WEBVTT 00:01.767 --> 00:03.867 J. MICHAEL MCBRIDE: OK, so we're ready for a new 00:03.867 --> 00:07.667 phase here, to talk about spectroscopy, the interaction 00:07.667 --> 00:09.867 of light with matter and what it can 00:09.867 --> 00:11.227 tell us about molecules. 00:13.933 --> 00:17.073 We'll talk today about electronic and infrared 00:17.067 --> 00:22.227 spectroscopy, and in particular, with infrared 00:22.233 --> 00:26.173 spectroscopy, about normal modes and the mixing and 00:26.167 --> 00:29.327 independence of vibrations. 00:29.333 --> 00:34.303 So the purposes we use spectroscopy for are to 00:34.300 --> 00:38.230 determine structure and to study dynamics. 00:38.233 --> 00:42.173 So we use electronic spectroscopy that's visible and 00:42.167 --> 00:47.697 UV, where it's motion of electrons that's being excited 00:47.700 --> 00:48.900 by the light. 00:48.900 --> 00:52.230 Or vibrational, where it's motion of the nuclei, the 00:52.233 --> 00:55.273 atoms, being excited by the light. 00:55.267 --> 00:59.667 Or NMR, where it's a magnetic interaction with 00:59.667 --> 01:00.967 light that's involved. 01:03.400 --> 01:06.800 Spectroscopy comes from the word specter. 01:06.800 --> 01:10.270 In 1605 it was used, according to the Oxford English 01:10.267 --> 01:11.767 Dictionary. 01:11.767 --> 01:15.127 to be straunge sights, visions and apparitions, so that's 01:15.133 --> 01:17.703 like the specters of ghosts, right? 01:17.700 --> 01:21.730 Or Newton used it in the 1670s to be Sunbeams... 01:21.733 --> 01:23.773 passing through a glass prism... 01:23.767 --> 01:27.127 exhibited there a spectrum of diverse colors... so this 01:27.133 --> 01:30.603 kind of ghost. So that's where the word comes from. 01:30.600 --> 01:33.330 Now Atom in a Box, which we used last semester and it's 01:33.333 --> 01:35.803 shown over on this screen, can be used to 01:35.800 --> 01:37.370 show a number of things. 01:37.367 --> 01:41.197 It can show spectral transitions for the H atom. 01:41.200 --> 01:44.100 Let's get this here. 01:44.100 --> 01:49.770 And if you click spectrum here, you get-- 01:52.400 --> 01:54.130 where is it now? 01:54.133 --> 01:55.633 I think it's off the screen. 01:55.633 --> 01:57.173 I enlarged things here. 01:57.167 --> 02:01.867 But anyhow, it gives you what the spectral transitions are, 02:01.867 --> 02:04.497 what energies are involved in going from one-- oh, I think 02:04.500 --> 02:08.770 it's because I didn't get simplified at work here. 02:08.767 --> 02:09.727 What's going on? 02:09.733 --> 02:11.003 Why isn't it simplifying? 02:17.433 --> 02:21.473 My guess is because I blew this up to be on the screen. 02:21.467 --> 02:22.167 It's not showing. 02:22.167 --> 02:24.467 Anyhow, we've done that before and seen that you can 02:24.467 --> 02:28.167 see the energy levels of different things, different 02:28.167 --> 02:31.467 atomic levels and the wavelength that's involved. 02:31.467 --> 02:34.267 We can see the static shift in electron density, from if 02:34.267 --> 02:37.497 mixing 2s with 2p orbitals. 02:37.500 --> 02:41.700 Maybe I'm going to have to bring this back down again, 02:41.700 --> 02:45.030 and see if it works now. 02:52.267 --> 02:55.727 I don't know why it's not working. 02:55.733 --> 02:58.103 Well, fortunately, the most important stuff I'm going to 02:58.100 --> 03:02.730 have is A, displaying there, and B, also on the PowerPoint, 03:02.733 --> 03:05.173 so you can do this on your own time. 03:05.167 --> 03:08.167 OK, you can see the shift, as we saw last semester, from 03:08.167 --> 03:09.897 mixing 2s with 2p. 03:09.900 --> 03:13.600 Remember, that'll shift the electrons from one side to the 03:13.600 --> 03:16.570 other of the nucleus, depending on the hybridization. 03:16.567 --> 03:20.167 We can see the oscillation of electron density that comes 03:20.167 --> 03:23.897 from mixing orbitals with different energy, and that's 03:23.900 --> 03:25.170 what's involved here. 03:25.167 --> 03:30.397 You'll notice over here, we've got a mixture of the 1s with a 03:30.400 --> 03:33.000 2p orbital. 03:33.000 --> 03:36.530 What we showed before was fixed in time, and it would 03:36.533 --> 03:39.003 shift it up or down. 03:39.000 --> 03:43.770 But if you look at it as time goes on, you see that it 03:43.767 --> 03:47.697 actually goes back and forth between being down and being 03:47.700 --> 03:49.600 up, being down and being up. 03:49.600 --> 03:54.330 So the electrons, when you mix 1s and 2p, oscillate up and 03:54.333 --> 03:57.103 down in time. 03:57.100 --> 04:01.030 And that's because of a change in relative phase with time. 04:01.033 --> 04:04.703 You add s with p, and then subtract s with p, and it goes 04:04.700 --> 04:06.300 one way and then the other. 04:06.300 --> 04:08.770 And I'm going to illustrate that. 04:08.767 --> 04:11.327 This is a feature of time-dependent quantum 04:11.333 --> 04:15.173 mechanics, where the phase of the wave function changes at a 04:15.167 --> 04:17.167 rate proportional to its energy. 04:17.167 --> 04:18.697 And I'll go through this just a little 04:18.700 --> 04:19.570 bit on the next slide. 04:19.567 --> 04:21.867 We're not going to spend too much time on it, because it's 04:21.867 --> 04:23.597 not really the business of this class. 04:23.600 --> 04:25.230 But it's so neat that I thought you'd like 04:25.233 --> 04:26.973 to know about it. 04:26.967 --> 04:30.067 But anyhow, when you have the electron shifting up and down 04:30.067 --> 04:32.697 like that, it's like an antenna. 04:32.700 --> 04:36.000 It gives off light. 04:36.000 --> 04:37.770 In fact, it can absorb light, too. 04:37.767 --> 04:41.027 Antennas can either transmit or receive. 04:41.033 --> 04:45.373 So that's what allows electrons in atoms to interact 04:45.367 --> 04:49.297 with light as an oscillating dipole. 04:49.300 --> 04:54.400 You can also do breathing by mixing 1s with 2s, but that 04:54.400 --> 04:56.200 doesn't interact with light, because it 04:56.200 --> 04:57.700 doesn't generate a dipole. 04:57.700 --> 05:00.800 And I'm going to illustrate that. 05:00.800 --> 05:04.900 So here's 1s, mixing 1s and 2p. 05:04.900 --> 05:09.230 So as we see here, if 2p is both up and down, but with 05:09.233 --> 05:13.933 opposite phases, 1s is a single phase, a single sign. 05:13.933 --> 05:17.073 If you add the two, it reinforces above. 05:17.067 --> 05:18.967 OK, and we've seen that before. 05:18.967 --> 05:20.727 But if you make it time dependent-- 05:20.733 --> 05:22.933 that's what's being shown over there-- 05:22.933 --> 05:28.403 then what happens in time, is that it goes up and down. 05:28.400 --> 05:31.600 it's And the oscillation frequency, how rapidly it goes 05:31.600 --> 05:34.630 up and down, that is what color of light would interact 05:34.633 --> 05:37.573 with it, what frequency of light, has to do with the 05:37.567 --> 05:42.127 energy difference between 1s and 2p. 05:42.133 --> 05:43.603 So here, this is just a footnote. 05:43.600 --> 05:46.170 You're not deeply responsible for this, but I 05:46.167 --> 05:47.967 wanted you to see it. 05:47.967 --> 05:49.497 So I'll just read it to you. 05:49.500 --> 05:52.900 A time-dependent wave function looks just like the 05:52.900 --> 05:56.430 psi's we've been talking about, functions of position. 05:56.433 --> 05:58.233 Except that it's also got something to 05:58.233 --> 06:00.303 do with time, obviously. 06:00.300 --> 06:05.870 It's multiplied by e to the i omega t. 06:05.867 --> 06:11.627 And you know e to the ix is cos x + i sin x. 06:11.633 --> 06:12.873 Have you done that? 06:12.867 --> 06:15.497 I think you may have seen that. 06:15.500 --> 06:19.870 So you have a cosine and a sine of omega t, one is real 06:19.867 --> 06:21.097 and one is imaginary. 06:21.100 --> 06:24.100 It's a complex number that you're multiplying the wave 06:24.100 --> 06:25.500 function by. 06:25.500 --> 06:27.370 So i is a square root of -1. 06:27.367 --> 06:30.797 Omega is the energy in frequency units. 06:30.800 --> 06:36.170 That's how rapidly things are changing in time, because it's 06:36.167 --> 06:38.197 cos omega t. 06:38.200 --> 06:41.830 So as time increases, the cosine goes up between plus 06:41.833 --> 06:44.103 and minus one. 06:44.100 --> 06:48.630 And how fast it goes up and down depends on how big omega 06:48.633 --> 06:53.133 is, because omega t is what you're taking the cosine of. 06:53.133 --> 06:57.673 So the higher frequency omega is, the faster it'll go up and 06:57.667 --> 07:01.767 down, the higher energy omega is. 07:01.767 --> 07:06.527 And now that's an interesting question, because it depends 07:06.533 --> 07:10.473 on what-- the magnitude of the energy for any given system-- 07:10.467 --> 07:15.567 depends on where you define 0 to be. 07:15.567 --> 07:18.667 If you to define 0 to be separated particles, that's 07:18.667 --> 07:19.667 one energy. 07:19.667 --> 07:21.767 If you define it to be the ground state, that's a 07:21.767 --> 07:22.827 different energy. 07:22.833 --> 07:25.673 And this would suggest that the rate of oscillation 07:25.667 --> 07:28.467 depends on what you call 0. 07:28.467 --> 07:29.827 That seems nuts, right? 07:29.833 --> 07:33.333 It can't depend on you, what the rate of oscillation is. 07:33.333 --> 07:36.603 And the reason is, you don't care what the rate of 07:36.600 --> 07:38.200 oscillation is. 07:38.200 --> 07:40.230 And I'll show you why. 07:40.233 --> 07:43.273 Because when you square the wave function to get the 07:43.267 --> 07:48.797 probability density, at any given time, you multiply psi 07:48.800 --> 07:52.730 times e to the i omega t, times psi to the e to the 07:52.733 --> 07:54.133 -i omega t. 07:54.133 --> 07:57.403 That's how you do squaring with complex numbers, multiply 07:57.400 --> 07:59.600 by the complex conjugate. 07:59.600 --> 08:01.000 And that gives psi squared. 08:01.000 --> 08:03.730 All the stuff about time cancels out. 08:03.733 --> 08:06.073 So you don't really care. 08:06.067 --> 08:09.127 So why do you have it in there in the first place? 08:09.133 --> 08:13.673 If you're mixing two different states that have different 08:13.667 --> 08:16.897 energy, then they oscillate at different frequencies. 08:19.967 --> 08:22.667 So really, you don't care how fast either one 08:22.667 --> 08:25.127 is oscillating alone. 08:25.133 --> 08:28.873 You only care what the difference in frequencies is. 08:28.867 --> 08:31.527 So now it doesn't depend on what you call 0, because the 08:31.533 --> 08:34.973 one state you're taking and the other state you're taking 08:34.967 --> 08:38.767 have the same difference, whatever 0 is. 08:38.767 --> 08:39.767 That's where you make a difference. 08:39.767 --> 08:43.267 So it says, when a problem involves actually mixing two 08:43.267 --> 08:46.697 states of different energy, one considers a wave function 08:46.700 --> 08:52.370 of the form, e to the i omega 1t, plus a different psi, the 08:52.367 --> 08:56.397 other wave function, times e to the I omega 2t. 08:56.400 --> 09:01.070 Now, if omega 1 and omega 2 are different, this means that 09:01.067 --> 09:05.567 the two spatial functions cycle in and out of phase with 09:05.567 --> 09:06.197 one another. 09:06.200 --> 09:10.700 If at a certain time they add at a time 1/2 divided by the 09:10.700 --> 09:13.530 difference in frequency later, they subtract. 09:13.533 --> 09:17.473 So 1s + 2pz will become 1s - 2pz. 09:17.467 --> 09:22.567 So if this is the energy here, the oscillation frequency of 09:22.567 --> 09:27.627 2pz, then 1s will have a lower oscillation frequency, by that 09:27.633 --> 09:30.033 energy difference between them. 09:30.033 --> 09:32.233 And it'll look like that. 09:32.233 --> 09:35.573 So here, they're in phase with one another, the cosine part, 09:35.567 --> 09:37.067 they're adding. 09:37.067 --> 09:39.397 But in the middle there, they're out of phase, and it's 09:39.400 --> 09:40.670 subtracting. 09:40.667 --> 09:44.497 And then it comes back into phase again at the far right. 09:44.500 --> 09:50.270 So as time goes along, it comes s+p, s-p, s+p, s-p, 09:50.267 --> 09:55.467 and the electrons go up and down. 09:55.467 --> 09:58.727 So if you mix these two orbitals-- 09:58.733 --> 10:04.473 so an electric field that's oscillating up and then down 10:04.467 --> 10:07.927 and then up and then down favors this at the first time, 10:07.933 --> 10:11.773 then plus, then minus, then plus, then minus. 10:11.767 --> 10:14.967 So the light interacts with the electrons and pushes them 10:14.967 --> 10:19.197 up and down, mixing 1s with 2p. 10:19.200 --> 10:22.470 Now, if you do that for a while, and then turn the light 10:22.467 --> 10:28.627 off, it may end up being in the s-p, when it started 10:28.633 --> 10:30.573 in the s-p, or vice versa. 10:30.567 --> 10:33.767 So you can get an absorption, or indeed, an 10:33.767 --> 10:36.767 emission of light, the interaction with light and 10:36.767 --> 10:38.827 things, because of this time dependence. 10:38.833 --> 10:42.803 But again this is not really our business, and you'll see 10:42.800 --> 10:43.300 that later. 10:43.300 --> 10:46.330 So this is the source of the oscillation we observe, when 10:46.333 --> 10:49.473 superimposing functions of different n 10:49.467 --> 10:51.597 using Atom in a Box, different energies. 10:51.600 --> 10:53.570 So that thing going up and down over there. 10:56.400 --> 11:00.100 And note, just as a footnote to a footnote, this is 11:00.100 --> 11:02.530 different from what we were doing when we made hybrids. 11:02.533 --> 11:04.873 We mixed s with p before. 11:04.867 --> 11:08.497 Usually we were mixing 2s with 2p, which have very similar 11:08.500 --> 11:10.530 energies, right? 11:10.533 --> 11:15.403 But in those cases, we weren't trying to mix two real states, 11:15.400 --> 11:19.800 that's why I said actually up there. 11:19.800 --> 11:23.670 There we were just trying to get in a reasonable form for a 11:23.667 --> 11:27.067 wave function of some particular energy. 11:27.067 --> 11:30.267 But when light is involved, you actually mix states of 11:30.267 --> 11:34.767 different energies, so it's a different situation. 11:34.767 --> 11:37.867 So we've got this oscillation up and down, which 11:37.867 --> 11:39.227 interacts with light. 11:39.233 --> 11:40.603 It can generate light. 11:40.600 --> 11:43.270 It can absorb light. 11:43.267 --> 11:47.697 Now, the 1s to 2p transition is said to be allowed, because 11:47.700 --> 11:50.600 it happens with light. 11:50.600 --> 11:54.700 But there are other mixtures that don't generate light. 11:54.700 --> 11:57.570 For example, if you mix 1s with 2s. 11:57.567 --> 12:00.497 If you add the two, it reinforces where they're blue, 12:00.500 --> 12:02.370 and subtracts when they're red. 12:02.367 --> 12:06.027 That makes a big circle, a big sphere. 12:06.033 --> 12:09.373 But if you subtract them, make the one on the left red and 12:09.367 --> 12:12.297 add it to the other one, then they'll reinforce in the 12:12.300 --> 12:15.700 middle and cancel on the outside, and it'll be inside. 12:15.700 --> 12:19.630 So if you mix those two, you get this dependence with time. 12:19.633 --> 12:20.873 I think it's going to do it. 12:23.300 --> 12:24.800 Whoops, I didn't wait long enough. 12:24.800 --> 12:26.830 But what happens, and you can do it yourself, it goes [makes 12:26.833 --> 12:28.073 expanding and contracting sounds]. 12:30.800 --> 12:32.670 It's breathing. 12:32.667 --> 12:35.467 But that's not separating the average position of the 12:35.467 --> 12:37.067 nucleus and the electron. 12:37.067 --> 12:41.267 It's not going up and down to make a vector, a light. 12:41.267 --> 12:44.697 It's just expanding and contracting. 12:44.700 --> 12:48.230 So that symmetrical breathing electron-density deformation 12:48.233 --> 12:49.873 has no oscillator strength. 12:49.867 --> 12:52.797 It doesn't interact with light's magnetic field. 12:52.800 --> 12:55.770 So that transition is said to be forbidden. 12:55.767 --> 12:58.467 You can't cause it to occur with light. 12:58.467 --> 13:02.197 Now, what does this have to do with organic molecules and the 13:02.200 --> 13:05.230 things we were just talking about, which were polyenes. 13:05.233 --> 13:08.333 You remember a bunch of bunch of double bonds in a row. 13:08.333 --> 13:11.433 Well, suppose you have C=X double bond, and X is some 13:11.433 --> 13:16.503 heteroatom, like oxygen or nitrogen, it's something 13:16.500 --> 13:19.000 that has an unshared pair of electrons. 13:19.000 --> 13:21.030 So it has n electrons. 13:21.033 --> 13:26.173 But it also has a pi* orbital, a vacant orbital. 13:26.167 --> 13:27.697 Now, can you mix those two? 13:27.700 --> 13:30.570 What would happen if you mixed those two orbitals? 13:30.567 --> 13:33.797 You could add them together, and they'd reinforce in the 13:33.800 --> 13:37.770 top-right and cancel on the bottom-right. 13:37.767 --> 13:40.897 And you get the electrons to move up. 13:40.900 --> 13:45.130 And if you changed the sign, they'd move down, if you 13:45.133 --> 13:47.973 subtracted one from the other. 13:47.967 --> 13:52.997 So here's a way that light gets a handle on the electrons 13:53.000 --> 13:56.330 that are an unshared pair, and can make them go into pi*, 13:56.333 --> 13:58.803 by mixing the sigma, 13:58.800 --> 14:03.830 unshared-pair electrons, with pi*. 14:03.833 --> 14:09.403 Now, that's neat, because as it goes up and down you absorb 14:09.400 --> 14:15.000 light, and the large energy gap between the unshared pair 14:15.000 --> 14:18.130 and pi* means that this transition occurs 14:18.133 --> 14:19.673 at very high frequency. 14:19.667 --> 14:21.897 Because remember, the frequency of cycling in and 14:21.900 --> 14:24.530 out of phase is the difference in the 14:24.533 --> 14:25.933 energies of the two things. 14:25.933 --> 14:29.073 So if they're fairly far apart, it'll be a very high 14:29.067 --> 14:31.327 frequency of light, not in the visible. 14:31.333 --> 14:35.233 So it's in the ultraviolet. 14:35.233 --> 14:38.673 How could you make those two orbitals closer in energy? 14:38.667 --> 14:41.567 The unshared pair you couldn't do much about, except maybe 14:41.567 --> 14:43.227 changing one atom what is involved, 14:43.233 --> 14:45.973 oxygen, nitrogen, sulfur, things like that. 14:45.967 --> 14:47.697 How could you change the energy of the 14:47.700 --> 14:51.230 LUMO in the pi system? 14:51.233 --> 14:53.303 Anybody got an idea? 14:53.300 --> 14:57.970 So if you put more double bonds conjugated with it-- 14:57.967 --> 15:01.267 remember, the LUMO comes down, the HOMO comes up. 15:01.267 --> 15:03.567 So you can bring it closer to the energy of 15:03.567 --> 15:05.767 the unshared pair. 15:05.767 --> 15:08.927 If we put more and more double bonds in there, then the LUMO 15:08.933 --> 15:10.503 is going to look like this. 15:10.500 --> 15:14.430 It approaches the energy of an isolated p orbital, so the 15:14.433 --> 15:17.303 light will get redder and redder that interacts. 15:17.300 --> 15:20.130 And this makes a lot of differences as the pi* 15:20.133 --> 15:23.333 approaches the energy of the 2p orbital. 15:23.333 --> 15:26.403 So for example, this molecule, which has an unshared pair on 15:26.400 --> 15:30.570 nitrogen here, which could mix with pi* of this really 15:30.567 --> 15:33.167 long conjugated system. 15:33.167 --> 15:36.467 That's the imine of retinaldehyde. 15:36.467 --> 15:37.867 That's what's in rhodopsin. 15:37.867 --> 15:40.467 That's the light sensitive stuff in your eye. 15:40.467 --> 15:44.667 So when light comes in, it excites this transition, and 15:44.667 --> 15:47.727 it triggers then to your brain and so on, because the cis 15:47.733 --> 15:53.303 isomer changes to the trans isomer at this double bond. 15:53.300 --> 15:57.330 And that's how you see. 15:57.333 --> 15:58.073 Incidentally-- 15:58.067 --> 16:03.427 that compound, I just put this in as another footnote: let's 16:03.433 --> 16:06.733 not spend time on it-- but this is the actual report of 16:06.733 --> 16:10.833 Lindlar's catalyst. Remember, the poisoned catalyst that'll 16:10.833 --> 16:13.203 reduce triple bonds to double bonds, but won't 16:13.200 --> 16:14.800 reduce double bonds. 16:14.800 --> 16:16.370 And he said it was in the context 16:16.367 --> 16:17.897 of vitamin A synthesis. 16:17.900 --> 16:21.630 During work on the synthesis of vitamin A, a palladium-lead 16:21.633 --> 16:24.673 catalyst was developed, which one could hydrogenate a triple 16:24.667 --> 16:28.627 bond without attacking double bonds already present. 16:28.633 --> 16:31.233 But the things he was working on we're things like this. 16:31.233 --> 16:36.773 Really long conjugated things, like b-carotenyne, which he 16:36.767 --> 16:40.597 made, which had a triple bond in the middle, as you see. 16:40.600 --> 16:43.330 And then he could react it with his special catalyst and 16:43.333 --> 16:48.333 get the cis addition of two hydrogens to give the 16:48.333 --> 16:49.973 b-carotene. 16:49.967 --> 16:55.667 And he says the hydrogens are added in cis arrangement to 16:55.667 --> 16:58.627 one another. 16:58.633 --> 17:03.473 But then he goes on to say that he could, with heated 17:03.467 --> 17:07.227 and light he was able quantitatively to convert the 17:07.233 --> 17:10.033 cis isomer into the trans isomer, which is what he 17:10.033 --> 17:11.273 wanted to have for b-carotene. 17:13.867 --> 17:18.327 OK, now notice, this was C40H56, this big long thing. 17:18.333 --> 17:21.473 And you know why it's that kind of number, because it's 17:21.467 --> 17:24.627 made up of these isoprene units that we talked about in 17:24.633 --> 17:28.033 the last quarter, polymerization of isoprene to 17:28.033 --> 17:31.233 give these natural products. 17:31.233 --> 17:34.003 OK, that's just a footnote to last semester, it's made from 17:34.000 --> 17:37.530 isopentenyl pyrophosphate. 17:37.533 --> 17:42.473 Now, retinal is the stuff that's involved in making this 17:42.467 --> 17:45.627 visual pigment. 17:45.633 --> 17:48.273 And b-carotene is that, and obviously, it's called 17:48.267 --> 17:50.997 b-carotene because that's what makes carrots that way. 17:51.000 --> 17:54.200 And that's why you eat carrots to make your eyes good, right? 17:54.200 --> 17:59.530 Bugs Bunny has good vision because of that. 17:59.533 --> 18:05.703 Now, this related compound is called isozeaxanthin. 18:05.700 --> 18:10.370 And it turns out to be the stuff that's in the feathers 18:10.367 --> 18:13.027 of the scarlet tanager. 18:13.033 --> 18:18.473 Now, what's weird about this, it's what makes the scarlet 18:18.467 --> 18:22.597 tanager yellow-green, right? 18:22.600 --> 18:24.530 What's wrong with that? 18:24.533 --> 18:27.473 It's supposed to be a scarlet tanager. 18:27.467 --> 18:30.297 But this is actually late in the fall. 18:30.300 --> 18:33.270 If you looked a little bit earlier in the fall, the 18:33.267 --> 18:36.167 Scarlet Tanager looks like this. 18:36.167 --> 18:39.827 So it's got a little bit of red in it. 18:39.833 --> 18:43.933 But notice that this OH out on the right, which has an 18:43.933 --> 18:48.903 unshared pair that could go into the pi system, that 18:48.900 --> 18:51.470 oxygen is not part of the pi system. 18:51.467 --> 18:55.767 You can't generate any overlap by that, because the oxygen is 18:55.767 --> 18:57.697 not where the pi system is. 18:57.700 --> 18:59.370 It's not conjugated. 18:59.367 --> 19:02.767 The OH unshared pair is isolated, so you can't do this 19:02.767 --> 19:06.967 thing of taking an unshared pair and putting it into the 19:06.967 --> 19:10.297 LUMO, the pi LUMO. 19:10.300 --> 19:15.170 But if you oxidize it to make that, then you get it 19:15.167 --> 19:20.367 conjugated, and that's the scarlet tanager in the summer. 19:20.367 --> 19:23.997 So it's exactly this changing of unshared pairs into the pi 19:24.000 --> 19:27.270 star orbital with a really long conjugated chain that 19:27.267 --> 19:30.397 gives this most vivid of our birds' colors. 19:30.400 --> 19:33.170 And these come in East Rock Park about a month or month 19:33.167 --> 19:35.727 and a half from now, so you can go see them yourselves. 19:35.733 --> 19:38.803 They knock your eyes out. 19:38.800 --> 19:40.930 OK, so we're talking about spectroscopy. 19:40.933 --> 19:44.603 A spectrum is usually presented as a graph. 19:44.600 --> 19:48.130 And when you see a graph you wonder what the axes are. 19:48.133 --> 19:49.303 That's the first thing. 19:49.300 --> 19:52.470 And depending on what point of view you're taking about 19:52.467 --> 19:55.297 spectroscopy, how you're understanding it there are 19:55.300 --> 19:58.200 different ways of labeling the graph. 19:58.200 --> 20:01.770 For example the horizontal and the vertical coordinates here 20:01.767 --> 20:04.367 in this particular graph are called wave number and 20:04.367 --> 20:09.467 transmittance, but the meaning of the axes, with respect to 20:09.467 --> 20:14.597 an experiment, is color, which light you're talking about 20:14.600 --> 20:18.470 along the horizontal axis, and vertically, what the light 20:18.467 --> 20:19.467 intensity is. 20:19.467 --> 20:23.727 For example, how much light of a certain color gets absorbed 20:23.733 --> 20:24.873 by your sample. 20:24.867 --> 20:28.427 Or on the other hand, how much light doesn't get absorbed and 20:28.433 --> 20:30.273 gets through the sample. 20:30.267 --> 20:33.397 And in fact, that's what's plotted here is transmitance, 20:33.400 --> 20:35.300 how much light gets through rather than 20:35.300 --> 20:38.170 how much gets absorbed. 20:38.167 --> 20:39.997 OK, so that's one way of looking at it, just 20:40.000 --> 20:41.130 experimentally. 20:41.133 --> 20:42.773 But another way is to look at it in 20:42.767 --> 20:45.467 terms of quantum mechanics. 20:45.467 --> 20:50.367 The horizontal axis is the molecular-energy gap. 20:50.367 --> 20:53.397 What are the orbitals that are involved? 20:53.400 --> 20:55.400 How far apart are they in energy? 20:55.400 --> 20:58.270 What does that have to do with the frequency of light? 20:58.267 --> 21:01.167 You remember, the rate of this oscillation back and forth has 21:01.167 --> 21:03.297 to do with the energy difference between the two 21:03.300 --> 21:05.130 states you're talking about. 21:05.133 --> 21:08.333 And if you're talking about quantum mechanics, the 21:08.333 --> 21:11.933 vertical axis is how much overlap you generate. 21:11.933 --> 21:16.873 So when that oxygen had the pi system on it, in the scarlet 21:16.867 --> 21:20.997 tanager, then you generated a lot of overlap by mixing the n 21:21.000 --> 21:22.170 with the pi. 21:22.167 --> 21:25.797 But if they were far apart and the light couldn't induce 21:25.800 --> 21:28.330 overlap, then you didn't get the fancy color. 21:28.333 --> 21:32.533 You got just the yellow-green color. 21:32.533 --> 21:35.703 Or you can look at it in terms of classical mechanics, which 21:35.700 --> 21:39.330 is the way we usually talk about infrared spectroscopy, 21:39.333 --> 21:42.603 where the horizontal axis is some actual vibration 21:42.600 --> 21:45.830 frequency of the atoms in a molecule. 21:45.833 --> 21:50.973 And the vertical axis is how much handle the light has on 21:50.967 --> 21:52.897 that particular vibration. 21:52.900 --> 21:56.630 For example, if you're vibrating H2, you don't change 21:56.633 --> 21:58.573 any electronics by doing that. 21:58.567 --> 21:59.967 You don't generated a dipole. 21:59.967 --> 22:01.627 It doesn't interact with light. 22:01.633 --> 22:05.673 But if you vibrate HCl, then you get a big separation of 22:05.667 --> 22:08.227 positive and negative charge as you do that, and it does 22:08.233 --> 22:09.203 interact with light. 22:09.200 --> 22:10.770 Light has a good handle on it. 22:14.067 --> 22:17.227 So it's molecular vibration frequency though-- 22:17.233 --> 22:22.873 of course, a molecule of H2 or HCl is just two atoms. But 22:22.867 --> 22:25.627 normally, the atoms whose bond you're interested in 22:25.633 --> 22:29.133 vibrating is part of a whole molecule, and then things get 22:29.133 --> 22:32.473 more complicated. As we will see. 22:32.467 --> 22:36.427 So infrared spectroscopy uses light 22:36.433 --> 22:37.673 for a number of purposes. 22:37.667 --> 22:39.697 One is to fingerprint molecules. 22:39.700 --> 22:42.130 And I think you've done this in lab, to see whether your 22:42.133 --> 22:44.803 spectrum corresponds with a known spectrum. 22:44.800 --> 22:49.800 Or even if you don't have an authentic sample, you may have 22:49.800 --> 22:53.000 a table of where functional groups, even in different 22:53.000 --> 22:55.670 molecules, if it's the same functional group there maybe 22:55.667 --> 22:58.727 some line that's characteristic. 22:58.733 --> 23:01.633 So you can identify functional groups and molecules that are 23:01.633 --> 23:03.903 otherwise unknown. 23:03.900 --> 23:09.870 And you can also use it to use the molecular dynamics that's 23:09.867 --> 23:14.197 involved to study bonding, to see how strong bonds are, 23:14.200 --> 23:17.430 whether atoms are linked by springs, for example. 23:17.433 --> 23:20.033 And that's what I'm going to concentrate on in the lecture, 23:20.033 --> 23:22.073 to use it to understand molecules. 23:22.067 --> 23:25.267 You you've used it in lab to identify molecules, to 23:25.267 --> 23:27.997 identify functional groups, but we're going to use this 23:28.000 --> 23:30.570 last thing to see what it tells us about how molecules 23:30.567 --> 23:31.967 hold together. 23:31.967 --> 23:36.627 Now, just a quick excursion into physics or math, to see 23:36.633 --> 23:39.403 what makes vibrations sinusoidal. 23:39.400 --> 23:41.970 When things vibrate we often think of them following 23:41.967 --> 23:47.167 a sine wave. But what is the condition under which they do 23:47.167 --> 23:51.097 actually vibrate according to a sine wave in time? 23:53.833 --> 23:56.703 So if it's vibrating according to a sine wave, then the 23:56.700 --> 24:02.970 displacement is some height times the sin of omega t. 24:02.967 --> 24:04.927 That's how fast it's going up and down. 24:04.933 --> 24:07.873 That describes the displacement. 24:07.867 --> 24:10.567 So that's the frequency, and t is the time, and 24:10.567 --> 24:11.767 h is the 1/2 amplitude. 24:11.767 --> 24:14.597 It can go from +1 to -1 as the sine 24:14.600 --> 24:16.570 goes back and forth. 24:16.567 --> 24:19.367 OK, and that says the velocity, the change in 24:19.367 --> 24:23.097 position with time, is the derivative of 24:23.100 --> 24:25.900 that, so the cosine. 24:25.900 --> 24:29.770 And the acceleration is the second 24:29.767 --> 24:33.127 derivative, so it's that. 24:33.133 --> 24:36.433 And from that then, if the motion is sinusoidal, as we 24:36.433 --> 24:39.773 said at the beginning, then the acceleration divided by 24:39.767 --> 24:42.967 the displacement is minus the frequency squared. 24:47.200 --> 24:50.170 Now, Newton said that acceleration 24:50.167 --> 24:52.327 is force over mass. 24:52.333 --> 24:57.003 And if things are obeying Hooke's Law, then the force is 24:57.000 --> 24:59.370 proportional to the displacement. 24:59.367 --> 25:02.667 And that means we can substitute in Newton with the 25:02.667 --> 25:12.327 force, -fx, and we get that a/x is -f/m. 25:12.333 --> 25:16.003 And a/x, we already knew, is -omega squared. 25:16.000 --> 25:19.600 And that means that the frequency squared is how 25:19.600 --> 25:22.600 strong the spring is, if it's Hooke's law, the force constant 25:22.600 --> 25:23.870 divided by the mass. 25:27.000 --> 25:29.870 Or, if we take the square root, the frequency is the 25:29.867 --> 25:34.697 square root of the force constant divided by the mass. 25:34.700 --> 25:38.500 So the frequency then is interesting. 25:38.500 --> 25:39.830 It's constant. 25:39.833 --> 25:44.773 It doesn't depend on the amplitude of the vibration. 25:44.767 --> 25:48.767 If you have a system that's obeying Hooke's law, it'll 25:48.767 --> 25:52.527 have the same frequency no matter what the amplitude. 25:52.533 --> 25:54.733 And that turned out to be very important. 25:54.733 --> 25:58.203 Incidentally, one of the texts we're involved in says the 25:58.200 --> 26:01.500 opposite, but it's not true. 26:01.500 --> 26:04.130 OK, so why is that so important? 26:04.133 --> 26:08.873 Hooke's law, Hooke's book, Of spring in 1678, says 26:08.867 --> 26:12.097 vibrations, if you're obeying Hooke's Law-- this is where he 26:12.100 --> 26:13.670 set out Hooke's law-- 26:13.667 --> 26:16.597 shall be of equal duration whether they 26:16.600 --> 26:18.670 be greater or less. 26:18.667 --> 26:24.927 Why did he care that the frequency be always the same 26:24.933 --> 26:28.603 no matter how big the displacement is? 26:28.600 --> 26:30.270 Can you see why that would make a difference, 26:30.267 --> 26:31.497 practically? 26:31.500 --> 26:31.830 Ellen? 26:31.833 --> 26:33.233 STUDENT: For clocks. 26:33.233 --> 26:34.503 PROFESSOR: For clocks. 26:36.733 --> 26:40.733 Or more particularly, for watches, because you know, 26:40.733 --> 26:45.403 about 90 years or 80 years later, John Harrison made this 26:45.400 --> 26:48.370 marine chronometer, which allowed to solve the problem 26:48.367 --> 26:50.197 of longitude. 26:50.200 --> 26:53.170 So ships could tell how far they were from Greenwich by 26:53.167 --> 26:54.767 having accurate time. 26:54.767 --> 26:58.697 And if you look inside this watch, it looks like that. 26:58.700 --> 27:00.730 There's a spring vibrating like that. 27:00.733 --> 27:02.173 And it's really, really clever. 27:02.167 --> 27:04.127 I'll show you one other thing about it. 27:04.133 --> 27:08.433 Notice here, there's a little rod that goes out here under 27:08.433 --> 27:09.333 the spring. 27:09.333 --> 27:10.973 It's right here. 27:10.967 --> 27:14.127 And it goes out until it makes a little fork 27:14.133 --> 27:17.633 there around the spring. 27:17.633 --> 27:21.803 Now, that little leaf is bimetal, so it'll bend with 27:21.800 --> 27:23.870 temperature. 27:23.867 --> 27:28.197 So it changes the length of the spring as temperature 27:28.200 --> 27:32.270 changes to correct for the temperature changing the 27:32.267 --> 27:33.897 stiffness of the spring. 27:33.900 --> 27:36.100 Isn't that clever? 27:36.100 --> 27:38.770 OK, that's obviously beside the point, but it's really a 27:38.767 --> 27:43.727 neat feature of Harrison's H4 chronometer. 27:43.733 --> 27:47.433 So anyhow, when Hooke's law applies, the frequency is 27:47.433 --> 27:49.973 proportional to the square root of the force constant 27:49.967 --> 27:52.627 divided by the mass. 27:52.633 --> 27:54.733 So m is the mass. 27:54.733 --> 27:57.703 And this means you could use this thing 27:57.700 --> 27:58.930 to measure the frequency. 27:58.933 --> 28:01.873 You could measure a mass that way. 28:01.867 --> 28:05.427 And that's what a quartz crystal microbalance does. 28:05.433 --> 28:07.803 You can have a quartz crystal that will vibrate. 28:07.800 --> 28:10.630 I mean, the quartz in my Timex watch does that, right? 28:10.633 --> 28:14.273 It vibrates as a given-- it keeps very good time. 28:14.267 --> 28:19.927 So the quartz crystal microbalance, if you change 28:19.933 --> 28:24.573 its mass by absorbing something on top of the quartz 28:24.567 --> 28:26.497 crystal, it'll change its frequency, and 28:26.500 --> 28:27.670 you can measure it. 28:27.667 --> 28:30.767 In fact, it's so sensitive, that if you coat it with 28:30.767 --> 28:35.897 platinum, and then let ethylene in to absorb on the 28:35.900 --> 28:38.930 platinum, it'll get heavier and the 28:38.933 --> 28:41.833 frequency will slow down. 28:41.833 --> 28:44.703 But if you then admit hydrogen, the platinum 28:44.700 --> 28:48.500 catalyzes the reaction and the ethane goes off, and you can 28:48.500 --> 28:53.800 measure that change of one monolayer of ethylene on 28:53.800 --> 28:57.800 platinum by using a quartz crystal microbalance. 28:57.800 --> 29:03.170 That's just a neat feature. 29:03.167 --> 29:06.867 So if we're talking not about what's going on the surface 29:06.867 --> 29:10.697 of a quartz crystal, but about molecules vibrating, then, for 29:10.700 --> 29:13.030 atoms, the force constant should be how 29:13.033 --> 29:14.603 stiff the bond is. 29:14.600 --> 29:19.030 A single bond should be easier to stretch than a double bond, 29:19.033 --> 29:20.233 than a triple bond. 29:20.233 --> 29:21.703 But are they really that? 29:21.700 --> 29:26.270 Is the force constant really proportional to 1, 2, 3? 29:26.267 --> 29:29.167 Is a double bond twice as strong as a single bond, for 29:29.167 --> 29:31.797 this purpose of how rapidly things vibrate? 29:31.800 --> 29:34.070 Or a triple bond three times as strong? 29:34.067 --> 29:37.197 So this is something we can check by using infrared 29:37.200 --> 29:38.670 spectroscopy. 29:38.667 --> 29:42.297 Now, with respect to the mass, things get more complicated, 29:42.300 --> 29:45.370 because it's not just one atom that's moving. 29:45.367 --> 29:49.827 Usually it would be at least two atoms that are moving. 29:49.833 --> 29:53.403 And then what do you use for the mass? 29:53.400 --> 29:56.370 It turns out, that in a diatomic, what you use is 29:56.367 --> 29:58.527 called the reduced mass. 29:58.533 --> 30:02.833 It's the product of the two masses divided by their sum. 30:02.833 --> 30:06.503 And we don't need to go into why that is. 30:06.500 --> 30:10.330 But what that means is that that effective mass-- 30:10.333 --> 30:14.703 use the Greek mu, the Greek m, mu instead of m-- 30:14.700 --> 30:18.670 that's dominated by the smaller mass. 30:18.667 --> 30:23.997 Because suppose m2 is really small. 30:24.000 --> 30:28.770 Then the denominator, for practical purposes, is m1. 30:28.767 --> 30:30.967 m2 has nothing to do with it. 30:30.967 --> 30:34.367 But the m1 in the denominator then cancels out the m1 in the 30:34.367 --> 30:36.767 numerator, and all you have is m2. 30:36.767 --> 30:38.797 So it's the smaller thing that counts. 30:38.800 --> 30:42.100 You'd usually think it would be the larger thing. 30:42.100 --> 30:43.730 OK, so let's look at what that would be. 30:43.733 --> 30:47.073 For example, for hydrogen and carbon that we're vibrating, 30:47.067 --> 30:50.397 it would be 1 x 12/(1+12). 30:50.400 --> 30:52.000 Almost 1, right? 30:52.000 --> 30:54.770 The 12's almost cancel. 30:54.767 --> 30:57.197 If it's carbon-carbon then it's going to be 30:57.200 --> 30:59.600 1/2 of carbon 6. 30:59.600 --> 31:02.770 If it's carbon-oxygen it's going to be 6.9. 31:02.767 --> 31:05.467 If it's carbon-chlorine it's 8.9. 31:05.467 --> 31:07.727 So even when it gets much heavier, it doesn't make much 31:07.733 --> 31:08.673 difference. 31:08.667 --> 31:11.597 It's mostly pretty much like other carbon bonds. 31:11.600 --> 31:17.400 So what that means is that bonds involving hydrogen have 31:17.400 --> 31:20.870 really, really different frequencies from those 31:20.867 --> 31:26.567 involving not hydrogen, because it's so much lighter. 31:26.567 --> 31:29.867 1 to 6 here, or more. 31:29.867 --> 31:33.867 So it stands apart, the mass of hydrogen. 31:33.867 --> 31:36.727 Now, how about the bonds then? 31:36.733 --> 31:40.333 So C-H then, is proportional to the square root of a single 31:40.333 --> 31:45.133 bond over 0.9, that's reduced mass. 31:45.133 --> 31:47.903 And that turns out to be around 3000 wave numbers, or 31:47.900 --> 31:49.600 10 to the 14th Hz. 31:49.600 --> 31:53.700 So that's how fast C-H bonds vibrate. 31:53.700 --> 31:59.130 A C-O bond has a heavier mass, 6.9 versus 0.9. 31:59.133 --> 32:02.773 If it's a single bond, that's going to be about 1100 wave 32:02.767 --> 32:06.767 numbers, or 3 x 10 to the 13th Hz. 32:06.767 --> 32:10.067 And that, remember, is that what you put in front in 32:10.067 --> 32:10.667 Eyring 32:10.667 --> 32:14.097 to get a rate, it's 10 to the 13th, times that equilibrium 32:14.100 --> 32:16.000 constant to the transition state. 32:16.000 --> 32:17.070 That's because of this. 32:17.067 --> 32:20.167 That's how fast atoms like carbon and oxygen vibrate. 32:22.933 --> 32:26.603 OK, so a C double bond, though, if a double bond is 32:26.600 --> 32:30.400 twice as high as a single bond, should be 2, the square 32:30.400 --> 32:34.430 root of 2/6.9, and that's about 1500. 32:34.433 --> 32:36.403 And that's about right. 32:36.400 --> 32:42.330 And a triple bond is higher still, with a 3 for the force 32:42.333 --> 32:44.833 constant, about 1900. 32:44.833 --> 32:48.873 So you can see that if you have a spectrum, where 3000 is 32:48.867 --> 32:54.827 on the left, and 1000 is toward the right, then you're 32:54.833 --> 32:57.673 going to have hydrogens up here, hydrogens stretching 32:57.667 --> 33:01.127 about 3000, and then you're going to get triple bonds, 33:01.133 --> 33:03.773 double bonds, single bonds involving 33:03.767 --> 33:06.067 other atoms, not hydrogen. 33:09.200 --> 33:13.430 But it's not that simple, because a single atom is 33:13.433 --> 33:16.473 connected, not to just one other atom, but others, and 33:16.467 --> 33:20.067 they couple with each other. 33:20.067 --> 33:23.697 So this, our study of coupled oscillators is going to 33:23.700 --> 33:25.230 illustrate several things. 33:25.233 --> 33:28.673 The complexity of what's really involved in vibration, 33:28.667 --> 33:31.097 and why physical chemists thought at the beginning that 33:31.100 --> 33:34.970 it was going to be impossible to interpret anything in IR 33:34.967 --> 33:36.327 spectroscopy. 33:36.333 --> 33:39.773 And then the idea of normal mode analysis, and what a 33:39.767 --> 33:46.097 normal mode is, and phase of mixing, and the possibility of 33:46.100 --> 33:50.200 things being independent, so you can think about a functional 33:50.200 --> 33:52.970 group having a particular thing, not being all mixed up 33:52.967 --> 33:54.667 with others. 33:54.667 --> 33:56.367 So for this purpose we're going to look at some 33:56.367 --> 34:00.997 oscillators, at this particular thing here. 34:01.000 --> 34:05.430 Let's see if I can get this, get the lights I need here. 34:05.433 --> 34:09.803 OK, so here are some things that'll oscillate. 34:12.367 --> 34:15.997 So if I take this, it vibrates at a certain frequency. 34:16.000 --> 34:19.200 It's a spring that's being bent back and forth, so it's 34:19.200 --> 34:20.370 Hooke's law. 34:20.367 --> 34:24.897 And that's what I've shown here. 34:24.900 --> 34:26.630 It's a simple oscillator. 34:26.633 --> 34:27.803 I bend it. 34:27.800 --> 34:28.570 I let it go. 34:28.567 --> 34:31.567 It flops back and forth at a given rate. 34:31.567 --> 34:34.327 And we know what that rate's going to be. 34:34.333 --> 34:37.173 The square of the frequency is going to be whatever the force 34:37.167 --> 34:39.397 constant-- how stiff the spring is-- 34:39.400 --> 34:42.300 divided by the mass of that thing up on top, and of the 34:42.300 --> 34:44.000 spring itself, of course. 34:44.000 --> 34:46.700 OK, that's fine. 34:46.700 --> 34:50.070 Now, suppose we put a spring in there as well. 34:54.467 --> 34:59.267 But let me hold this one fixed, or hold this one fixed. 34:59.267 --> 35:02.327 And I'm going to do this then. 35:02.333 --> 35:05.503 Now, can you tell me whether that vibration should be 35:05.500 --> 35:08.830 faster or slower than it was when I didn't 35:08.833 --> 35:10.073 have the spring there? 35:14.100 --> 35:16.530 What's the difference? 35:16.533 --> 35:20.403 The difference is that now we have a stronger spring. 35:20.400 --> 35:21.170 Everybody see that? 35:21.167 --> 35:23.567 Because we've added this spring to however hard it is 35:23.567 --> 35:25.067 to bend that. 35:25.067 --> 35:27.697 So it's going to be a higher frequency. 35:27.700 --> 35:29.530 And we could time it, and figure it out. 35:29.533 --> 35:34.173 We don't have time to do that, but it's faster. 35:34.167 --> 35:37.067 If it's coupled to a frozen partner like that-- 35:37.067 --> 35:38.467 I'm holding the partner-- 35:38.467 --> 35:44.397 then I let it go and it stretches back and forth, and 35:44.400 --> 35:46.230 it has a stronger spring. 35:46.233 --> 35:50.733 It's the main spring plus this little one, plus s. 35:50.733 --> 35:55.203 We could couple that in, so that's easy enough. 35:55.200 --> 35:58.570 Now we're going to look at it when I'm not holding it. 35:58.567 --> 36:00.867 It's going to be in-phase coupling. 36:00.867 --> 36:02.897 So they're going to be moving the same direction. 36:02.900 --> 36:06.070 So I move them both out here, and I let them go, and they go 36:06.067 --> 36:07.297 back and forth. 36:07.300 --> 36:09.670 Now, what should that frequency be? 36:09.667 --> 36:12.427 Is this spring being stretched? 36:12.433 --> 36:17.473 No, so it's just as it was originally. 36:17.467 --> 36:23.967 So if we do this and do that, and let go, then it goes back 36:23.967 --> 36:27.767 and forth, not stretching the spring. 36:27.767 --> 36:31.427 Or if you look at the thing as a whole, there are two weights 36:31.433 --> 36:36.703 and two springs being bent, so it's 2f/2m, but it's the same 36:36.700 --> 36:39.200 as we started with. 36:39.200 --> 36:44.130 Now, the interesting one is to do out-of-phase coupling, 36:44.133 --> 36:47.003 where they don't go in parallel but antiparallel to 36:47.000 --> 36:49.900 one another. 36:49.900 --> 36:54.800 Now, what about this situation here now? 36:54.800 --> 36:58.670 Is that spring being stretched? 36:58.667 --> 37:03.127 In fact, it's being stretched twice as much as it was 37:03.133 --> 37:07.373 before, because the middle is staying in place, and both 37:07.367 --> 37:09.667 things are stretching it. 37:09.667 --> 37:13.167 So if we do that, if we do this one. 37:13.167 --> 37:15.867 Out-of-phase coupling-- 37:15.867 --> 37:19.567 and notice that the center stays fixed-- 37:19.567 --> 37:22.697 now as it does that, we have a much stronger spring. 37:22.700 --> 37:24.970 It's 2s in the middle now. 37:24.967 --> 37:27.427 I'm sorry you can't see this very well, but you can look at 37:27.433 --> 37:29.733 what we review. 37:29.733 --> 37:32.473 So it's 2s in the middle, so now frequency is higher. 37:36.167 --> 37:39.767 Now, so when the two were isolated from one another, 37:39.767 --> 37:42.267 that is, when we held one fixed and just looked at one 37:42.267 --> 37:44.597 vibrate, all we had was that little extra spring in the 37:44.600 --> 37:46.900 middle, then they would both vibrate at the 37:46.900 --> 37:49.330 same frequency, isolated. 37:49.333 --> 37:50.103 Can you see it there? 37:50.100 --> 37:52.270 I think you can. 37:52.267 --> 37:54.597 Actually, let me just put it on the other screen and then 37:54.600 --> 37:55.830 you'll be able to see it. 37:58.933 --> 38:00.273 Yeah, OK, good. 38:03.167 --> 38:08.267 But once we let them both move and they couple their motion, 38:08.267 --> 38:11.427 then there's an out-of-phase and an in-phase. One is higher 38:11.433 --> 38:15.073 frequency. One doesn't stretch the spring, the other 38:15.067 --> 38:17.567 stretches it twice as much. 38:17.567 --> 38:21.427 Does this remind you of anything you've seen before? 38:21.433 --> 38:22.703 That diagram? 38:24.800 --> 38:27.570 It's the same thing as orbitals mixing, to give an 38:27.567 --> 38:29.067 in-phase and an out-of-phase. 38:29.067 --> 38:31.727 The math is just the same. 38:31.733 --> 38:35.333 So this is called, either of these, the in-phase or the 38:35.333 --> 38:38.403 out-of-phase, is called a normal mode. 38:38.400 --> 38:42.500 The meaning of it is that in that pattern of vibration, all 38:42.500 --> 38:44.330 the atoms are oscillating at the same 38:44.333 --> 38:47.703 frequency in a normal mode. 38:47.700 --> 38:55.170 It's a lower frequency here and a higher frequency here, 38:55.167 --> 38:57.767 but both atoms are moving in phase with one another, you 38:57.767 --> 39:02.227 know, at the same oscillation frequency. 39:02.233 --> 39:08.673 Now we're going to do another one, in which-- 39:08.667 --> 39:11.767 so they move back and forth at the same amplitude, the same 39:11.767 --> 39:15.067 frequency, or when they started the same. 39:15.067 --> 39:18.827 So that's out-of-phase and this one was in-phase. 39:18.833 --> 39:27.273 Now, notice that if I added those two together, those two 39:27.267 --> 39:30.467 displacements, those two vibration patterns, I would 39:30.467 --> 39:34.627 get something where one moved and the other didn't. 39:34.633 --> 39:37.873 So I could do that. 39:37.867 --> 39:41.327 And what I'm saying is, that that is the sum of the 39:41.333 --> 39:47.233 in-phase motion and the out-of-phase motion. 39:47.233 --> 39:50.073 So if I sum them, I get this one to move and these cancel. 39:53.033 --> 39:57.903 So when I let go now, I'm actually exciting two normal 39:57.900 --> 40:00.800 modes, the in-phase and the out-of-phase. 40:00.800 --> 40:02.170 Does everybody see what I'm doing? 40:02.167 --> 40:05.267 Because what I've done here is the sum of the two of them. 40:05.267 --> 40:07.367 So now when I let go, something neat happens. 40:16.067 --> 40:18.067 STUDENT: That is cool. 40:21.800 --> 40:23.270 PROFESSOR: So what's happening? 40:23.267 --> 40:25.267 STUDENTS: murmurs. 40:25.267 --> 40:26.727 PROFESSOR: It's going back and forth 40:26.733 --> 40:30.673 between one vibrating and the other vibrating. 40:30.667 --> 40:32.527 Why? 40:32.533 --> 40:36.503 Because those two modes have different frequencies, and 40:36.500 --> 40:39.930 they get in step and then out of step with one another, and 40:39.933 --> 40:43.373 when they're in step with one another, this one is moving, 40:43.367 --> 40:46.967 that's how we started it. And not this one, and when it's 40:46.967 --> 40:50.497 one minus the other it's this. 40:50.500 --> 40:52.600 And because they have different frequencies, they're 40:52.600 --> 40:54.930 cycling in and out of phase with one another. 40:58.767 --> 41:00.267 I think that's just so wonderful. 41:00.267 --> 41:04.667 [LAUGHTER] 41:04.667 --> 41:07.367 So that's exactly what we were looking at at the beginning, 41:07.367 --> 41:10.497 where things went in and out of phase with one another, 41:10.500 --> 41:12.270 where it was 1s going to 2p. 41:15.367 --> 41:17.967 What we started, when we moved just one of them and held the 41:17.967 --> 41:20.697 other one fixed, was a superposition of two normal 41:20.700 --> 41:22.930 modes of different frequency. 41:22.933 --> 41:27.433 And then the vibration beats in and out of phase. 41:27.433 --> 41:31.573 So now, what happens, if one of them's heavy and the other 41:31.567 --> 41:34.797 one's-- so then you can't talk about just one of them 41:34.800 --> 41:38.200 vibrating. When they're coupled this way-- 41:38.200 --> 41:41.900 but suppose I made one of them heavier than the other, so it 41:41.900 --> 41:45.430 vibrates normally at a very different frequency. 41:45.433 --> 41:46.703 If I can get this on there... 41:50.300 --> 41:52.700 And now let me move this one. 41:52.700 --> 41:55.300 Let me move this one and not this one. 41:55.300 --> 41:57.470 And what should happen-- what we saw before was the 41:57.467 --> 42:01.167 vibration goes from there, to there, to there, to there-- 42:01.167 --> 42:03.667 but now look what happens. 42:03.667 --> 42:07.597 I actually moved that one a little bit at the beginning. 42:07.600 --> 42:10.200 This one's not moving nearly as much as that one is. 42:10.200 --> 42:11.270 This one keeps moving. 42:11.267 --> 42:14.197 Remember, the other one went dead still and then the other 42:14.200 --> 42:15.070 one and then the other. 42:15.067 --> 42:18.297 Now it's staying localized mostly. 42:18.300 --> 42:22.370 And if I did this one, it stays mostly here. Very little 42:22.367 --> 42:24.667 comes over there. 42:24.667 --> 42:29.197 So if the two things have very different frequencies, then 42:29.200 --> 42:32.830 they don't couple very much. 42:32.833 --> 42:36.333 They stay mostly independent, if they have different 42:36.333 --> 42:39.673 independent... different individual frequencies. 42:39.667 --> 42:43.897 And that's exactly like the wave functions mixing. 42:43.900 --> 42:46.930 If we have one that's low energy and one that's high 42:46.933 --> 42:51.633 frequency, and we couple them, you'll get one that's in phase 42:51.633 --> 42:55.373 and one that's out of phase, but they won't be very 42:55.367 --> 42:56.397 different from one another. 42:56.400 --> 43:00.670 It's an exact analogue of the energy-match and overlap 43:00.667 --> 43:03.327 thing, where the energy-match is now how different the 43:03.333 --> 43:08.073 frequencies are, or the energy-mismatch, and the overlap 43:08.067 --> 43:11.827 is how strong this spring is between them. 43:11.833 --> 43:15.503 So if I make the spring really strong, then even though they 43:15.500 --> 43:18.630 have different frequencies, they'll be more 43:18.633 --> 43:20.373 mixed with one another. 43:20.367 --> 43:23.627 Now this, it's weird, but this one is moving more. 43:23.633 --> 43:27.003 But if I make it very weak coupling, like that, then they 43:27.000 --> 43:30.470 really stay independent of one another. 43:30.467 --> 43:34.027 So it's a really neat physical demonstration of what we saw 43:34.033 --> 43:35.973 last semester. 43:35.967 --> 43:37.497 OK, that's enough of that for now. 43:37.500 --> 43:39.800 If I can get this off. 43:42.733 --> 43:45.133 So you can come play with that afterwards if you want to. 43:49.600 --> 43:54.100 So vibration remains localized when the coupling is weak, 43:54.100 --> 43:58.300 compared to the energy mismatch. 43:58.300 --> 44:01.670 These illustrate that. 44:01.667 --> 44:04.997 So if you have a general molecule that has N atoms in 44:05.000 --> 44:09.670 it, there are 3N independent geometric parameters, x, y, 44:09.667 --> 44:18.467 and z for all the N atoms. But it takes three numbers to say 44:18.467 --> 44:21.567 where the center of the molecule is. 44:21.567 --> 44:24.297 And it takes another three numbers to tell how much you 44:24.300 --> 44:27.200 rotated around this axis, how much you rotated around this 44:27.200 --> 44:30.630 axis, how much you rotated around this axis, so that's 44:30.633 --> 44:33.903 three more numbers to fix the orientation. 44:33.900 --> 44:38.900 So you have 3N-6 coordinates that involve 44:38.900 --> 44:40.670 internal vibration. 44:40.667 --> 44:43.397 But it's not just two atoms that are vibrating, it's the 44:43.400 --> 44:45.700 whole set of atoms that are vibrating. 44:45.700 --> 44:49.830 And in a normal mode, they all vibrate at the same frequency. 44:49.833 --> 44:53.633 But there are going to be 3N-6 normal modes, and this 44:53.633 --> 44:57.873 is where physical chemists threw up their hands, and 44:57.867 --> 45:00.997 said, it's just so complicated how all these springs are 45:01.000 --> 45:03.400 interacting with each other, that we're never going to 45:03.400 --> 45:04.830 understand it. 45:04.833 --> 45:06.373 So forget trying to interpret. 45:06.367 --> 45:12.197 OK for a fingerprint, but forget trying to interpret it. 45:12.200 --> 45:14.970 So it sounds hopelessly complex, though it's good for 45:14.967 --> 45:16.297 a fingerprint. 45:16.300 --> 45:20.030 But remember, to get mixing, you have to have frequency 45:20.033 --> 45:23.733 match and some coupling mechanism. 45:23.733 --> 45:27.133 So if you have some of these bonds that vibrate without 45:27.133 --> 45:30.233 similar frequencies to anything in the neighborhood, 45:30.233 --> 45:33.933 or not coupled to things in the neighborhood, then they'll 45:33.933 --> 45:36.873 appear independently, and you can hope to identify a 45:36.867 --> 45:38.867 particular functional group. 45:38.867 --> 45:42.667 So if they're isolated, they're independent, but if 45:42.667 --> 45:45.197 they're coupled, then you see complication. 45:45.200 --> 45:48.530 So it's again this question of energy-match and overlap. 45:48.533 --> 45:53.503 Now let's look at the butane, C4H10 . 45:53.500 --> 45:58.930 It's got 42 degrees of freedom, 42 of these, minus 45:58.933 --> 46:02.403 the 3 translations and the 3 rotations, so there are 36 46:02.400 --> 46:06.600 vibrations, 36 normal modes that are involved. 46:06.600 --> 46:09.000 If you just had the four carbons, there'd be three 46:09.000 --> 46:11.900 stretches, two bends and a twist, the 46:11.900 --> 46:13.670 torsion around the middle. 46:13.667 --> 46:16.967 With 10 C-H's, you have 10 stretches, 46:16.967 --> 46:19.967 and 20 bends or twists. 46:19.967 --> 46:22.727 But it's not that simple, because they get mixed up, 46:22.733 --> 46:26.373 according to frequency-match and coupling, into 36 46:26.367 --> 46:28.267 complicated normal modes. 46:28.267 --> 46:30.197 Let's see if we can understand anything about 46:30.200 --> 46:31.070 these normal modes. 46:31.067 --> 46:34.927 So here's a spectrum of a hydrocarbon, it's C8H18. 46:34.933 --> 46:38.403 You've seen a spectrum like this, I bet, in lab. 46:38.400 --> 46:40.930 Let's see if we can understand what any of the peaks are. 46:40.933 --> 46:43.773 First notice, that there are peaks at the far left, around 46:43.767 --> 46:46.827 3000, and the others are all 1500 or below. 46:46.833 --> 46:48.603 What do you think's up at the top, high frequencies? 46:48.600 --> 46:50.270 STUDENTS: C-H 46:50.267 --> 46:51.227 PROFESSOR: C-H's, right. 46:51.233 --> 46:53.203 Because the H is so light. 46:53.200 --> 46:57.170 OK, so there are 72 normal modes here, but not all of 46:57.167 --> 47:01.127 them are IR active with this C8H18. 47:01.133 --> 47:03.303 So let's look at that particular peak there. 47:03.300 --> 47:05.170 There are actually several there but, anyhow, 47:05.167 --> 47:06.527 one of them is this. 47:06.533 --> 47:11.873 So there we have a molecule and here we distort it. 47:11.867 --> 47:15.967 Now, tell me what's happening in the distortion? 47:15.967 --> 47:17.227 What's mostly changing? 47:21.400 --> 47:23.770 What's mostly changing? 47:23.767 --> 47:24.967 STUDENTS: C-H bonds. 47:24.967 --> 47:27.427 PROFESSOR: Yeah, its C-H bonds are stretching 47:27.433 --> 47:29.603 and shrinking, right? 47:29.600 --> 47:32.330 And notice the way they're doing it. 47:32.333 --> 47:35.103 Focus on the two central CH2s. 47:35.100 --> 47:39.770 The hydrogens are moving up and down, up and down. 47:39.767 --> 47:44.397 So the charge is moving up and down, up and down. 47:44.400 --> 47:48.100 So that's going to interact then with light, with an 47:48.100 --> 47:50.830 electric field of light that's pointing in that way. 47:50.833 --> 47:56.673 So light can help push those four central H's up and down. 47:56.667 --> 47:59.197 That particular vibration, that particular normal mode, 47:59.200 --> 48:02.270 interacts with light, and you get absorption of light at 48:02.267 --> 48:03.927 that position. 48:03.933 --> 48:05.473 When it's up, it pushes it one way. 48:05.467 --> 48:07.767 When the field is down, it pushes it the other way, and 48:07.767 --> 48:08.797 we interact with light. 48:08.800 --> 48:10.200 So that's a C-H stretch. 48:10.200 --> 48:12.330 Now, how about this one? 48:12.333 --> 48:15.203 Here we have-- or one of the peaks under there at least-- 48:15.200 --> 48:17.430 here it's this and then that. 48:17.433 --> 48:18.673 What's happening now? 48:21.467 --> 48:23.167 What bonds are changing? 48:23.167 --> 48:24.627 What kinds of bonds? 48:24.633 --> 48:26.273 Is that C-C or C-H? 48:26.267 --> 48:28.327 STUDENTS: C-H 48:28.333 --> 48:29.973 PROFESSOR: It's C-H. And notice how 48:29.967 --> 48:30.767 they're doing. 48:30.767 --> 48:34.667 They're all going in or out together. 48:34.667 --> 48:35.927 So that's going to do it. 48:35.933 --> 48:37.873 What direction of the light's electric 48:37.867 --> 48:41.397 vector will excite this? 48:41.400 --> 48:43.830 It's going to be perpendicular to the screen, to push them 48:43.833 --> 48:44.903 all in, all out. 48:44.900 --> 48:47.400 So it's a different polarization of the light 48:47.400 --> 48:48.470 that's going to do this one. 48:48.467 --> 48:50.497 It's going to be the light that goes that way 48:50.500 --> 48:52.600 or goes that way. 48:52.600 --> 48:54.700 Now there are a lot of others that we won't go into. 48:54.700 --> 48:56.700 One of them is this. 48:56.700 --> 48:58.870 Look at this now. 48:58.867 --> 48:59.897 What's happening now? 48:59.900 --> 49:03.070 Again, we're stretching C-H bonds. 49:03.067 --> 49:05.397 How strongly is this going to interact with light? 49:10.733 --> 49:14.733 Notice, for every H that goes one way, there's another H that 49:14.733 --> 49:19.373 goes exactly the opposite way, so those cancel out and 49:19.367 --> 49:21.427 there's no interaction with light. 49:21.433 --> 49:23.873 So that sort of breathing, where they're all going out 49:23.867 --> 49:26.467 and in at the same time doesn't interact. 49:26.467 --> 49:28.327 You don't see that in the IR. 49:28.333 --> 49:35.573 So in fact, half of the 10 C-H stretching normal modes have 49:35.567 --> 49:36.867 no handle on them. 49:36.867 --> 49:38.927 They don't change the dipole moment. 49:38.933 --> 49:42.203 So they don't absorb light. 49:42.200 --> 49:44.400 And that's where we're going to have to stop now and go on 49:44.400 --> 49:45.830 to the other peaks next time.