1 00:00:00,090 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,820 Commons license. 3 00:00:03,820 --> 00:00:06,030 Your support will help MIT Open Courseware 4 00:00:06,030 --> 00:00:10,120 continue to offer high quality educational resources for free. 5 00:00:10,120 --> 00:00:12,660 To make a donation or to view additional materials 6 00:00:12,660 --> 00:00:16,150 from hundreds of MIT courses, visit MIT OpenCourseware 7 00:00:16,150 --> 00:00:17,150 at ocw.mit.edu. 8 00:00:21,895 --> 00:00:23,520 PROFESSOR ROBERT FIELD: So last time we 9 00:00:23,520 --> 00:00:30,030 talked about intermolecular interactions. 10 00:00:30,030 --> 00:00:32,250 Intermolecular. 11 00:00:32,250 --> 00:00:35,790 It's complicated enough talking about individual molecules, 12 00:00:35,790 --> 00:00:39,480 what molecules can do, but we could also 13 00:00:39,480 --> 00:00:43,830 talk about interactions between molecules, 14 00:00:43,830 --> 00:00:47,220 and we can use perturbation theory, and what we discover 15 00:00:47,220 --> 00:00:51,540 is something universal about all pairs of molecules. 16 00:00:51,540 --> 00:00:54,000 Molecules which don't have any reason 17 00:00:54,000 --> 00:00:57,450 to interact with each other, like being charged or even 18 00:00:57,450 --> 00:01:05,700 having dipole moments, and we discover that all molecules 19 00:01:05,700 --> 00:01:07,020 are attracted to each other. 20 00:01:09,710 --> 00:01:14,630 And we know the force law, we know how everything scales, 21 00:01:14,630 --> 00:01:21,950 and we also know that we can look at molecules, 22 00:01:21,950 --> 00:01:24,350 and say this molecule is going to be 23 00:01:24,350 --> 00:01:28,160 a good molecule for intermolecular interactions 24 00:01:28,160 --> 00:01:33,170 because either it has a lot of low-lying transitions, 25 00:01:33,170 --> 00:01:37,260 or they have very strong transitions. 26 00:01:37,260 --> 00:01:44,300 And so you can compare different atoms or different molecules. 27 00:01:44,300 --> 00:01:46,760 And one of the important messages 28 00:01:46,760 --> 00:01:51,500 is that really big molecules are really sticky. 29 00:01:51,500 --> 00:01:54,080 They want to attract each other because they 30 00:01:54,080 --> 00:01:57,950 have a lot of vibrations, and each vibrational node 31 00:01:57,950 --> 00:02:02,130 can act as a dipole in this dipole-dipole interaction, 32 00:02:02,130 --> 00:02:05,360 whether it's induced dipole-induced dipole 33 00:02:05,360 --> 00:02:08,090 or whatever. 34 00:02:08,090 --> 00:02:10,669 So it's one of these things where 35 00:02:10,669 --> 00:02:13,400 something from one half of your brain 36 00:02:13,400 --> 00:02:17,810 is able to explain something from the other half, 37 00:02:17,810 --> 00:02:20,900 and that's really wonderful, and we're always aiming for that. 38 00:02:20,900 --> 00:02:23,769 Now, today we're talking about photochemistry. 39 00:02:29,760 --> 00:02:32,340 And this is an enormous topic. 40 00:02:32,340 --> 00:02:36,870 And I would say that there are vastly more physical chemists 41 00:02:36,870 --> 00:02:40,980 and biophysical chemists working on photochemistry 42 00:02:40,980 --> 00:02:42,300 than on spectroscopy. 43 00:02:46,110 --> 00:02:52,260 So what happens when a molecule gets excited by a photon? 44 00:02:52,260 --> 00:02:56,370 Does it just fluoresce or does it do interesting stuff? 45 00:02:56,370 --> 00:03:04,020 And there's a lot of really beautiful semi-empirical theory 46 00:03:04,020 --> 00:03:07,140 that enables you to estimate the rates of everything 47 00:03:07,140 --> 00:03:12,510 that a molecule can do, and the uses for what these things do. 48 00:03:16,340 --> 00:03:18,850 But in order to put this in perspective, 49 00:03:18,850 --> 00:03:22,690 I have to do a little bit of review of the different kinds 50 00:03:22,690 --> 00:03:24,280 of spectroscopy-- 51 00:03:24,280 --> 00:03:29,140 rotation, rotation-vibration, rotation-vibration-electronic 52 00:03:29,140 --> 00:03:31,180 in order to get the energy scales 53 00:03:31,180 --> 00:03:36,138 and to describe the actors in this problem of photochemistry. 54 00:03:40,260 --> 00:03:42,030 There's two sets of notes, what I'm 55 00:03:42,030 --> 00:03:46,590 going to be working from, which is because I'm a small molecule 56 00:03:46,590 --> 00:03:49,770 person, bottom-up, and I'm trying 57 00:03:49,770 --> 00:03:53,160 to take what I know and I've taught you 58 00:03:53,160 --> 00:03:55,950 about small molecules, and extend it 59 00:03:55,950 --> 00:03:59,210 to regions of incredible complexity, 60 00:03:59,210 --> 00:04:01,290 but using most of the same concepts. 61 00:04:01,290 --> 00:04:05,550 And Troy's notes, which are top-down, 62 00:04:05,550 --> 00:04:09,990 and he's basically interested in photochemistry, 63 00:04:09,990 --> 00:04:13,230 and condensed phases, and big molecules. 64 00:04:13,230 --> 00:04:15,180 And I'm afraid to go to condensed phases 65 00:04:15,180 --> 00:04:18,269 and big molecules, but the two shall meet, 66 00:04:18,269 --> 00:04:24,600 and many of the topics will be understandable 67 00:04:24,600 --> 00:04:26,640 with both approaches. 68 00:04:26,640 --> 00:04:30,690 OK, so let's just set the framework. 69 00:04:30,690 --> 00:04:40,330 We have three kinds of spectra, and the typical energy 70 00:04:40,330 --> 00:04:42,700 associated with that is one wave number. 71 00:04:45,340 --> 00:04:53,170 And we have rotation-vibration, and the typical energy scale 72 00:04:53,170 --> 00:04:57,550 is 1,000 wave numbers. 73 00:04:57,550 --> 00:05:05,310 And then there is the rotation-vibration-electronic, 74 00:05:05,310 --> 00:05:13,380 and that's, going to say 20,000 wave numbers and higher. 75 00:05:13,380 --> 00:05:18,900 Now, this is peanuts compared to the strength of molecular bonds 76 00:05:18,900 --> 00:05:21,800 and interactions between molecules, 77 00:05:21,800 --> 00:05:26,220 but this is big news because now the photon 78 00:05:26,220 --> 00:05:34,230 that excites the molecule is sort of acting like a reagent. 79 00:05:34,230 --> 00:05:39,960 This energy, it goes up as far as you want. 80 00:05:39,960 --> 00:05:46,230 These energies are comparable to the energies of chemical bonds, 81 00:05:46,230 --> 00:05:50,520 and the electronically excited molecules 82 00:05:50,520 --> 00:05:54,360 can do chemistry that the rotational or vibrationally 83 00:05:54,360 --> 00:05:57,110 excited molecules can't do. 84 00:05:57,110 --> 00:05:58,860 That's why it's so interesting, and that's 85 00:05:58,860 --> 00:06:00,364 why it's so complicated. 86 00:06:03,150 --> 00:06:17,476 OK, now, what can an excited molecule do? 87 00:06:21,450 --> 00:06:22,730 Well, maybe I should ask you. 88 00:06:25,910 --> 00:06:26,480 Yes? 89 00:06:26,480 --> 00:06:28,260 AUDIENCE: Rearrange. 90 00:06:28,260 --> 00:06:31,025 PROFESSOR ROBERT FIELD: OK, so we can call it isomerization. 91 00:06:34,750 --> 00:06:35,900 Anything else? 92 00:06:35,900 --> 00:06:37,180 AUDIENCE: Fragmentation. 93 00:06:37,180 --> 00:06:37,660 PROFESSOR ROBERT FIELD: I'm sorry? 94 00:06:37,660 --> 00:06:38,798 AUDIENCE: Fragmentation. 95 00:06:48,124 --> 00:06:49,290 PROFESSOR ROBERT FIELD: Yes. 96 00:06:49,290 --> 00:06:50,530 AUDIENCE: It can relax. 97 00:06:50,530 --> 00:06:52,334 PROFESSOR ROBERT FIELD: By? 98 00:06:52,334 --> 00:06:53,500 AUDIENCE: Emitting a photon. 99 00:06:53,500 --> 00:06:55,445 PROFESSOR ROBERT FIELD: Yes, fluorescence. 100 00:06:59,360 --> 00:07:00,110 That's what we do. 101 00:07:03,270 --> 00:07:05,540 There's lots of things that can happen 102 00:07:05,540 --> 00:07:10,610 and the kinds of things that can happen 103 00:07:10,610 --> 00:07:15,360 depends on what kind of exaltation we've produced, 104 00:07:15,360 --> 00:07:18,300 but the big photons are going to produce 105 00:07:18,300 --> 00:07:21,845 really complicated stuff. 106 00:07:21,845 --> 00:07:28,140 Now, one framework we can talk about is what is the rate of-- 107 00:07:32,452 --> 00:07:33,910 I can't imagine what I wrote there. 108 00:07:39,330 --> 00:07:43,260 So this is the total rate, and it 109 00:07:43,260 --> 00:07:50,470 can be composed of the radiative decay 110 00:07:50,470 --> 00:07:56,020 and the non-radiative decay. 111 00:07:56,020 --> 00:08:00,782 Now, there's a size scale here. 112 00:08:00,782 --> 00:08:01,990 Oh, I know what I wrote here. 113 00:08:01,990 --> 00:08:04,750 That's measured. 114 00:08:04,750 --> 00:08:11,050 So if you had a system and you measured the exponential decay 115 00:08:11,050 --> 00:08:14,300 of the population in that system, 116 00:08:14,300 --> 00:08:19,880 that's composed of the radiative part and everything else, 117 00:08:19,880 --> 00:08:23,990 and the radiative part corresponds 118 00:08:23,990 --> 00:08:28,950 to lifetimes no shorter than 10 nanoseconds. 119 00:08:28,950 --> 00:08:34,320 There is absolutely no way that molecules or atoms can 120 00:08:34,320 --> 00:08:42,980 fluoresce at a rate much faster than one over 10 121 00:08:42,980 --> 00:08:48,750 to the minus eight seconds, and then there's other stuff. 122 00:08:48,750 --> 00:08:52,500 And so when the other stuff, the non-radiative decay 123 00:08:52,500 --> 00:08:55,950 is fast compared to the fastest the molecule 124 00:08:55,950 --> 00:08:58,830 could decay by emitting a photon, 125 00:08:58,830 --> 00:09:00,300 then we're getting into something 126 00:09:00,300 --> 00:09:02,340 complicated and interesting. 127 00:09:02,340 --> 00:09:05,610 When the molecule just radiates a photon, 128 00:09:05,610 --> 00:09:10,180 and this stuff is very small, well, that's nice, 129 00:09:10,180 --> 00:09:12,450 but it doesn't tell us very much except what 130 00:09:12,450 --> 00:09:16,990 is the radiative lifetime of the particular excited state. 131 00:09:16,990 --> 00:09:21,300 So there's various kinds of de-excitation, 132 00:09:21,300 --> 00:09:31,750 and there's collisional, and there's-- 133 00:09:31,750 --> 00:09:36,400 well, we can call it collision-free. 134 00:09:36,400 --> 00:09:41,550 Now, remember, if there's no collision, energy is conserved. 135 00:09:41,550 --> 00:09:43,280 We have a Hamiltonian. 136 00:09:43,280 --> 00:09:46,670 The expectation of the Hamiltonian for an isolated 137 00:09:46,670 --> 00:09:49,530 system is not time dependent. 138 00:09:49,530 --> 00:09:54,830 So we have energy conservation, yet in the absence of-- 139 00:09:54,830 --> 00:09:56,730 collisions are what change the energy. 140 00:09:56,730 --> 00:09:58,910 We remove energy from the system. 141 00:09:58,910 --> 00:10:03,260 We can have an incredibly complicated range of processes 142 00:10:03,260 --> 00:10:11,350 which are collision-free, and these collision-free processes 143 00:10:11,350 --> 00:10:14,190 have the signature of the molecule all over it. 144 00:10:14,190 --> 00:10:17,670 They are telling you something about what the molecule thinks 145 00:10:17,670 --> 00:10:22,080 it can do and does, whereas the collisional stuff is 146 00:10:22,080 --> 00:10:23,220 purely statistical. 147 00:10:32,210 --> 00:10:41,853 So the collisional processes, we can say-- 148 00:10:41,853 --> 00:10:45,100 we can estimate how fast they are. 149 00:10:47,640 --> 00:10:51,220 And first of all, there is this number 150 00:10:51,220 --> 00:10:55,270 that many physical chemists carry in their head, 151 00:10:55,270 --> 00:10:57,420 especially if we work in the gas phase. 152 00:10:57,420 --> 00:11:04,750 A collisional rate is on the order of 10 megahertz per torr. 153 00:11:04,750 --> 00:11:05,740 Now, I'm an old guy. 154 00:11:05,740 --> 00:11:09,940 I do two torr instead of bar or millibar, 155 00:11:09,940 --> 00:11:14,760 but a torr and a millibar are about the same thing. 156 00:11:14,760 --> 00:11:18,100 And at atmospheric pressure, that corresponds 157 00:11:18,100 --> 00:11:32,790 to 10 gigahertz per atmosphere, and so that means 10 158 00:11:32,790 --> 00:11:36,275 to the minus 10 seconds. 159 00:11:43,780 --> 00:11:50,910 So the collisional rates can be competing with radiative rates 160 00:11:50,910 --> 00:11:53,020 at atmospheric pressure. 161 00:11:53,020 --> 00:11:56,170 Or in condensed phase, they really can compete. 162 00:11:56,170 --> 00:11:59,860 But this number, 10 megahertz per torr, 163 00:11:59,860 --> 00:12:03,730 is a good number to carry around for estimating 164 00:12:03,730 --> 00:12:05,620 the frequency of collisions. 165 00:12:08,820 --> 00:12:12,960 Now, there are different kinds of collisions. 166 00:12:12,960 --> 00:12:23,110 And one collision with this sort of rate 167 00:12:23,110 --> 00:12:30,420 is all it takes to relax rotation, 168 00:12:30,420 --> 00:12:38,821 and about 1,000 solutions are required to relax vibration. 169 00:12:43,150 --> 00:12:46,960 And now, it's very hard to estimate 170 00:12:46,960 --> 00:12:57,750 what it takes to relax electronic excitation 171 00:12:57,750 --> 00:13:01,830 because the electronic excitation is so big, 172 00:13:01,830 --> 00:13:05,310 there's so many different things that can happen. 173 00:13:05,310 --> 00:13:09,870 And so you could say, well, if nothing really chemical 174 00:13:09,870 --> 00:13:12,930 happened, it would take about a million collisions 175 00:13:12,930 --> 00:13:18,060 to relax electronic, but there are so many other things. 176 00:13:18,060 --> 00:13:20,520 I don't want to put a number here 177 00:13:20,520 --> 00:13:23,410 because this is really the interesting and complicated 178 00:13:23,410 --> 00:13:23,910 stuff. 179 00:13:27,191 --> 00:13:27,690 OK. 180 00:13:31,330 --> 00:13:35,860 In particular, suppose you have an electronically excited 181 00:13:35,860 --> 00:13:39,550 molecule, and it collides with an unexcited molecule, 182 00:13:39,550 --> 00:13:44,850 and you end up doing A plus BCD or all sorts of things. 183 00:13:44,850 --> 00:13:46,210 That's chemistry, right? 184 00:13:46,210 --> 00:13:49,990 But this wouldn't happen if this star wasn't there. 185 00:13:52,500 --> 00:13:56,580 And there's a tremendous complexity to chemistry. 186 00:13:56,580 --> 00:13:58,470 That's why we have-- 187 00:13:58,470 --> 00:14:00,690 it's a BSD subject. 188 00:14:00,690 --> 00:14:04,230 It's a major area of science, and so we're 189 00:14:04,230 --> 00:14:07,050 engaging with chemistry when we start 190 00:14:07,050 --> 00:14:09,750 talking about electronically excited atoms, 191 00:14:09,750 --> 00:14:12,600 and vibration and rotation excitation 192 00:14:12,600 --> 00:14:17,140 is largely irrelevant to chemistry. 193 00:14:17,140 --> 00:14:19,080 it's small potatoes. 194 00:14:19,080 --> 00:14:22,690 You can see chemical effects by rotation and vibrational 195 00:14:22,690 --> 00:14:26,200 excitation, but that's for the purists like me. 196 00:14:26,200 --> 00:14:36,780 OK, now collision-free effects are initially surprising. 197 00:14:36,780 --> 00:14:41,370 We can have several, and we've got some of those 198 00:14:41,370 --> 00:14:44,370 from the initial discussion, but I'm 199 00:14:44,370 --> 00:14:46,170 going to just list them again. 200 00:14:46,170 --> 00:14:55,020 We can have the molecule breaks, and that could 201 00:14:55,020 --> 00:14:58,930 be dissociation or ionization. 202 00:15:02,630 --> 00:15:04,340 This is something that all molecules 203 00:15:04,340 --> 00:15:05,720 do if you excite them enough. 204 00:15:05,720 --> 00:15:13,220 They either fall apart into smaller molecules or ionize. 205 00:15:13,220 --> 00:15:15,190 There's nothing surprising there. 206 00:15:15,190 --> 00:15:20,820 But then there's the unexpected processes, 207 00:15:20,820 --> 00:15:22,600 or at least they used to be unexpected. 208 00:15:22,600 --> 00:15:24,099 When I was a graduate student, there 209 00:15:24,099 --> 00:15:30,310 was still a lot of confusion about what happens 210 00:15:30,310 --> 00:15:32,770 in the absence of collisions. 211 00:15:32,770 --> 00:15:35,440 And there are several names for them. 212 00:15:35,440 --> 00:15:41,750 IVR-- intramolecular vibrational redistribution. 213 00:15:41,750 --> 00:15:46,060 This process, which you understand 214 00:15:46,060 --> 00:15:47,320 from perturbation theory-- 215 00:15:47,320 --> 00:15:50,020 I talked about this early in the semester. 216 00:15:50,020 --> 00:15:58,660 This put closed to the idea of vibration 217 00:15:58,660 --> 00:16:02,740 or mode-specific chemistry by putting an excitation 218 00:16:02,740 --> 00:16:05,980 into a molecule-- a high vibrational excitation 219 00:16:05,980 --> 00:16:11,170 into a particular molecule, activate a bond to chemistry. 220 00:16:11,170 --> 00:16:15,720 IVR is always faster than chemistry. 221 00:16:19,050 --> 00:16:23,420 Or faster than collisions until you get to the condensed phase. 222 00:16:23,420 --> 00:16:25,280 IVR, that's one. 223 00:16:27,930 --> 00:16:32,820 There was so much confusion about IVR in the old days 224 00:16:32,820 --> 00:16:34,830 that people didn't even know what it meant. 225 00:16:34,830 --> 00:16:39,600 It just meant I don't understand what's going on. 226 00:16:39,600 --> 00:16:43,080 But it is intramolecular vibrational redistribution. 227 00:16:43,080 --> 00:16:47,150 Then there's another process called internal conversion, 228 00:16:47,150 --> 00:16:52,980 and another process called intersystem crossing. 229 00:16:52,980 --> 00:16:57,390 So IVR is something that happens in one electronic state, 230 00:16:57,390 --> 00:17:01,740 internal conversion involves relaxation 231 00:17:01,740 --> 00:17:04,920 into high vibrational levels of a lower 232 00:17:04,920 --> 00:17:09,300 electronic state of the same spin, 233 00:17:09,300 --> 00:17:13,349 and intersystem crossing is a relaxation 234 00:17:13,349 --> 00:17:17,099 into a high vibrational levels of another electronic state 235 00:17:17,099 --> 00:17:20,119 with a different spin. 236 00:17:20,119 --> 00:17:22,430 These are really two sides of the same coin, 237 00:17:22,430 --> 00:17:29,270 except that they depend on different molecular properties, 238 00:17:29,270 --> 00:17:31,220 and one can make generalizations that 239 00:17:31,220 --> 00:17:33,725 are different for IC and ISC. 240 00:17:43,840 --> 00:17:49,240 So for a small molecule, we've looked at this before, but-- 241 00:17:56,810 --> 00:18:01,520 we can excite directly to an excited state, 242 00:18:01,520 --> 00:18:05,480 and that's direct association that comes like this, 243 00:18:05,480 --> 00:18:08,750 and there's all sorts of really neat things you can do, 244 00:18:08,750 --> 00:18:11,810 where you can calculate the Franck-Condon factors 245 00:18:11,810 --> 00:18:16,100 or the vibrational intensities for the different energies, 246 00:18:16,100 --> 00:18:21,310 here, by knowing that you have-- 247 00:18:21,310 --> 00:18:24,880 you can calculate the wave function for the continuum, 248 00:18:24,880 --> 00:18:27,280 and you know you have a big lobe here, 249 00:18:27,280 --> 00:18:28,840 and as it gets faster and faster, 250 00:18:28,840 --> 00:18:32,290 the lobes get smaller, and smaller, and closer, and closer 251 00:18:32,290 --> 00:18:33,130 together. 252 00:18:33,130 --> 00:18:35,260 And there's a thing called the reflection principle 253 00:18:35,260 --> 00:18:38,680 that describes the rate of excitation 254 00:18:38,680 --> 00:18:40,270 to a repulsive state. 255 00:18:40,270 --> 00:18:42,070 And by looking at the spectrum, you 256 00:18:42,070 --> 00:18:45,480 can learn the slope and position of this state. 257 00:18:45,480 --> 00:18:50,260 OK, there's also suppose you have a level here 258 00:18:50,260 --> 00:18:52,170 of this excited state. 259 00:18:52,170 --> 00:18:56,620 Well, that excited state has access to this crossing point, 260 00:18:56,620 --> 00:18:58,810 and so that can free-disassociate. 261 00:18:58,810 --> 00:19:03,970 So there's direct and free-dissociation. 262 00:19:07,430 --> 00:19:11,100 I like this stuff too because if I 263 00:19:11,100 --> 00:19:16,980 know the rate of free-disassociation, 264 00:19:16,980 --> 00:19:19,200 and what happens with free disassociation 265 00:19:19,200 --> 00:19:22,050 is you have a spectrum where you measure 266 00:19:22,050 --> 00:19:24,690 several vibrational levels in this state, 267 00:19:24,690 --> 00:19:28,650 and the vibrational lifetimes of these states 268 00:19:28,650 --> 00:19:31,260 are more or less the same, and all of a sudden 269 00:19:31,260 --> 00:19:34,380 the lifetime decreases. 270 00:19:34,380 --> 00:19:40,860 Or all of a sudden the spectrum goes from being sharp to broad. 271 00:19:40,860 --> 00:19:43,200 Or the fluorescence decreases. 272 00:19:43,200 --> 00:19:49,200 The intensity decreases because the quantum yield 273 00:19:49,200 --> 00:19:55,160 or the fluorescence quantum yield 274 00:19:55,160 --> 00:20:02,930 is one over tau radiated over one over tau radiated plus one 275 00:20:02,930 --> 00:20:05,080 over tau non-radiated. 276 00:20:05,080 --> 00:20:09,320 And the pre-disassociation rates can be much faster 277 00:20:09,320 --> 00:20:10,700 than the radiative rates. 278 00:20:10,700 --> 00:20:14,460 So this fluorescence quantum yield goes down. 279 00:20:14,460 --> 00:20:17,120 But the neat thing is that you generally 280 00:20:17,120 --> 00:20:22,100 know what the radiative component of the decay is, 281 00:20:22,100 --> 00:20:26,570 and so by measuring what the actual fluorescence 282 00:20:26,570 --> 00:20:29,120 quantum yield or the decrease in intensity, 283 00:20:29,120 --> 00:20:32,020 you learn something about the non-radiative decay. 284 00:20:35,090 --> 00:20:42,900 OK, I've also taught you we can also ionize. 285 00:20:42,900 --> 00:20:44,615 And we can have direct ionization, 286 00:20:44,615 --> 00:20:47,310 and it looks sort of like this, or we 287 00:20:47,310 --> 00:20:50,040 can have what's called auto-ionization 288 00:20:50,040 --> 00:20:54,120 where somehow, the molecule is able to convert rotation 289 00:20:54,120 --> 00:20:57,720 and vibration of the core, and transfer it 290 00:20:57,720 --> 00:21:02,460 into the electronic excitation, and the electron is free. 291 00:21:02,460 --> 00:21:06,030 So before you're actually accessing directly, 292 00:21:06,030 --> 00:21:09,780 an ionization continue, you can have this other process. 293 00:21:09,780 --> 00:21:13,690 These are things that I've studied for my whole career, 294 00:21:13,690 --> 00:21:16,710 and I know about it, and I love to talk about them, 295 00:21:16,710 --> 00:21:19,630 and we're not going to talk about them. 296 00:21:19,630 --> 00:21:23,720 OK, I also told you about quantum beats. 297 00:21:27,000 --> 00:21:31,510 So suppose we have a bright state and a dark state. 298 00:21:31,510 --> 00:21:35,190 In other words, we have two states, one of which 299 00:21:35,190 --> 00:21:38,520 has an allowed transition with the ground state, 300 00:21:38,520 --> 00:21:41,070 and one has a forbidden transition 301 00:21:41,070 --> 00:21:43,030 with the ground state. 302 00:21:43,030 --> 00:21:45,420 But these are zero order states, and they 303 00:21:45,420 --> 00:21:51,240 can interact to make mixed states because there's 304 00:21:51,240 --> 00:21:55,100 some term in the Hamiltonian connects the bright state 305 00:21:55,100 --> 00:21:55,990 to the dark state. 306 00:21:59,410 --> 00:22:03,370 So what you do with a short excitation pulse 307 00:22:03,370 --> 00:22:05,440 is you make some coherent superposition 308 00:22:05,440 --> 00:22:08,620 of these bright and dark states, which at t equals 309 00:22:08,620 --> 00:22:13,600 zero is the bright state, and you get quantum beats, 310 00:22:13,600 --> 00:22:15,540 and quantum beats can look like this. 311 00:22:15,540 --> 00:22:19,790 They start out phased up, and they go down 312 00:22:19,790 --> 00:22:24,410 like that, and so we have modulation of the fluorescence. 313 00:22:24,410 --> 00:22:28,020 Now, it doesn't have to be 100% modulation. 314 00:22:28,020 --> 00:22:32,944 It could be something really small, 315 00:22:32,944 --> 00:22:34,860 but it's always going to be phased up if we're 316 00:22:34,860 --> 00:22:36,690 looking at the bright state. 317 00:22:41,160 --> 00:22:46,470 So we understand quantum beats. 318 00:22:46,470 --> 00:22:50,190 Now, suppose instead of having one bright state and one 319 00:22:50,190 --> 00:22:55,155 dark state, light, dark, we have a whole bunch of dark states. 320 00:22:58,060 --> 00:23:03,060 Well, in that case, if you make this coherent superposition, 321 00:23:03,060 --> 00:23:06,660 you'll get many quantum beats, but they'll all 322 00:23:06,660 --> 00:23:11,070 have different frequencies, and the quantum beats will dephase, 323 00:23:11,070 --> 00:23:16,380 and it will look just like the fluorescence decays 324 00:23:16,380 --> 00:23:23,020 to zero faster than it's supposed to be able to. 325 00:23:23,020 --> 00:23:26,800 The ceiling on decay rate of one over 10 326 00:23:26,800 --> 00:23:29,020 to the minus eight or 10 to the eight 327 00:23:29,020 --> 00:23:34,840 per second, that can be violated by mixing of the bright state 328 00:23:34,840 --> 00:23:36,700 into the dark state. 329 00:23:36,700 --> 00:23:42,370 So the ability of the molecule to fluoresce goes away fast, 330 00:23:42,370 --> 00:23:45,760 but the excitation doesn't decay. 331 00:23:45,760 --> 00:23:50,200 What you've done is you've mixed a bright state, a decaying zero 332 00:23:50,200 --> 00:23:53,050 order state, with states that don't decay, 333 00:23:53,050 --> 00:23:56,500 and the average lifetime is very long, 334 00:23:56,500 --> 00:24:01,420 but the experiment says the lifetime is really short. 335 00:24:01,420 --> 00:24:04,180 Because what's happening is not that the population 336 00:24:04,180 --> 00:24:07,540 is decaying, but the ability to decay 337 00:24:07,540 --> 00:24:10,840 has been spread among many eigenstates, 338 00:24:10,840 --> 00:24:12,630 and so none of them are very good at it. 339 00:24:20,820 --> 00:24:23,020 OK, so now you're starting to get 340 00:24:23,020 --> 00:24:30,030 the idea of how we can have fast decay without collisions. 341 00:24:30,030 --> 00:24:39,600 And all of these three processes, which I've hidden, 342 00:24:39,600 --> 00:24:43,160 IVR, internal conversion, intersystem crossing, 343 00:24:43,160 --> 00:24:47,810 are based on relaxation of one kind of state 344 00:24:47,810 --> 00:24:52,970 into many dark states. 345 00:24:52,970 --> 00:24:55,340 So nothing is happening without collisions. 346 00:24:55,340 --> 00:24:57,860 Energy is conserved without collisions, 347 00:24:57,860 --> 00:25:00,890 but the signal goes away, and it's 348 00:25:00,890 --> 00:25:06,110 tempting to say that either something magic has happened 349 00:25:06,110 --> 00:25:09,320 and the molecule has decayed, or you really 350 00:25:09,320 --> 00:25:11,960 haven't gone to low enough pressure, 351 00:25:11,960 --> 00:25:15,990 and there really are collisions. 352 00:25:15,990 --> 00:25:25,770 This was a very bitter battle in the mid 1960s. 353 00:25:25,770 --> 00:25:30,010 There was one faculty member who taught the quantum mechanics 354 00:25:30,010 --> 00:25:33,050 course, very much like the one I've been teaching for years, 355 00:25:33,050 --> 00:25:35,680 but he believed that there was no such thing 356 00:25:35,680 --> 00:25:37,780 as radiationless transitions. 357 00:25:37,780 --> 00:25:42,025 It's always that the fluorescence was quenched, 358 00:25:42,025 --> 00:25:42,650 but he's wrong. 359 00:26:01,120 --> 00:26:02,920 In the absence of collision, what decays? 360 00:26:11,080 --> 00:26:16,990 What decays is the ability to fluoresce 361 00:26:16,990 --> 00:26:20,650 or the ability to do other things 362 00:26:20,650 --> 00:26:24,950 like absorb another photon to some other excited state. 363 00:26:28,120 --> 00:26:33,190 You've produced the molecule not just in one eigenstate, 364 00:26:33,190 --> 00:26:38,140 but in a bunch of eigenstates, and this bunch of eigenstates, 365 00:26:38,140 --> 00:26:41,290 since the initial preparation, is 366 00:26:41,290 --> 00:26:44,110 the bright state that's in that bunch, 367 00:26:44,110 --> 00:26:46,810 and there's a couple among them. 368 00:26:46,810 --> 00:26:50,860 What happens is it's time dependent, 369 00:26:50,860 --> 00:26:54,700 and the evolution of this coherent superposition state 370 00:26:54,700 --> 00:26:56,140 is the key. 371 00:27:03,840 --> 00:27:08,160 Let's talk a little bit about IVR some more. 372 00:27:08,160 --> 00:27:15,300 When we have 3n minus six vibrational modes, 373 00:27:15,300 --> 00:27:20,470 there can be a very large number of dark states. 374 00:27:20,470 --> 00:27:26,100 States that couldn't be excited by whatever method 375 00:27:26,100 --> 00:27:30,660 you use to excite them, whether it be an ultraviolet photon, 376 00:27:30,660 --> 00:27:32,770 or a microwave-- 377 00:27:32,770 --> 00:27:35,370 anything. 378 00:27:35,370 --> 00:27:37,410 You have a bright state and a whole bunch 379 00:27:37,410 --> 00:27:40,725 of states that you are not supposed to be able to excite, 380 00:27:40,725 --> 00:27:42,960 an anharmonic interactions among them. 381 00:27:46,210 --> 00:27:49,850 And we know some things. 382 00:27:49,850 --> 00:27:54,740 So if we have a cubic interaction, 383 00:27:54,740 --> 00:27:57,620 where we have one normal mode. 384 00:28:04,120 --> 00:28:07,090 So this would be a term in the Hamiltonian. 385 00:28:07,090 --> 00:28:12,520 And again, I lectured on this before at a time 386 00:28:12,520 --> 00:28:15,220 when it was probably impossible to understand 387 00:28:15,220 --> 00:28:19,120 the significance of this, but you used perturbation theory 388 00:28:19,120 --> 00:28:24,970 to say OK, what's happening when you have an anharmonic coupling 389 00:28:24,970 --> 00:28:29,210 term that couples one mode to another? 390 00:28:29,210 --> 00:28:32,410 And we know how do all that sort of stuff. 391 00:28:32,410 --> 00:28:37,750 And the selection rules for that are delta vi 392 00:28:37,750 --> 00:28:41,140 equals plus and minus one, delta vj 393 00:28:41,140 --> 00:28:43,060 equals plus and minus two and zero. 394 00:28:46,530 --> 00:28:51,200 We also know when we go from the real coordinate 395 00:28:51,200 --> 00:28:58,520 to the dimensionless coordinate, we factor something out. 396 00:28:58,520 --> 00:29:02,540 And for each power of Q, that thing that we factor out 397 00:29:02,540 --> 00:29:05,315 is a factor of 100 smaller. 398 00:29:08,630 --> 00:29:11,320 We have cubic terms that we have quartic terms, 399 00:29:11,320 --> 00:29:15,010 and the quartic terms are a factor of roughly 100 smaller, 400 00:29:15,010 --> 00:29:17,930 but there's more of them. 401 00:29:17,930 --> 00:29:20,550 And so there is an order sorting thing, which 402 00:29:20,550 --> 00:29:25,440 we can call delta capital V, which is the sum from i 403 00:29:25,440 --> 00:29:33,580 equals one to 3n minus six of the absolute value of delta vi. 404 00:29:36,460 --> 00:29:44,560 So if the total change in number of vibrational quanta is three, 405 00:29:44,560 --> 00:29:47,090 well, we have a cubic term. 406 00:29:47,090 --> 00:29:49,910 If it's four, it's quartic term, and the quartic term 407 00:29:49,910 --> 00:29:53,630 has a coefficient, a factor of 100, roughly, 408 00:29:53,630 --> 00:29:58,520 smaller than the cubic one, but there's more possibilities. 409 00:29:58,520 --> 00:30:03,495 And so suppose we are going to talk about benzene. 410 00:30:09,540 --> 00:30:11,310 Well, it has 30 nodes. 411 00:30:16,950 --> 00:30:24,310 And so we could imagine delta v on the order o 30. 412 00:30:27,410 --> 00:30:37,260 Well, it's 10 to the 60 smaller than the delta v of three, 413 00:30:37,260 --> 00:30:40,600 except that there's a lot more possibilities. 414 00:30:40,600 --> 00:30:44,820 So we have to think about how big is the coupling matrix 415 00:30:44,820 --> 00:30:49,580 element, and how many states are being coupled? 416 00:30:49,580 --> 00:30:52,270 And so there's a thing that's really relevant 417 00:30:52,270 --> 00:30:55,530 called the vibrational density of states. 418 00:30:55,530 --> 00:30:58,080 So at a particular excitation energy, 419 00:30:58,080 --> 00:31:00,750 you want to be able to know how many vibrational states there 420 00:31:00,750 --> 00:31:03,960 are because that, more or less, tells you OK, 421 00:31:03,960 --> 00:31:07,590 we're going to have some kind of statistical coupling. 422 00:31:07,590 --> 00:31:11,850 And if we know the density of states and the average matrix 423 00:31:11,850 --> 00:31:14,445 element, we could do a Fermi golden rule of calculation, 424 00:31:14,445 --> 00:31:16,270 and we can predict what's going to happen. 425 00:31:22,490 --> 00:31:24,710 Now, there are ways of calculating 426 00:31:24,710 --> 00:31:31,050 the density of states, which are rigorous and beautiful, 427 00:31:31,050 --> 00:31:34,290 but there's also a very simple minded way of doing it, 428 00:31:34,290 --> 00:31:35,860 which I'm going to present here. 429 00:31:48,980 --> 00:31:50,625 So the vibrational density of states. 430 00:32:26,230 --> 00:32:30,190 This is one of the most primitive, crude estimates 431 00:32:30,190 --> 00:32:33,610 of density of states, and I'll explain how it works, 432 00:32:33,610 --> 00:32:35,980 but I'll explain it by going even cruder. 433 00:32:41,100 --> 00:32:45,850 And I also want to make sure that I have it-- 434 00:32:45,850 --> 00:32:49,380 OK, this frequency is in wave numbers, 435 00:32:49,380 --> 00:32:50,760 and this is in wave numbers. 436 00:32:50,760 --> 00:32:55,400 So we just changed both quantities. 437 00:32:55,400 --> 00:32:57,410 This is OK, and this will give me 438 00:32:57,410 --> 00:33:05,920 the number of states per wave number. 439 00:33:05,920 --> 00:33:08,620 OK, so let me do an example for benzene. 440 00:33:08,620 --> 00:33:15,770 We have 30 modes, and here's a big assumption, 441 00:33:15,770 --> 00:33:20,810 which is completely wrong, but it leads to an underestimate. 442 00:33:20,810 --> 00:33:25,840 Let us say that all of the modes have the same frequency-- 443 00:33:25,840 --> 00:33:26,960 1000 wave numbers. 444 00:33:26,960 --> 00:33:30,610 That's a typical number for a vibrational frequency, 445 00:33:30,610 --> 00:33:32,690 but benzene has a lot of modes that 446 00:33:32,690 --> 00:33:35,660 have much lower frequencies, and only a few 447 00:33:35,660 --> 00:33:38,510 that have higher frequency, and so 448 00:33:38,510 --> 00:33:41,690 this is going to be a gross underestimate. 449 00:33:41,690 --> 00:33:48,380 And now let's say we have the vibrational energy divided 450 00:33:48,380 --> 00:33:57,150 by Hc, and that that is 10,000 wave number. 451 00:33:57,150 --> 00:34:00,470 So we have 10,000 wave numbers of vibrational excitation 452 00:34:00,470 --> 00:34:04,670 in benzene, and we have all the modes 453 00:34:04,670 --> 00:34:06,480 having the same frequency. 454 00:34:06,480 --> 00:34:17,929 So we need 10 quanta to make 10,000, and there's 30 choices. 455 00:34:17,929 --> 00:34:21,170 So we have 30 to the 10. 456 00:34:24,409 --> 00:34:31,300 So each quanta we pick, we have 30 choices. 457 00:34:31,300 --> 00:34:34,530 And we have to do 10 of them, and so it's 30 to the 10, 458 00:34:34,530 --> 00:34:39,420 but now we have 10 factorial. 459 00:34:39,420 --> 00:34:43,560 We have to divide that by that because the order of the 10 460 00:34:43,560 --> 00:34:48,300 choices has to be corrected. 461 00:34:48,300 --> 00:34:54,870 OK, and so this number is 1.6 times 10 to the eighth. 462 00:34:57,940 --> 00:34:59,920 That's a big number. 463 00:34:59,920 --> 00:35:05,680 I'm used to talking about states one at a time, 464 00:35:05,680 --> 00:35:10,690 and it's very rare that I have two states within one wave 465 00:35:10,690 --> 00:35:14,930 number, and here we have 10 of the eight. 466 00:35:14,930 --> 00:35:17,020 So let's go down in energy a little bit. 467 00:35:17,020 --> 00:35:27,320 Let's say instead of 10,000, let's go to 3,000. 468 00:35:27,320 --> 00:35:29,870 And when we do the same calculation for 3,000, 469 00:35:29,870 --> 00:35:38,190 we get 4,500 states instead of 100 million states. 470 00:35:38,190 --> 00:35:40,060 So two messages. 471 00:35:40,060 --> 00:35:48,520 One is the number of states is really large, 472 00:35:48,520 --> 00:35:53,490 and it goes up really, really fast. 473 00:35:53,490 --> 00:35:56,160 And this takes us into a region of quantum mechanics 474 00:35:56,160 --> 00:35:59,980 that we hadn't thought about before because I'm 475 00:35:59,980 --> 00:36:02,950 doing bottom-up, and there is no place 476 00:36:02,950 --> 00:36:07,195 in what I do for a million states or even 100 states. 477 00:36:12,180 --> 00:36:14,177 OK. 478 00:36:14,177 --> 00:36:28,090 Now, let's talk about a typical energy level diagram. 479 00:36:28,090 --> 00:36:33,070 This is the ground state, This is the excited triplet state, 480 00:36:33,070 --> 00:36:36,460 which is almost always the first excited state, 481 00:36:36,460 --> 00:36:40,570 and then here is the first excited sigma state. 482 00:36:43,340 --> 00:36:54,360 And so for small polyphonic molecules, 483 00:36:54,360 --> 00:36:58,630 we have a very low density of states here, 484 00:36:58,630 --> 00:37:01,670 a somewhat higher density of vibrationally excited levels 485 00:37:01,670 --> 00:37:06,530 of the triplet here, and a very high density of states 486 00:37:06,530 --> 00:37:07,460 from the ground state. 487 00:37:10,380 --> 00:37:12,670 So you normally look at relatively low vibrational 488 00:37:12,670 --> 00:37:15,190 levels, and there's nothing much happening here, 489 00:37:15,190 --> 00:37:17,020 and maybe there's some perturbations 490 00:37:17,020 --> 00:37:18,280 by a triplet state. 491 00:37:18,280 --> 00:37:21,700 So we get local glitches in the energy levels 492 00:37:21,700 --> 00:37:24,790 and spectroscopic properties, and the density 493 00:37:24,790 --> 00:37:26,650 of high vibrational level in a ground state 494 00:37:26,650 --> 00:37:29,430 is so high that they might as well not be there. 495 00:37:33,440 --> 00:37:40,050 But now when we talk about these collisional processes of bigger 496 00:37:40,050 --> 00:37:51,100 molecules, we want to use Fermi's golden rule, 497 00:37:51,100 --> 00:37:54,070 and you've seen Fermi's golden rule. 498 00:37:54,070 --> 00:37:57,250 It tells you the rate of various processes. 499 00:37:57,250 --> 00:38:01,450 And so a rate, we can call gamma. 500 00:38:01,450 --> 00:38:08,380 Two pi over h bar times the vibrational density of states 501 00:38:08,380 --> 00:38:18,760 times H bright, dark squared. 502 00:38:18,760 --> 00:38:21,160 So that's the Fermi's golden rule 503 00:38:21,160 --> 00:38:27,250 rewritten in terms to describe radiationless processes. 504 00:38:27,250 --> 00:38:33,100 It's directly related to the first way we saw it. 505 00:38:33,100 --> 00:38:36,370 And so we have the vibrational density of states, 506 00:38:36,370 --> 00:38:39,490 which as you go up in excitation energy, 507 00:38:39,490 --> 00:38:42,170 increases really rapidly. 508 00:38:42,170 --> 00:38:45,590 You have the average of the matrix 509 00:38:45,590 --> 00:38:50,580 elements between the coupled states, squared. 510 00:38:50,580 --> 00:38:54,570 This is going to go down because remember 511 00:38:54,570 --> 00:38:58,740 when I talked about vibrational matrix elements, 512 00:38:58,740 --> 00:39:03,960 each additional number in the change 513 00:39:03,960 --> 00:39:07,530 in total vibrational quanta causes this to go down 514 00:39:07,530 --> 00:39:12,330 by roughly a factor of 100. 515 00:39:12,330 --> 00:39:16,320 We have a big increase here, and a big decrease here, 516 00:39:16,320 --> 00:39:19,780 but this guy wins. 517 00:39:19,780 --> 00:39:20,620 You can show that. 518 00:39:24,930 --> 00:39:34,645 So now, we can draw sort of a manifold of states. 519 00:39:45,190 --> 00:39:50,410 So what's happening is the density of triplet states 520 00:39:50,410 --> 00:39:53,690 is much higher than the density of singlet states. 521 00:39:53,690 --> 00:39:56,290 And so if you were just interested in IVR, well, 522 00:39:56,290 --> 00:39:57,680 you'd look at that. 523 00:39:57,680 --> 00:40:00,010 But this is a much faster process, 524 00:40:00,010 --> 00:40:02,890 and this is enormously faster because the energy 525 00:40:02,890 --> 00:40:09,670 gap between s1 and t1 is much smaller than in the energy 526 00:40:09,670 --> 00:40:11,440 gap between s1 and s0. 527 00:40:14,260 --> 00:40:21,550 And so the s1-s0 interaction is called internal conversion, 528 00:40:21,550 --> 00:40:29,090 and that's usually way bigger than the s1-t1 intersystem 529 00:40:29,090 --> 00:40:33,910 crossing, but not always. 530 00:40:37,380 --> 00:40:44,990 The intersystem crossing is due to spin orbit interactions. 531 00:40:44,990 --> 00:40:51,110 Spin orbit interactions are predictable for each atom. 532 00:40:51,110 --> 00:40:53,960 Extending what you got in five-eleven-one 533 00:40:53,960 --> 00:40:57,080 and five-eleven-two, you can predict what the spin orbit 534 00:40:57,080 --> 00:41:03,950 interaction is, and it's related to the amplitude of the wave 535 00:41:03,950 --> 00:41:05,990 function at the nucleus. 536 00:41:05,990 --> 00:41:10,940 But anyway, what happens is that carbon has a spin orbit 537 00:41:10,940 --> 00:41:13,760 coupling constant of 10 wave numbers, 538 00:41:13,760 --> 00:41:17,420 and oxygen has one of about 150 wave numbers. 539 00:41:17,420 --> 00:41:21,410 And since we're talking about squared matrix elements, 540 00:41:21,410 --> 00:41:26,480 oxygen is 225 times more effective than carbon. 541 00:41:26,480 --> 00:41:31,220 And so if we have a couple of oxygen atoms in the molecule-- 542 00:41:31,220 --> 00:41:33,310 or nitrogen atoms-- 543 00:41:33,310 --> 00:41:36,730 the spin orbit interactions are much bigger, 544 00:41:36,730 --> 00:41:44,100 and they can win over internal conversion sometimes. 545 00:41:44,100 --> 00:41:46,560 Depends on what the energy gap is. 546 00:41:46,560 --> 00:41:52,450 And now, molecules which have strong electronic transitions 547 00:41:52,450 --> 00:41:54,770 have chroma force. 548 00:41:54,770 --> 00:41:56,180 It's not the whole molecule. 549 00:41:56,180 --> 00:41:59,370 It's something about a part of the molecule. 550 00:41:59,370 --> 00:42:01,790 And if you have a strong transition 551 00:42:01,790 --> 00:42:08,020 at relatively low energy, there is always oxygen or nitrogen. 552 00:42:08,020 --> 00:42:13,345 And so the thing that you're exciting 553 00:42:13,345 --> 00:42:17,410 is going to have a fast intersystem crossing rate 554 00:42:17,410 --> 00:42:26,470 because it involves oxygen and nitrogen. 555 00:42:26,470 --> 00:42:31,060 But if you have just a pure hydrocarbon, 556 00:42:31,060 --> 00:42:33,700 intersystem crossing is probably not so important, 557 00:42:33,700 --> 00:42:37,130 but internal conversion is going to win. 558 00:42:37,130 --> 00:42:41,320 And for most hydrocarbons, you can 559 00:42:41,320 --> 00:42:45,040 have a nice, strong absorption spectrum, but very 560 00:42:45,040 --> 00:42:47,980 little fluorescence, and that's mostly 561 00:42:47,980 --> 00:42:50,031 because of internal conversion. 562 00:42:58,780 --> 00:43:06,870 But the crucial thing is the energy gap s1-t1, or s1-s0 563 00:43:06,870 --> 00:43:12,720 controlling the relative importance of ISC versus IC. 564 00:43:12,720 --> 00:43:16,780 Now, you could also have several different excited 565 00:43:16,780 --> 00:43:19,890 states like s1 and s2, and they could 566 00:43:19,890 --> 00:43:22,110 be talking to each other through a small gap 567 00:43:22,110 --> 00:43:24,540 or to the ground state by an even larger gap. 568 00:43:24,540 --> 00:43:25,740 There's all sorts of stuff. 569 00:43:25,740 --> 00:43:26,330 Yes? 570 00:43:26,330 --> 00:43:29,820 AUDIENCE: The internal conversion process, you're 571 00:43:29,820 --> 00:43:32,310 going from the first singlet excited state 572 00:43:32,310 --> 00:43:35,430 to the lowest level singlet ground state. 573 00:43:35,430 --> 00:43:39,025 Where does the energy get redistributed to? 574 00:43:39,025 --> 00:43:40,650 PROFESSOR ROBERT FIELD: It gets excited 575 00:43:40,650 --> 00:43:44,780 into a vibrational excited level of the ground state, 576 00:43:44,780 --> 00:43:47,340 but the energy hasn't gone anywhere. 577 00:43:47,340 --> 00:43:55,600 It's just now these guys are not fluorescing, 578 00:43:55,600 --> 00:43:59,560 and if there are collisions, the collisions 579 00:43:59,560 --> 00:44:06,660 can cause removal of energy from the molecule. 580 00:44:06,660 --> 00:44:10,830 And since the vibrational energy gaps are really small, 581 00:44:10,830 --> 00:44:15,040 collisions start to be very effective in cooling. 582 00:44:15,040 --> 00:44:21,370 But if you have a laser, and the laser involves somehow exciting 583 00:44:21,370 --> 00:44:25,302 the s1 state, and the s1 state likes 584 00:44:25,302 --> 00:44:27,510 to fluoresce to high vibrational levels of the ground 585 00:44:27,510 --> 00:44:32,240 state because of Franck-Condon, so it has gain, 586 00:44:32,240 --> 00:44:37,250 but there is often a t1 to t2 excitation, which 587 00:44:37,250 --> 00:44:44,050 is in the region of the gain of the laser, and it quenches it. 588 00:44:44,050 --> 00:44:47,630 And so diolasers, which are a fantastic way of generating 589 00:44:47,630 --> 00:44:50,270 tunable radiation, are always worried 590 00:44:50,270 --> 00:44:53,630 about quenching by triplets, and you 591 00:44:53,630 --> 00:44:55,520 have to do something clever to quench 592 00:44:55,520 --> 00:44:59,000 the triplets to remove that. 593 00:44:59,000 --> 00:45:02,630 So there's all sorts of stuff about competing processes 594 00:45:02,630 --> 00:45:05,920 that you can use it as insights. 595 00:45:15,970 --> 00:45:20,720 OK, we don't have much more time, and the most important 596 00:45:20,720 --> 00:45:23,300 topic, I'm not going to talk about at all. 597 00:45:32,000 --> 00:45:34,760 So we can have isomerization, and isomerization 598 00:45:34,760 --> 00:45:35,570 takes many forms. 599 00:45:40,210 --> 00:45:42,150 I've spent the last 30 years looking 600 00:45:42,150 --> 00:45:45,810 at isomerization in a really simple polyatomic called 601 00:45:45,810 --> 00:45:46,840 acetylene. 602 00:45:46,840 --> 00:45:51,650 And in the ground state, you can isomerize 603 00:45:51,650 --> 00:45:54,170 from high vibrational levels of the ground state 604 00:45:54,170 --> 00:46:01,270 to another isomer called [? venility, ?] 605 00:46:01,270 --> 00:46:03,310 and this is a really interesting problem. 606 00:46:03,310 --> 00:46:10,240 And in the excited state, we have two conformers. 607 00:46:10,240 --> 00:46:12,680 The trans-bent conformer and the cis-bent 608 00:46:12,680 --> 00:46:15,410 conformer, and they're separated by a barrier, 609 00:46:15,410 --> 00:46:18,050 and we can understand both of those processes. 610 00:46:18,050 --> 00:46:21,190 But the important thing is if the molecule isomerizes, 611 00:46:21,190 --> 00:46:28,220 its chemistry changes, and so it will act differently. 612 00:46:28,220 --> 00:46:31,310 Now, there's all sorts of kinds of isomerizations. 613 00:46:31,310 --> 00:46:36,570 This is a 1,2 hydrogen shift, but there's also 614 00:46:36,570 --> 00:46:40,020 intramolecular proton transfer. 615 00:46:40,020 --> 00:46:43,100 There's torsions where a structure-- 616 00:46:43,100 --> 00:46:45,290 one isomer or conformer is locked 617 00:46:45,290 --> 00:46:48,920 in by a lot of hydrogen bonding, and the bigger 618 00:46:48,920 --> 00:46:53,510 the molecule, the larger number of isomerization structures 619 00:46:53,510 --> 00:46:58,010 you have to consider, and there's a lot of insight there. 620 00:46:58,010 --> 00:47:01,710 So isomerization is a very crucial thing 621 00:47:01,710 --> 00:47:06,510 in the behavior of large molecules. 622 00:47:06,510 --> 00:47:09,810 The topic that I don't really have time for is FRED-- 623 00:47:15,630 --> 00:47:17,655 fluorescence resonance energy transfer. 624 00:47:20,340 --> 00:47:23,550 Let's just draw a little picture of a molecule doing 625 00:47:23,550 --> 00:47:28,770 all sorts of neat things, and another confirmation 626 00:47:28,770 --> 00:47:33,430 of that molecule, and we have donor and acceptor. 627 00:47:33,430 --> 00:47:35,730 So at the opposite ends of this thing, 628 00:47:35,730 --> 00:47:39,990 clever chemists can put things that-- 629 00:47:39,990 --> 00:47:45,090 and so this is a molecule which has an electronically excited 630 00:47:45,090 --> 00:47:45,790 state. 631 00:47:45,790 --> 00:47:47,670 This fluoresces in the loop. 632 00:47:51,050 --> 00:47:53,050 We excited, say, in the UV, and it 633 00:47:53,050 --> 00:47:55,130 fluoresces to the red of the excitation 634 00:47:55,130 --> 00:47:56,510 because that would happen. 635 00:47:56,510 --> 00:47:59,330 In condensed phases, you remove some energy, 636 00:47:59,330 --> 00:48:01,840 and you fluoresce from v equals zero. 637 00:48:01,840 --> 00:48:04,730 And we have an acceptor which absorbs in the blue, 638 00:48:04,730 --> 00:48:07,820 and fluoresces in the red. 639 00:48:07,820 --> 00:48:13,130 And the donor-acceptor energy transfer 640 00:48:13,130 --> 00:48:15,545 is related to one over r to the six. 641 00:48:15,545 --> 00:48:16,670 Doesn't that look familiar? 642 00:48:19,930 --> 00:48:22,810 It's a dipole-dipole interaction, 643 00:48:22,810 --> 00:48:25,570 or an induced dipole-induced dipole interaction. 644 00:48:25,570 --> 00:48:27,460 It goes as one over r to the six, 645 00:48:27,460 --> 00:48:33,190 and so we might get a lot of red fluorescence 646 00:48:33,190 --> 00:48:37,960 from this molecule exciting in the UV, and much less red 647 00:48:37,960 --> 00:48:41,620 fluorescence or none because we've increased the distance. 648 00:48:41,620 --> 00:48:53,480 And this works in the range of I think one to 10 nanometers. 649 00:48:53,480 --> 00:48:53,980 Yeah. 650 00:48:57,180 --> 00:48:59,550 So it's a fantastic ruler. 651 00:48:59,550 --> 00:49:01,830 How much red shifted fluorescence 652 00:49:01,830 --> 00:49:05,580 do you get from donor to acceptor energy transfer? 653 00:49:05,580 --> 00:49:08,020 And it's a measure of the distance. 654 00:49:08,020 --> 00:49:11,170 And so you have a protein and a denatured protein. 655 00:49:11,170 --> 00:49:13,710 This distance changes, and one can 656 00:49:13,710 --> 00:49:18,600 use the way in which the red fluorescence appears 657 00:49:18,600 --> 00:49:22,420 as a measure of the structure. 658 00:49:22,420 --> 00:49:24,960 So this is not like small molecule spectroscopy 659 00:49:24,960 --> 00:49:27,300 where you calculate moments of inertia and vibrational 660 00:49:27,300 --> 00:49:28,230 frequency. 661 00:49:28,230 --> 00:49:30,394 This is really crude. 662 00:49:30,394 --> 00:49:32,310 This has nothing to do with quantum mechanics, 663 00:49:32,310 --> 00:49:38,530 except it is, and it's just a simple measurement of how far 664 00:49:38,530 --> 00:49:41,810 two things are apart. 665 00:49:41,810 --> 00:49:45,560 And there are all sorts of ways of using this, including time 666 00:49:45,560 --> 00:49:47,720 resolved waves, where you actually 667 00:49:47,720 --> 00:49:51,380 look at the rate at which the one kind of fluorescence 668 00:49:51,380 --> 00:49:54,920 goes away, and the other kind of fluorescence comes in, 669 00:49:54,920 --> 00:49:57,050 and many other things. 670 00:49:57,050 --> 00:50:00,440 OK, so that's it for me on photochemistry, 671 00:50:00,440 --> 00:50:04,280 and you should read Troy's notes because they 672 00:50:04,280 --> 00:50:06,470 are much more germane to what you 673 00:50:06,470 --> 00:50:08,910 might encounter in real life. 674 00:50:08,910 --> 00:50:10,670 But the bottom-up approach, I think, 675 00:50:10,670 --> 00:50:13,370 is useful too, especially in the importance 676 00:50:13,370 --> 00:50:16,630 of how the matrix elements and the density of states 677 00:50:16,630 --> 00:50:20,130 scale using simple ideas. 678 00:50:20,130 --> 00:50:25,330 So I'll see you on Monday and blow you away on Monday.