds of things that we can get out of electron expected but a lot of what they're actually used for in practical applications or more like things that we saw earlier on when and when I talk about just some applications so a big thing that is done with electronic spectroscopy is just beers not just looking at OK how I have I have some substance that absorbs light and I wanted the concentration of it and you just use years lot figure out how much of it you have that's very common application of electronic spectroscopy costs there are a lot of other users involving learning something about the molecule as we've been talking about here and an important branch of physical chemistry research is taking these kinds of electronic spectra and using that to find out about the bonding energy of molecules what kind of bonding is being formed what do some of these excited states look like and of course that feeds into a lot of things like in synthetic chemistry learning about how the symmetry of different excited states affects what kinds of molecules you can make and before we finish this off and talk about 1 more applications so so far we've mostly been talking about electronic spectroscopy in you the invisible range so that has to do with valence electrons being promoted there relatively low energy transitions of go Of course the higher energy than the vibrational rotational transitions but were mostly talking about builds electrons jumping up and down if we want to learn more about the the bonding structure of the the molecule aura or added we can do for electron spectroscopy and so what we're doing here is itself a brute-force approach so instead of sweeping the frequency and looking at where things for we are just bombarding the sample with high-energy photons and fix wave like this is this is often In the X-ray so the idea is we have plenty of energy available to ionize all kinds of electrons even deep within the core of the molecule and then we can measure the kinetic energy of the electrons sorter detected and here's a schematic of how that works so we haven't been Of here shown as Adams could be molecules depends on what you're trying to measure and that is being blasted with high-energy photon sold again a lot of times as X-rays extended synchrotron so pretty often and then the electrons get ejected out and they are placed an electric field and so the baby band so the faster ones are over here this law ones are there and can measure the kinetic energy of the electrons that they come out of the sample and that tells us something about the bonding energy because of course the amount of energy that it takes to dissociate those electrons is related to the the energy that bond and so that can teach us about good bonding structure so here are some of the typical values so this is our energy in making tools from also it takes a lot of energy to knock these things off and you know as we get you as we get into the 1st so that if we look at war here the valence electrons are relatively easy to knock off and it starts to get a little bit harder but then we get down to that 1 s shall it takes a lot of energy to to electrons so it as you'd expect indeed electrons that are closest to the nucleus of most tightly bound but we do have plenty of energy to I nice although and so when you do this and look at all the peaks that you get it tells you something about the the bonding In the actors it tells you something about the electronic structure of the atom or molecule OK so in this case where we're just looking at Adams you might think it's really boring because surely somebody has measured all of the year the ionization energies for different electronic states in common Adams and that's true but you can use that to your advantage so 1 of the primary uses factory for electron spectroscopy is looking at a surface and figuring out what kinds of Adams are on that surface so since these things are well on the tables of what these energies look like you can find you know it really low levels of different kinds of things on the surface and and learn about you what that looks like you can also do this for molecules so here's 1 for into so again here's our general chemistry molecular orbital wobble die molecular orbital diagram for end to which is the reason most description of the bonding OK so as we saw before we're kind of I'm talking about this in a theoretical sense he here there there's 3 bands in In the spectrum so it is what we get when we remove a had a weekly bonding electron so that's the 2 clean Sigma gene orbital N that transition has relatively few lines so ionizing that it tells us that popping up from the from the ground state that state doesn't change in a clear separation for a much whereas B it is removing a strongly bonding electron that see the pie you it's from the high you molecular orbital so that's that's down here that requires a lot more deviation in the Internet we're distance and so we see a bunch more by racial lines and then see comes from removing a weekly entered binding electron and so on yet here we have a weaker transition and we only see 1 peak said that it's a relatively short progression so just to give you an idea of fun how these things work and how that's used OK so we don't have a lot of time left but I do want to start talking about X-ray crystallography a little bit and will finish up product next time so just to give you an idea of where we're going with this there's a whole chapter on solids it contains a bunch of stuff about crystallography I think it's Chapter 9 we mostly skipped it it might be useful to go in and skin and have a review of things like the difference between Crystal and an amorphous solids of something a crystal it's in really regular repeating lattice if it's amorphous it's still solid but it's a lot more disordered a lot of this stuff that's in that chapter is pretty descriptive and there's not a lot that we can really do with so it's it's it's useful to look at it but when I spent a lot of time on it what I want to talk about
it is crystallography as an interaction between the periodic lattice of your molecules in In the crystal and X-rays and of course this happens because we can have a constructive and destructive interference between the wave function of the electrons and the incoming X-ray photons and crystallography this is not spectroscopy were just looking at X-rays diffraction off the wave function of electrons but it's related to 1 of the other stuff we're doing because it involves these ideas of symmetry so it so instead of .period groups when we start talking about crystal lattices we need to assign things to space groups and anybody who is in error crystallography lava has all the crystal structure of an organic molecule has seen some of these things it's kind of the next level of symmetry arguments there were talking about and the periodic structure of the crystal is what enables it to the fact X-rays so How many of you have been involved in solving the crystal structure and some in some way either and researcher In loves OK so if you but how about crystallizing stuff in organic chemistry lab purify at the ready seems to me that way yes so we were able to get so close crystallizing your your compound is a good purification method because you make this really regular lattice were molecules that are the wrong shape don't fit in there and then we end up with this periodic function that can actually missed the fact X-rays and so that happens because electrons have some wave character making interact constructively and effectively with the photons and so you get something that looks like this so we should the X-ray beam at year crystallized molecule and you know that crystal in this illustration looks pretty messy but you know in general you need a very nice crystal in order to get diffraction and then the X-rays to get scattered off the molecule are there undetected and you get a regular pattern of spots that has something to do with the crystal lattice it the fact it gives you the the inverse of the dimensions of the crystal lattice indirect and when and then that enables you to get an idea of what the the unit-cell looks like for molecules so here's 1 from a crystal structure of rhodopsins so we talked about Robson when when we were talking about how our eyes work and how we have to be careful about calibrating our instruments so we understand rhodopsins because it's been crystallize there's also been a bunch of animal structures and different kinds of about and that so here's what the units all of this looks like an again if you want to review White unit sales of crystals look like go check out I think it's Chapter 9 there are a bunch of simple examples in here this is a complicated 1 but but it it obeys the same principles so here a B and C are the dimensions of the of the unit-cell so that's are repeating unit so this is the origin here were looking down the a axis and then B and C. shown here good here are just some
examples of diffraction patterns that can be used to solve molecular structures so this is the original fiber diffraction pattern of the DNA double helix might in a picture didn't show up here but hopefully everybody knows what it looks like so we see these regular repeating units in case the DNA we've got patterns here and then reflections here that's that's reflecting the repeating pattern in the DNA of course we don't end in that case it's a fiber so it's it's only crystal and in 1 dimension whereas if we have a three-dimensional crystal we see really regular patterns of spots which we can then analyzing used to get the molecular structure and I'm going to quit therefore take his word time next time we're talking about this mysterious process by which that happens here Friday
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