1 00:00:00,090 --> 00:00:02,490 The following content is provided under a Creative 2 00:00:02,490 --> 00:00:04,030 Commons license. 3 00:00:04,030 --> 00:00:06,330 Your support will help MIT OpenCourseWare 4 00:00:06,330 --> 00:00:10,690 continue to offer high-quality educational resources for free. 5 00:00:10,690 --> 00:00:13,320 To make a donation or view additional materials 6 00:00:13,320 --> 00:00:17,250 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,250 --> 00:00:18,200 at ocw.mit.edu. 8 00:00:23,339 --> 00:00:25,310 ROBERT FIELD: My spies tell me that there 9 00:00:25,310 --> 00:00:27,800 was a good mood after the exam. 10 00:00:27,800 --> 00:00:31,430 And it was an exam that was created 11 00:00:31,430 --> 00:00:36,590 to show the power of intuition and how you build intuition 12 00:00:36,590 --> 00:00:42,610 based on stuff that seems kind of ordinary. 13 00:00:42,610 --> 00:00:45,380 And all of a sudden you have the power 14 00:00:45,380 --> 00:00:50,300 to exercise chemical insight in ways 15 00:00:50,300 --> 00:00:52,730 which are more than just textbook 16 00:00:52,730 --> 00:00:59,510 ways of solving differential equations, memorizing pictures, 17 00:00:59,510 --> 00:01:00,180 and so on. 18 00:01:00,180 --> 00:01:03,900 So this is my purpose, and at the end of the course 19 00:01:03,900 --> 00:01:06,990 I'm going to try to really stretch your imagination. 20 00:01:10,880 --> 00:01:15,290 That's the probable schedule. 21 00:01:15,290 --> 00:01:23,870 And so I'm taking more time with the lecture 22 00:01:23,870 --> 00:01:26,480 on electronic spectroscopy and dynamics 23 00:01:26,480 --> 00:01:29,540 because this is really the core of what I do 24 00:01:29,540 --> 00:01:31,260 and what I care about. 25 00:01:31,260 --> 00:01:36,030 And so I don't know what I'm going to say in this lecture. 26 00:01:36,030 --> 00:01:41,210 I want to spend some time talking about Zewail's Nobel 27 00:01:41,210 --> 00:01:46,020 Prize work, and certainly that will be partly on Monday. 28 00:01:49,700 --> 00:01:52,220 Then, intermolecular interactions 29 00:01:52,220 --> 00:01:56,030 is basically why isn't everything in the gas phase? 30 00:01:56,030 --> 00:01:57,950 You know everything isn't in the gas phase, 31 00:01:57,950 --> 00:02:01,190 and this is the first step towards not being in the gas 32 00:02:01,190 --> 00:02:03,530 phase, kind of important. 33 00:02:03,530 --> 00:02:06,890 And then probably photochemistry, 34 00:02:06,890 --> 00:02:09,979 which is a little bit more of electronic spectroscopy 35 00:02:09,979 --> 00:02:12,470 but in a different framework. 36 00:02:12,470 --> 00:02:16,400 Delta functions is a way of dealing 37 00:02:16,400 --> 00:02:22,270 with complicated potentials without perturbation theory. 38 00:02:22,270 --> 00:02:25,310 And it's really neat and it's very abstract, 39 00:02:25,310 --> 00:02:33,120 and it's called the discrete variable representation, 40 00:02:33,120 --> 00:02:36,690 and it's a very powerful way of approaching 41 00:02:36,690 --> 00:02:43,080 complicated problems without having to do a lot of algebra 42 00:02:43,080 --> 00:02:44,700 because the computer does all of it, 43 00:02:44,700 --> 00:02:47,480 but it does it in a funny way. 44 00:02:47,480 --> 00:02:50,320 And I've been putting off this lecture 45 00:02:50,320 --> 00:02:53,650 on time-dependent Hamiltonians for a long time, 46 00:02:53,650 --> 00:02:57,610 and I hope that the last lecture will be an honest approach 47 00:02:57,610 --> 00:03:00,100 to time-dependent Hamiltonians. 48 00:03:00,100 --> 00:03:04,260 So this is kind of a motto for me. 49 00:03:04,260 --> 00:03:06,960 Small is a template for large. 50 00:03:06,960 --> 00:03:08,970 If you really understand everything 51 00:03:08,970 --> 00:03:12,420 a diatomic molecule can do, you're 52 00:03:12,420 --> 00:03:18,410 prepared to understand most of what big molecules do. 53 00:03:18,410 --> 00:03:21,690 And so this is sort of a bottom-up approach. 54 00:03:21,690 --> 00:03:24,510 And what I presented last time was 55 00:03:24,510 --> 00:03:26,970 sort of a template for everything 56 00:03:26,970 --> 00:03:29,400 a diatomic molecule can do. 57 00:03:29,400 --> 00:03:34,050 You have a ground state, and that dissociates 58 00:03:34,050 --> 00:03:35,550 the ground-state atoms. 59 00:03:35,550 --> 00:03:37,500 You have a repulsive state. 60 00:03:37,500 --> 00:03:39,510 Now it's not always just two states, 61 00:03:39,510 --> 00:03:47,220 but for H2+ or for H2 we sort of expect this sort of structure. 62 00:03:47,220 --> 00:03:48,840 And then there are excited states 63 00:03:48,840 --> 00:03:51,600 which are usually less bound than the ground states. 64 00:03:51,600 --> 00:03:55,500 So they have smaller rotational constants, larger internuclear 65 00:03:55,500 --> 00:03:56,760 distance. 66 00:03:56,760 --> 00:03:58,840 And if they don't, there's a good reason for it 67 00:03:58,840 --> 00:04:02,750 which you're supposed to be able to produce. 68 00:04:02,750 --> 00:04:06,740 Now the repulsive states often cross 69 00:04:06,740 --> 00:04:11,390 through a bound state, and this results in what we 70 00:04:11,390 --> 00:04:13,040 call predissociation. 71 00:04:13,040 --> 00:04:16,910 In other words, it happens before it was intended to. 72 00:04:16,910 --> 00:04:19,279 And it also is an example for all sorts 73 00:04:19,279 --> 00:04:21,050 of interesting effects associated 74 00:04:21,050 --> 00:04:24,230 with this curve crossing. 75 00:04:24,230 --> 00:04:27,290 And we'll talk more about that. 76 00:04:27,290 --> 00:04:30,530 And so predissociation and autoionization, 77 00:04:30,530 --> 00:04:33,800 these are dynamical effects that occur as you 78 00:04:33,800 --> 00:04:35,750 approach some special limit. 79 00:04:35,750 --> 00:04:38,600 Now this is you're above the dissociation limit, 80 00:04:38,600 --> 00:04:39,500 so it could happen. 81 00:04:39,500 --> 00:04:42,680 But as far as this data is concerned, you're not, 82 00:04:42,680 --> 00:04:44,480 and so it happens earlier. 83 00:04:44,480 --> 00:04:48,740 Now here you have ionization. 84 00:04:48,740 --> 00:04:53,450 And below the ionization there's a whole infinite manifold 85 00:04:53,450 --> 00:04:56,000 of Rydberg states which look almost 86 00:04:56,000 --> 00:05:00,330 identical to the potential energy curve for the ion. 87 00:05:00,330 --> 00:05:06,200 And there's all sorts of stuff that you 88 00:05:06,200 --> 00:05:10,760 can understand about the electron-ion interaction 89 00:05:10,760 --> 00:05:12,080 by studying Rydberg states. 90 00:05:12,080 --> 00:05:17,530 And that's been, for the last 20 years, roughly half 91 00:05:17,530 --> 00:05:18,155 of my research. 92 00:05:20,750 --> 00:05:25,100 Now encoded in Rydberg states is autoionization. 93 00:05:25,100 --> 00:05:28,580 If you have a vibrational level of a Rydberg state 94 00:05:28,580 --> 00:05:31,640 which lies above the ionization limit, well, 95 00:05:31,640 --> 00:05:35,980 then it can ionize, and that's interesting too. 96 00:05:35,980 --> 00:05:41,610 So this is a very quick summary of what I talked about before, 97 00:05:41,610 --> 00:05:44,450 and I want to add to that. 98 00:05:51,990 --> 00:05:55,970 So in order for a transition to occur, 99 00:05:55,970 --> 00:06:01,430 you either need a permanent dipole moment, a dipole moment 100 00:06:01,430 --> 00:06:06,620 derivative with respect to the displacement coordinate, 101 00:06:06,620 --> 00:06:09,810 or an electronic transition. 102 00:06:09,810 --> 00:06:11,720 So this is the rule. 103 00:06:11,720 --> 00:06:15,290 This is what you need for a pure rotation transition which 104 00:06:15,290 --> 00:06:17,270 is looked at in the microwave. 105 00:06:17,270 --> 00:06:20,220 This is what you need for a vibrational transition. 106 00:06:20,220 --> 00:06:25,040 The dipole moment has to depend on displacement 107 00:06:25,040 --> 00:06:28,280 from equilibrium for one of the coordinates. 108 00:06:28,280 --> 00:06:29,990 If it's a diatomic, there's only one. 109 00:06:29,990 --> 00:06:33,560 If it's a polyatomic, there's 3n minus 6. 110 00:06:33,560 --> 00:06:36,420 And so these two things are very important. 111 00:06:36,420 --> 00:06:38,480 And then the electronic transition moment, 112 00:06:38,480 --> 00:06:40,760 you can always have transitions where 113 00:06:40,760 --> 00:06:43,910 you promote an electron from the ground state 114 00:06:43,910 --> 00:06:45,640 to an excited state. 115 00:06:45,640 --> 00:06:48,780 But since the operator is a one-electron operator, 116 00:06:48,780 --> 00:06:52,010 the strong transitions are a very small subset 117 00:06:52,010 --> 00:06:53,240 of all the possible ones. 118 00:06:56,690 --> 00:07:02,500 And one of the important things for dealing 119 00:07:02,500 --> 00:07:07,430 with electronic transitions is the Franck-Condon principle. 120 00:07:12,030 --> 00:07:14,460 The Franck-Condon principle is basically 121 00:07:14,460 --> 00:07:18,830 a restatement of the Born-Oppenheimer approximation 122 00:07:18,830 --> 00:07:23,620 that the electrons move fast, nuclei move slowly. 123 00:07:23,620 --> 00:07:32,540 And as a result, delta R equals 0, delta P equals 0. 124 00:07:32,540 --> 00:07:34,970 Now I'm using capital letters just 125 00:07:34,970 --> 00:07:39,350 to mean all of the coordinates. 126 00:07:39,350 --> 00:07:42,710 And this is what we call a vertical transition. 127 00:07:42,710 --> 00:07:48,790 And delta P equals 0 is stationary phase. 128 00:07:48,790 --> 00:07:51,610 Now I like stationary phase. 129 00:07:51,610 --> 00:07:55,390 You have integrals of oscillating functions, 130 00:07:55,390 --> 00:08:00,320 and you're integrating usually over all space. 131 00:08:00,320 --> 00:08:04,010 But the integral accumulates to its final value 132 00:08:04,010 --> 00:08:10,160 in a very small region of space, and that region of space 133 00:08:10,160 --> 00:08:15,050 corresponds to where the momenta on the upper and lower states, 134 00:08:15,050 --> 00:08:16,940 or whatever you're looking at, where 135 00:08:16,940 --> 00:08:19,510 the momentum are the same. 136 00:08:19,510 --> 00:08:26,280 And this enables you to use classical insights because 137 00:08:26,280 --> 00:08:30,120 instead of having quantum mechanics where you're thinking 138 00:08:30,120 --> 00:08:33,650 about wave functions and thinking like I've 139 00:08:33,650 --> 00:08:37,140 got an integral to do and I can't say anything simple 140 00:08:37,140 --> 00:08:41,610 about it, but if you know that the integral accumulates 141 00:08:41,610 --> 00:08:47,630 in a particular geometry, then you can even estimate it. 142 00:08:47,630 --> 00:08:51,590 You know what determines how big that integral is. 143 00:08:51,590 --> 00:08:53,420 And this is almost always neglected 144 00:08:53,420 --> 00:08:56,580 in talking about the Franck-Condon principle, 145 00:08:56,580 --> 00:09:00,110 but it's a very important part, especially for me, 146 00:09:00,110 --> 00:09:03,680 because I want to find out simple things, 147 00:09:03,680 --> 00:09:08,210 and the simple things are always in simple places in state space 148 00:09:08,210 --> 00:09:10,986 or in coordinate space. 149 00:09:10,986 --> 00:09:12,735 And then there's the Franck-Condon factor. 150 00:09:16,890 --> 00:09:19,700 The Franck-Condon factor is something you calculate. 151 00:09:19,700 --> 00:09:25,160 If you know the potential or you have a reasonable estimate 152 00:09:25,160 --> 00:09:27,620 of the shape of a potential, you can 153 00:09:27,620 --> 00:09:30,020 calculate all the vibrational wave functions 154 00:09:30,020 --> 00:09:31,930 in that potential. 155 00:09:31,930 --> 00:09:34,600 Not a big deal. 156 00:09:34,600 --> 00:09:36,770 I haven't taught you how to do it. 157 00:09:36,770 --> 00:09:39,910 I will talk about it in 573, but that's next year, 158 00:09:39,910 --> 00:09:43,660 and that's a different life for most of you. 159 00:09:43,660 --> 00:09:49,150 But you can calculate the vibrational wave functions. 160 00:09:49,150 --> 00:09:52,000 And the Franck-Condon factor is the square 161 00:09:52,000 --> 00:09:55,000 of the overlap between the vibrational wave 162 00:09:55,000 --> 00:09:59,710 function for the initial state and the final state. 163 00:09:59,710 --> 00:10:04,260 So principle, factor, big difference. 164 00:10:08,220 --> 00:10:10,470 We want ideas. 165 00:10:10,470 --> 00:10:12,990 Franck-Condon factors are numerical. 166 00:10:12,990 --> 00:10:16,210 We want to know what's behind the Franck-Condon factors, 167 00:10:16,210 --> 00:10:19,030 and the Franck-Condon principle and stationary phase 168 00:10:19,030 --> 00:10:20,850 is what's behind it. 169 00:10:20,850 --> 00:10:24,360 And so you're now charged with being 170 00:10:24,360 --> 00:10:26,130 able to understand everything that 171 00:10:26,130 --> 00:10:30,870 happens in electronic transitions guided by this very 172 00:10:30,870 --> 00:10:33,810 important principle, which is really relegated only 173 00:10:33,810 --> 00:10:38,786 to calculating Franck-Condon factors, which is just 174 00:10:38,786 --> 00:10:41,160 something you do as opposed to something you think about. 175 00:10:46,790 --> 00:10:52,190 So that was kind of a summary of what we did last time. 176 00:10:56,040 --> 00:11:04,980 So we can have an electronic band system. 177 00:11:04,980 --> 00:11:08,480 So that's a transition between two electronic states, 178 00:11:08,480 --> 00:11:12,370 and these electronic states have vibrational levels, 179 00:11:12,370 --> 00:11:15,930 and the vibrational levels have rotation levels. 180 00:11:15,930 --> 00:11:18,320 And so it depends on how deep you 181 00:11:18,320 --> 00:11:24,110 want to go into understanding electronic transitions 182 00:11:24,110 --> 00:11:27,470 but what are the questions we want to answer? 183 00:11:27,470 --> 00:11:32,470 When we record a spectrum, we record a spectrum 184 00:11:32,470 --> 00:11:36,660 not just to publish a paper or to fulfill an assignment 185 00:11:36,660 --> 00:11:40,620 but to ask questions, and so what do we want to know? 186 00:11:40,620 --> 00:11:46,140 And there's how questions and why questions. 187 00:11:46,140 --> 00:11:49,807 How is a particular excited state 188 00:11:49,807 --> 00:11:51,140 different from the ground state? 189 00:12:01,250 --> 00:12:02,790 This means excited state. 190 00:12:02,790 --> 00:12:03,800 This means ground state. 191 00:12:03,800 --> 00:12:05,719 Spectroscopists use that notation. 192 00:12:05,719 --> 00:12:07,760 People who don't know anything about spectroscopy 193 00:12:07,760 --> 00:12:11,330 use whatever notation they feel like, and that's really stupid. 194 00:12:11,330 --> 00:12:14,420 But anyway, that's a different sort of thing. 195 00:12:14,420 --> 00:12:16,670 And so how are states different? 196 00:12:16,670 --> 00:12:21,230 Well, they have different equilibrium geometries. 197 00:12:21,230 --> 00:12:24,920 They have different vibrational frequencies. 198 00:12:24,920 --> 00:12:26,720 They have different energies. 199 00:12:26,720 --> 00:12:30,450 It's a transition between states pretty far apart in energy. 200 00:12:30,450 --> 00:12:32,840 There's permanent dipole moment. 201 00:12:32,840 --> 00:12:34,820 There's transition dipole moments. 202 00:12:34,820 --> 00:12:36,350 There's radiative lifetimes. 203 00:12:36,350 --> 00:12:39,410 There's all sorts of things that are distinct from one 204 00:12:39,410 --> 00:12:42,510 electronic state to another. 205 00:12:42,510 --> 00:12:45,970 And so this is how they're different, but then why? 206 00:12:45,970 --> 00:12:49,760 This is much more interesting, but you do this in order 207 00:12:49,760 --> 00:12:53,670 to start asking why. 208 00:12:53,670 --> 00:13:00,260 And so you already have qualitative electronic 209 00:13:00,260 --> 00:13:07,450 structure stuff like LCAO, MO. 210 00:13:07,450 --> 00:13:10,570 Now you could calculate things really accurately, 211 00:13:10,570 --> 00:13:14,050 but you wouldn't be using your brain, 212 00:13:14,050 --> 00:13:18,430 and this is MIT for God's sake. 213 00:13:18,430 --> 00:13:23,560 You do want to use your brain to explain why one state is 214 00:13:23,560 --> 00:13:25,210 different from another, and there's 215 00:13:25,210 --> 00:13:27,070 all sorts of qualitative theories 216 00:13:27,070 --> 00:13:30,460 that are your guide or your framework for doing this. 217 00:13:30,460 --> 00:13:33,490 And LCAO-MO, Huckel theory, these 218 00:13:33,490 --> 00:13:37,060 are the kinds of things that you can use. 219 00:13:37,060 --> 00:13:45,605 And we also have ideas about orbitals, bonding. 220 00:13:48,250 --> 00:13:51,440 So we have orbitals that are bonding, nonbinding, 221 00:13:51,440 --> 00:13:54,370 antibonding, and we know this by drawing 222 00:13:54,370 --> 00:13:56,610 a molecular orbital diagram. 223 00:13:56,610 --> 00:13:59,700 And we know the properties of what 224 00:13:59,700 --> 00:14:06,480 happens when you have bonding and antibonding orbitals. 225 00:14:06,480 --> 00:14:09,217 We have hybridization. 226 00:14:15,190 --> 00:14:22,230 So a tremendous amount is gained by asking for a carbon atom, 227 00:14:22,230 --> 00:14:28,920 and for many other atoms, what is the spn hybridization? 228 00:14:28,920 --> 00:14:31,950 We make a special set of orbitals 229 00:14:31,950 --> 00:14:38,130 which focus on the structure around each atom. 230 00:14:38,130 --> 00:14:45,570 And again, you can be guided by what you know from the spectrum 231 00:14:45,570 --> 00:14:49,930 or what you know from simple rules to saying, OK, 232 00:14:49,930 --> 00:14:52,200 if we have this hybridization, there 233 00:14:52,200 --> 00:14:54,300 is a certain geometry around that atom. 234 00:14:54,300 --> 00:14:56,730 Or if we have that geometry or if it's 235 00:14:56,730 --> 00:14:58,610 constrained to have that geometry, 236 00:14:58,610 --> 00:15:00,490 it will have this hybridization. 237 00:15:00,490 --> 00:15:02,860 And we haven't talked about this very much, 238 00:15:02,860 --> 00:15:07,770 but it's a very important part of understanding chemistry. 239 00:15:07,770 --> 00:15:11,040 And then we have these things where we-- 240 00:15:20,570 --> 00:15:23,510 so we look at families of molecules 241 00:15:23,510 --> 00:15:26,820 where you have the same number of electrons. 242 00:15:26,820 --> 00:15:30,300 And that was on the exam, and it's really beautiful 243 00:15:30,300 --> 00:15:32,940 how you can say, OK, even though we 244 00:15:32,940 --> 00:15:34,810 have the same number of electrons, 245 00:15:34,810 --> 00:15:39,000 if we change the difference in ionization energy 246 00:15:39,000 --> 00:15:41,430 between the two atoms, terrible things happen 247 00:15:41,430 --> 00:15:43,250 or wonderful, beautiful things happen. 248 00:15:43,250 --> 00:15:45,450 It depends on what you like. 249 00:15:45,450 --> 00:15:50,520 And homologous is just the same number of valence electrons 250 00:15:50,520 --> 00:15:53,160 but from different rows of the periodic table, 251 00:15:53,160 --> 00:15:56,030 and you had that on the exam too. 252 00:15:56,030 --> 00:15:58,430 These are the tricks we use. 253 00:15:58,430 --> 00:16:02,925 And then there's dynamics. 254 00:16:06,510 --> 00:16:09,545 And some people might say we study structure so that we 255 00:16:09,545 --> 00:16:10,545 can understand dynamics. 256 00:16:13,540 --> 00:16:17,300 I'm not quite there yet, but dynamics is interesting 257 00:16:17,300 --> 00:16:21,220 because it's harder than structure. 258 00:16:21,220 --> 00:16:22,570 You have a static structure. 259 00:16:22,570 --> 00:16:24,830 The spectrum is telling you what that is. 260 00:16:24,830 --> 00:16:26,710 But it's also telling you, if you 261 00:16:26,710 --> 00:16:29,680 look at it the right way, what the molecule can 262 00:16:29,680 --> 00:16:32,870 do when it gets excited. 263 00:16:32,870 --> 00:16:40,280 And I frequently start my talks with two slides, one called 264 00:16:40,280 --> 00:16:43,700 molecules at play where the molecules are in the ground 265 00:16:43,700 --> 00:16:46,850 state, and they're not doing anything interesting, and then 266 00:16:46,850 --> 00:16:50,040 molecules at work where molecules are highly excited 267 00:16:50,040 --> 00:16:52,230 and doing what they're supposed to do. 268 00:16:52,230 --> 00:16:55,230 And our job is really not to understand play. 269 00:16:55,230 --> 00:16:57,210 Let them do what they want, but we'd 270 00:16:57,210 --> 00:16:59,100 like to understand when they're working 271 00:16:59,100 --> 00:17:00,630 and how do we work with them? 272 00:17:00,630 --> 00:17:04,560 So dynamics is really that kind of a question. 273 00:17:04,560 --> 00:17:08,700 There's all sorts of kinds of dynamics. 274 00:17:08,700 --> 00:17:09,869 There's dissociation. 275 00:17:12,680 --> 00:17:13,819 There's ionization. 276 00:17:17,980 --> 00:17:21,150 There's Born-Oppenheimer breakdown. 277 00:17:24,579 --> 00:17:28,119 And you probably notice these letters, and that's what I do. 278 00:17:28,119 --> 00:17:33,465 I'm known for being a specialist in Born-Oppenheimer breakdown. 279 00:17:33,465 --> 00:17:35,870 It appears in many different ways. 280 00:17:35,870 --> 00:17:39,400 And so there's predissociation. 281 00:17:39,400 --> 00:17:41,280 There's autoionization. 282 00:17:41,280 --> 00:17:42,940 There's avoided crossings. 283 00:17:53,380 --> 00:17:59,405 And there's adiabtic versus diabatic. 284 00:18:03,340 --> 00:18:06,940 So these two things are really different sides 285 00:18:06,940 --> 00:18:08,200 of the same coin. 286 00:18:08,200 --> 00:18:11,965 Suppose you have two potential curves that cross. 287 00:18:15,970 --> 00:18:18,520 Well, this is what we think about as chemists where 288 00:18:18,520 --> 00:18:21,490 a potential curve corresponds to following 289 00:18:21,490 --> 00:18:24,730 the energy without really significantly changing 290 00:18:24,730 --> 00:18:27,770 the electronic structure. 291 00:18:27,770 --> 00:18:30,130 And so these crossing curves are what we call diabatic. 292 00:18:34,800 --> 00:18:37,950 But if you're a quantum chemistry, what you would do 293 00:18:37,950 --> 00:18:42,040 is you would calculate the adiabatic curves, 294 00:18:42,040 --> 00:18:43,392 and they would look like that. 295 00:18:43,392 --> 00:18:44,100 They don't cross. 296 00:18:46,950 --> 00:18:50,400 And so we have two ways of looking 297 00:18:50,400 --> 00:18:54,190 at the interaction between two electronic states, 298 00:18:54,190 --> 00:18:57,060 the adiabatic one and the diabatic one, 299 00:18:57,060 --> 00:19:01,150 and we use whichever one is simpler 300 00:19:01,150 --> 00:19:03,930 for the particular case. 301 00:19:03,930 --> 00:19:07,330 And at some point later in this lecture 302 00:19:07,330 --> 00:19:11,184 I hope to talk about a thing called Landau-Zener. 303 00:19:16,360 --> 00:19:22,090 And it basically is suppose you're driving 304 00:19:22,090 --> 00:19:30,530 at night on a very curvy road. 305 00:19:30,530 --> 00:19:35,420 And you're mostly awake, but you're driving too fast. 306 00:19:35,420 --> 00:19:39,230 And so if you have a situation like this 307 00:19:39,230 --> 00:19:43,730 where there's a sharp curve, and maybe if you're lucky 308 00:19:43,730 --> 00:19:46,430 there is another sharp curve on another road somewhere 309 00:19:46,430 --> 00:19:47,320 over here. 310 00:19:47,320 --> 00:19:48,770 You're going too fast. 311 00:19:48,770 --> 00:19:50,811 You're going to go off the road, and maybe you'll 312 00:19:50,811 --> 00:19:56,060 end up on this other road or you'll end up hitting a tree. 313 00:19:56,060 --> 00:20:00,560 So if you're going fast, you're going to jump off the curve. 314 00:20:00,560 --> 00:20:04,120 That's diabatic. 315 00:20:04,120 --> 00:20:07,710 And that's the point of view we take as chemists. 316 00:20:07,710 --> 00:20:09,480 And if you're going really slowly, 317 00:20:09,480 --> 00:20:11,610 you'll stay on the road. 318 00:20:11,610 --> 00:20:13,412 You won't even remember this intersection 319 00:20:13,412 --> 00:20:14,620 because you didn't die at it. 320 00:20:18,650 --> 00:20:20,730 And that's adiabatic. 321 00:20:20,730 --> 00:20:25,920 And depending on the gap and the curvature 322 00:20:25,920 --> 00:20:28,470 for a particular situation, the molecule 323 00:20:28,470 --> 00:20:32,090 knows how to either do this or do that. 324 00:20:32,090 --> 00:20:33,980 And it's not fatal for the molecule, 325 00:20:33,980 --> 00:20:38,270 but if the molecule is going through a curve-crossing region 326 00:20:38,270 --> 00:20:42,610 fast, it's going to jump the gap. 327 00:20:42,610 --> 00:20:46,510 And that's one of the things that Zewail looked at. 328 00:20:46,510 --> 00:20:52,650 If you can start a system at energy 329 00:20:52,650 --> 00:20:57,930 high above the energy where the curves cross, 330 00:20:57,930 --> 00:20:59,670 you're going through really fast. 331 00:20:59,670 --> 00:21:02,730 If you excite it really close to the energy of the curve 332 00:21:02,730 --> 00:21:05,670 crossing, you're going through slowly. 333 00:21:05,670 --> 00:21:08,400 And so by changing the conditions, 334 00:21:08,400 --> 00:21:10,560 you can understand what's going to happen. 335 00:21:10,560 --> 00:21:12,360 This is really powerful for insight. 336 00:21:20,590 --> 00:21:23,320 What I'm trying to convey is that there 337 00:21:23,320 --> 00:21:26,950 are very simple pictures to describe really 338 00:21:26,950 --> 00:21:29,330 complicated-looking things. 339 00:21:29,330 --> 00:21:33,610 And sometimes the data on these complicated things 340 00:21:33,610 --> 00:21:38,770 are very hard to either obtain or to interpret 341 00:21:38,770 --> 00:21:40,890 because it looks-- 342 00:21:40,890 --> 00:21:43,620 well, often it looks-- what would people say? 343 00:21:43,620 --> 00:21:46,560 It looks statistical. 344 00:21:46,560 --> 00:21:55,120 Now statistical is really a cop out. 345 00:21:55,120 --> 00:21:57,670 It says, I don't understand what's going on here, 346 00:21:57,670 --> 00:22:01,192 and so I'll approach it as if there isn't any law. 347 00:22:01,192 --> 00:22:03,810 And we just count the density of states, 348 00:22:03,810 --> 00:22:05,670 and we'd use simple formulas. 349 00:22:05,670 --> 00:22:10,830 And the shameful thing is that that usually works, 350 00:22:10,830 --> 00:22:12,450 but it only works so far. 351 00:22:12,450 --> 00:22:13,920 It doesn't lead to insight. 352 00:22:13,920 --> 00:22:16,710 It just leads to a representation, 353 00:22:16,710 --> 00:22:21,810 and our job is to understand, not just to represent. 354 00:22:26,350 --> 00:22:33,460 So back to this question of electronic transitions 355 00:22:33,460 --> 00:22:36,260 and the Franck-Condon principle. 356 00:22:36,260 --> 00:22:39,550 So if we have a transition between two potential curves 357 00:22:39,550 --> 00:22:43,120 that have the same geometry, we get a delta v 358 00:22:43,120 --> 00:22:45,080 equals 0 propensity rule. 359 00:22:49,080 --> 00:22:51,800 It has good and bad sides. 360 00:22:51,800 --> 00:22:56,420 One is the spectrum gets to be really simple because you 361 00:22:56,420 --> 00:23:03,020 only see transitions between the same vibrational quantum 362 00:23:03,020 --> 00:23:04,490 upstairs and downstairs. 363 00:23:04,490 --> 00:23:07,820 And this is true for polyatomic and diatomics as well. 364 00:23:07,820 --> 00:23:10,010 You get a simple spectrum and you say, oh crap, I 365 00:23:10,010 --> 00:23:12,000 can go home early. 366 00:23:12,000 --> 00:23:16,870 But you don't know anything about other vibrational levels, 367 00:23:16,870 --> 00:23:23,750 and if you're starting in the zero vibrational 368 00:23:23,750 --> 00:23:25,740 level of the ground state, well, you only 369 00:23:25,740 --> 00:23:28,040 know about the zero vibrational level of the excited 370 00:23:28,040 --> 00:23:30,300 state if the potential cures are the same, 371 00:23:30,300 --> 00:23:32,510 and there's all sorts of stuff you don't know. 372 00:23:32,510 --> 00:23:35,510 And if you're doing emission, well, maybe 373 00:23:35,510 --> 00:23:39,910 in an emission spectrum you excite more vibrational levels. 374 00:23:39,910 --> 00:23:43,600 But what's going to happen is if they're all have the same-- 375 00:23:43,600 --> 00:23:47,350 if the potential curves are the same, 376 00:23:47,350 --> 00:23:49,240 well, then all the vibrational transitions 377 00:23:49,240 --> 00:23:52,120 are going to be on top of each other in emission, 378 00:23:52,120 --> 00:23:55,380 and you might as well not have bothered. 379 00:23:55,380 --> 00:23:58,020 It's just a horrible situation. 380 00:23:58,020 --> 00:24:01,600 So delta v equals 0 depends on what your point of view is. 381 00:24:01,600 --> 00:24:03,570 If you want to understand things, this is bad. 382 00:24:06,090 --> 00:24:09,940 And then you can have transitions between states 383 00:24:09,940 --> 00:24:14,730 which have different shapes or displaced, 384 00:24:14,730 --> 00:24:16,600 and the Franck-Condon calculation 385 00:24:16,600 --> 00:24:19,390 tells you how this works. 386 00:24:19,390 --> 00:24:24,460 But here you have delta v equals many. 387 00:24:27,830 --> 00:24:30,320 But now for a polyatomic molecule 388 00:24:30,320 --> 00:24:40,490 where you have n atoms, you have 3n minus 6 normal modes. 389 00:24:40,490 --> 00:24:45,920 And some of them are going to be like this, and some of them 390 00:24:45,920 --> 00:24:48,590 are going to be like this. 391 00:24:48,590 --> 00:24:52,120 And that's good and bad because what it's saying is, 392 00:24:52,120 --> 00:24:55,220 yeah, you could have had a really complicated spectrum 393 00:24:55,220 --> 00:24:57,320 because there's so many vibrational-- 394 00:24:57,320 --> 00:25:01,580 I mean, for example, benzene has 30 vibrational levels, 30 395 00:25:01,580 --> 00:25:04,130 vibrational modes-- 396 00:25:04,130 --> 00:25:09,920 not 1 but 30, and some of them have relatively low frequency. 397 00:25:09,920 --> 00:25:12,620 And benzene for most of you is a simple molecule. 398 00:25:12,620 --> 00:25:17,700 For me, it's really just beyond complex. 399 00:25:17,700 --> 00:25:20,990 And what happens when you have a lot of vibrational levels 400 00:25:20,990 --> 00:25:24,110 is the vibrational density states gets very high, very 401 00:25:24,110 --> 00:25:27,920 fast, so high that it's hopeless to be able to resolve 402 00:25:27,920 --> 00:25:31,370 the individual eigenstates. 403 00:25:31,370 --> 00:25:35,060 When that happens, frequency domain spectroscopy 404 00:25:35,060 --> 00:25:39,680 stops being so useful because a lot of the key details 405 00:25:39,680 --> 00:25:42,040 are hidden. 406 00:25:42,040 --> 00:25:46,350 So if it's not frequency domain, it wants to be time domain, 407 00:25:46,350 --> 00:25:49,620 and you can ask really good questions 408 00:25:49,620 --> 00:25:51,630 using time-domain techniques, which 409 00:25:51,630 --> 00:25:55,750 is what I'm going to talk about when I spend some time with Mr. 410 00:25:55,750 --> 00:25:56,250 Zewail. 411 00:25:58,780 --> 00:26:04,460 So you're going to have certain normal modes which 412 00:26:04,460 --> 00:26:10,970 are what we call Franck-Condon dark because they don't 413 00:26:10,970 --> 00:26:12,380 contribute to the spectrum. 414 00:26:12,380 --> 00:26:16,370 You only see delta v of 0 for modes. 415 00:26:16,370 --> 00:26:22,020 And the ones that lead to a change in geometry 416 00:26:22,020 --> 00:26:25,440 or a change in bond structure, those are the ones you see. 417 00:26:25,440 --> 00:26:27,930 Those are the Franck-Condon bright ones, 418 00:26:27,930 --> 00:26:32,100 and they're also much more interesting because why 419 00:26:32,100 --> 00:26:35,510 did the geometry change? 420 00:26:35,510 --> 00:26:37,520 What part of the molecule was responsible 421 00:26:37,520 --> 00:26:39,380 for the geometry change? 422 00:26:39,380 --> 00:26:40,990 This is what chemists want to ask. 423 00:26:45,270 --> 00:26:47,130 So that's the framework. 424 00:26:47,130 --> 00:26:53,920 Now, I've spent the last 30 years of my life looking 425 00:26:53,920 --> 00:26:55,840 at the acetylene molecule. 426 00:26:58,960 --> 00:27:04,490 Acetylene, for me, it's as big as I want to get, 427 00:27:04,490 --> 00:27:10,240 but for most of you that's really, really small. 428 00:27:10,240 --> 00:27:13,620 And acetylene has ground state which 429 00:27:13,620 --> 00:27:18,930 we can denote by a zero here, s0, lowest singlet. 430 00:27:18,930 --> 00:27:21,480 If we had a different number of electrons 431 00:27:21,480 --> 00:27:23,820 we might say-- if we had an odd number of electrons, 432 00:27:23,820 --> 00:27:27,510 the lowest state would be D0 or T0 433 00:27:27,510 --> 00:27:33,960 if it had a triplet ground state like oxygen. 434 00:27:33,960 --> 00:27:35,005 The notation is simple. 435 00:27:38,370 --> 00:27:40,450 But we also use-- 436 00:27:40,450 --> 00:27:46,720 spectroscopists use notation where we use a Roman capital 437 00:27:46,720 --> 00:27:50,000 letter with a tilde over it for polyatomic molecules 438 00:27:50,000 --> 00:27:53,480 and not for diatomics, and the electronic state, 439 00:27:53,480 --> 00:27:55,330 the ground state is this. 440 00:27:55,330 --> 00:28:05,140 And have to be careful because the notation 441 00:28:05,140 --> 00:28:11,180 that organic chemists would use for acetylene is just this. 442 00:28:11,180 --> 00:28:15,700 And my point is I want to talk about where the hydrogens are. 443 00:28:15,700 --> 00:28:19,240 And so this is kind of a cheat because it 444 00:28:19,240 --> 00:28:24,790 sounds like I put a hydrogen on a butene 445 00:28:24,790 --> 00:28:27,480 because you have carbon here, these bonds. 446 00:28:27,480 --> 00:28:29,380 OK, you know the [INAUDIBLE]. 447 00:28:29,380 --> 00:28:35,100 And then there's an excited state which we could call S1. 448 00:28:35,100 --> 00:28:38,600 And the excited state looks like this. 449 00:28:43,370 --> 00:28:44,910 It's trans bent. 450 00:28:44,910 --> 00:28:45,960 This has a triple bond. 451 00:28:45,960 --> 00:28:47,884 This has a double bond. 452 00:28:47,884 --> 00:28:49,528 AUDIENCE: [INAUDIBLE] 453 00:28:49,528 --> 00:28:50,319 ROBERT FIELD: What? 454 00:28:50,319 --> 00:28:51,780 AUDIENCE: There's also [INAUDIBLE].. 455 00:28:51,780 --> 00:28:53,030 ROBERT FIELD: Yes, there's a-- 456 00:28:56,340 --> 00:28:57,690 you know about this paper here. 457 00:29:01,560 --> 00:29:05,820 But the lowest equilibrium geometry for the excited state 458 00:29:05,820 --> 00:29:08,040 is trans bent. 459 00:29:08,040 --> 00:29:11,400 You can have this structure too, and we 460 00:29:11,400 --> 00:29:15,000 have looked at the isomerization between these two, 461 00:29:15,000 --> 00:29:18,220 and how did we do that? 462 00:29:18,220 --> 00:29:21,420 How did we characterize the transition state 463 00:29:21,420 --> 00:29:23,070 for the isomerization? 464 00:29:23,070 --> 00:29:30,690 This is 20, 30 person years of work getting to the transition 465 00:29:30,690 --> 00:29:32,670 state, and it led to a paper in Science, 466 00:29:32,670 --> 00:29:37,590 my first in 40 years of trying. 467 00:29:37,590 --> 00:29:41,750 And so this is a molecule I really 468 00:29:41,750 --> 00:29:46,100 like because there are four modes which 469 00:29:46,100 --> 00:29:50,600 are Franck-Condon dark and two that are Franck-Condon bright. 470 00:29:50,600 --> 00:29:55,565 And we can do all sorts of really neat things. 471 00:29:58,150 --> 00:30:09,090 So in the ground state at high vibrational excitation, 472 00:30:09,090 --> 00:30:10,572 what do we expect? 473 00:30:10,572 --> 00:30:12,030 Well, one thing is nothing special. 474 00:30:16,431 --> 00:30:21,040 Well, the molecule could just go on doing nothing interesting, 475 00:30:21,040 --> 00:30:25,030 having four modes which are Franck-Condon dark and two 476 00:30:25,030 --> 00:30:27,150 modes that are Franck-Condon bright. 477 00:30:27,150 --> 00:30:31,870 It will remain boring. 478 00:30:31,870 --> 00:30:43,170 And another would be just increasing complexity 479 00:30:43,170 --> 00:30:47,760 because there can be anharmonic interactions 480 00:30:47,760 --> 00:30:51,450 between different normal modes. 481 00:30:51,450 --> 00:30:56,970 And so when that starts to happen people start to say, 482 00:30:56,970 --> 00:30:59,060 let me out of here. 483 00:30:59,060 --> 00:31:01,730 It gets complicated, and everything gets destroyed, 484 00:31:01,730 --> 00:31:03,810 and the spectrum just becomes uninterpretable, 485 00:31:03,810 --> 00:31:06,690 which is wrong. 486 00:31:06,690 --> 00:31:12,210 And then there is chaos which is another way-- 487 00:31:12,210 --> 00:31:14,130 or quantum chaos-- which is another way 488 00:31:14,130 --> 00:31:16,480 of waving your hands and saying it's statistical. 489 00:31:16,480 --> 00:31:19,650 And we know my opinion about that 490 00:31:19,650 --> 00:31:23,340 because bonds are really sacred in chemistry 491 00:31:23,340 --> 00:31:28,500 and if there are bonds, there isn't bag of atoms behavior. 492 00:31:28,500 --> 00:31:32,670 And then there's other possibility, isomerization. 493 00:31:38,010 --> 00:31:49,930 So this guy at high exaltation can go to that vinylidene. 494 00:31:49,930 --> 00:31:54,990 And I spent a hundred person years chasing after this. 495 00:31:54,990 --> 00:32:01,670 So there is a very shallow vinylidene well, 496 00:32:01,670 --> 00:32:03,840 and how is this kind of isomerization 497 00:32:03,840 --> 00:32:05,060 encoded in the spectrum? 498 00:32:08,350 --> 00:32:12,830 So in order to have a chance of understanding about vinylidene 499 00:32:12,830 --> 00:32:14,420 or things that happen in the ground 500 00:32:14,420 --> 00:32:18,860 state at very high excitation, I invented a fairly important 501 00:32:18,860 --> 00:32:23,550 method for looking at high vibrational levels. 502 00:32:23,550 --> 00:32:34,765 It's called stimulated emission pumping, 503 00:32:34,765 --> 00:32:36,890 and it looks like this. 504 00:32:36,890 --> 00:32:40,770 So we have two-- 505 00:32:40,770 --> 00:32:43,890 now this initially was demonstrated 506 00:32:43,890 --> 00:32:47,040 on a diatomic molecule, but its true importance 507 00:32:47,040 --> 00:32:49,230 is for something like acetylene. 508 00:32:49,230 --> 00:33:03,300 So what happens is you can excite to this distorted 509 00:33:03,300 --> 00:33:09,720 molecule from the ground state, and some vibrational levels 510 00:33:09,720 --> 00:33:12,510 are accessible because you have a little bit of room 511 00:33:12,510 --> 00:33:14,580 between two turning points. 512 00:33:14,580 --> 00:33:17,160 So you can excite a few vibrational levels 513 00:33:17,160 --> 00:33:19,800 by vertical transitions. 514 00:33:19,800 --> 00:33:22,560 But the important thing is that each vibrational level 515 00:33:22,560 --> 00:33:26,590 has an inner turning point, which is how you access it, 516 00:33:26,590 --> 00:33:30,480 and an outer turning point, which enables you to do-- 517 00:33:30,480 --> 00:33:35,540 so this is called the pump, and this is called the dump. 518 00:33:35,540 --> 00:33:37,700 Now I'm not sure whether I came up with pump 519 00:33:37,700 --> 00:33:41,510 and dump before it was talked about on Wall Street, 520 00:33:41,510 --> 00:33:47,390 but it was a very apt name for stimulated emission pumping. 521 00:33:47,390 --> 00:33:50,780 And so what we can do then is to access 522 00:33:50,780 --> 00:33:54,440 very high vibrational levels in the electronic ground state 523 00:33:54,440 --> 00:33:56,750 by pump and dump. 524 00:33:56,750 --> 00:33:59,060 And the way we detect it is we get fluorescence 525 00:33:59,060 --> 00:34:00,170 from this level. 526 00:34:00,170 --> 00:34:02,150 And when we hit the dump transition, 527 00:34:02,150 --> 00:34:05,850 the fluorescences decrease in intensity. 528 00:34:05,850 --> 00:34:08,480 And we can do a very significant map 529 00:34:08,480 --> 00:34:12,170 of what's going on at high excitation in the ground state. 530 00:34:12,170 --> 00:34:17,824 And when I invented SEP, I believed in quantum chaos. 531 00:34:21,639 --> 00:34:25,940 So I expected as we went up higher and higher 532 00:34:25,940 --> 00:34:30,310 we would see breaking of all the usual patterns. 533 00:34:30,310 --> 00:34:31,960 And I even wrote a paper saying we 534 00:34:31,960 --> 00:34:36,010 had seen quantum chaos when we excited to very 535 00:34:36,010 --> 00:34:37,480 high vibrational levels. 536 00:34:37,480 --> 00:34:40,719 And the reasoning for that is complicated, 537 00:34:40,719 --> 00:34:45,969 but the reasoning was correct except it 538 00:34:45,969 --> 00:34:47,170 didn't apply to chaos. 539 00:34:47,170 --> 00:34:50,650 It just applied to the spectrum getting complicated, really 540 00:34:50,650 --> 00:34:53,170 complicated. 541 00:34:53,170 --> 00:34:56,520 So what I really wanted to be able to do 542 00:34:56,520 --> 00:35:02,340 was to be able to somehow sample this transition state. 543 00:35:05,550 --> 00:35:09,420 And that experiment in its initial form 544 00:35:09,420 --> 00:35:16,710 was doomed to fail because this transition state involves 545 00:35:16,710 --> 00:35:17,980 a local bend. 546 00:35:17,980 --> 00:35:23,430 In other words, acetylene has normal modes, suspend, 547 00:35:23,430 --> 00:35:27,280 trans bend, CH symmetric stretch, 548 00:35:27,280 --> 00:35:30,630 CH antisymmetric stretch, and CC stretch. 549 00:35:30,630 --> 00:35:36,700 And this coordinate is mostly just that, 550 00:35:36,700 --> 00:35:39,600 a large-amplitude local band. 551 00:35:39,600 --> 00:35:42,300 And so when I started this, I didn't 552 00:35:42,300 --> 00:35:44,190 know that local bands would magically 553 00:35:44,190 --> 00:35:47,460 emerge from the spectrum, but they do and we saw them, 554 00:35:47,460 --> 00:35:50,040 and that led to a lot of good stuff. 555 00:35:50,040 --> 00:35:52,560 I should mention that I got tenure at MIT because 556 00:35:52,560 --> 00:35:56,090 of stimulated emission pumping. 557 00:35:56,090 --> 00:35:57,980 That was a long time ago. 558 00:35:57,980 --> 00:36:04,640 So we had not seen the isomerization in the ground 559 00:36:04,640 --> 00:36:07,880 state because we couldn't get high enough 560 00:36:07,880 --> 00:36:11,390 because Franck-Condon factors prevented us 561 00:36:11,390 --> 00:36:13,550 from getting high enough. 562 00:36:13,550 --> 00:36:15,380 And the spectrum also gets complicated, 563 00:36:15,380 --> 00:36:17,600 and there's all sorts of reasons why it didn't work. 564 00:36:17,600 --> 00:36:22,010 But as far as the cis-trans isomerization in the excited 565 00:36:22,010 --> 00:36:25,190 state, we killed that, and we killed 566 00:36:25,190 --> 00:36:30,920 that because we saw new patterns emerge, 567 00:36:30,920 --> 00:36:34,190 and that was more robust than normal modes. 568 00:36:34,190 --> 00:36:38,040 And then we saw those new patterns break, 569 00:36:38,040 --> 00:36:41,594 and the breaking is due to isomerization. 570 00:36:41,594 --> 00:36:43,260 And we worked out the theory, and that's 571 00:36:43,260 --> 00:36:44,961 what the Science paper was all about. 572 00:36:48,070 --> 00:37:04,650 So now, gas phase versus condensed phase. 573 00:37:10,230 --> 00:37:13,470 People who work in the gas phase don't 574 00:37:13,470 --> 00:37:15,990 talk to people who work in the condensed phase and vice 575 00:37:15,990 --> 00:37:23,960 versa because the spectra are profoundly different. 576 00:37:23,960 --> 00:37:27,940 So we have a ground state and we have some excited state. 577 00:37:27,940 --> 00:37:29,800 And whether it's a diatomic molecule 578 00:37:29,800 --> 00:37:33,230 or a polyatomic molecule, it doesn't matter that much. 579 00:37:33,230 --> 00:37:36,610 So what we have in the absorption spectrum 580 00:37:36,610 --> 00:37:41,590 is vertical transitions to a few vibrational levels, 581 00:37:41,590 --> 00:37:45,750 depending on the difference in geometry. 582 00:37:45,750 --> 00:37:47,290 And in the condensed phase, instead 583 00:37:47,290 --> 00:37:50,710 of staying in the vibrational level we populated, 584 00:37:50,710 --> 00:37:52,930 there is rapid transfer of energy 585 00:37:52,930 --> 00:37:56,660 from the molecule into its surroundings, 586 00:37:56,660 --> 00:38:01,250 and you end up in v equals 0 of the excited state. 587 00:38:01,250 --> 00:38:05,620 And then the spectrum is to a few vibrational levels 588 00:38:05,620 --> 00:38:07,270 of the ground state. 589 00:38:07,270 --> 00:38:11,020 And so you get something that looks like this. 590 00:38:11,020 --> 00:38:13,470 This is the sort of classic diagram 591 00:38:13,470 --> 00:38:17,160 for absorption versus emission spectra 592 00:38:17,160 --> 00:38:18,880 of a polyatomic molecule. 593 00:38:18,880 --> 00:38:22,270 So this is emission. 594 00:38:22,270 --> 00:38:24,570 This is absorption. 595 00:38:24,570 --> 00:38:28,200 And frequency is on the right. 596 00:38:31,860 --> 00:38:38,160 So what happens is in the absorption spectrum you observe 597 00:38:38,160 --> 00:38:40,110 transitions to higher vibrational 598 00:38:40,110 --> 00:38:43,140 levels-- to several vibrational levels, 599 00:38:43,140 --> 00:38:45,600 v prime equals 0 and higher. 600 00:38:45,600 --> 00:38:50,010 And so those are to the blue of the band origin. 601 00:38:50,010 --> 00:38:53,280 And in emission, you get emission only from v 602 00:38:53,280 --> 00:38:56,460 equals 0 in the excited state, and that's 603 00:38:56,460 --> 00:38:58,640 to the red of the origin. 604 00:38:58,640 --> 00:39:03,810 And so you get this classic double-hump picture. 605 00:39:03,810 --> 00:39:06,300 And there's all sorts of vibrational levels 606 00:39:06,300 --> 00:39:08,880 that are not resolved, and this is basically 607 00:39:08,880 --> 00:39:11,550 the kind of crappy spectrum you get 608 00:39:11,550 --> 00:39:14,940 when you look at a big molecule in the condensed phase. 609 00:39:14,940 --> 00:39:18,900 And so it's telling you frequency domain 610 00:39:18,900 --> 00:39:23,114 for this sort of thing is the wrong approach 611 00:39:23,114 --> 00:39:24,530 because there's nothing much here. 612 00:39:30,080 --> 00:39:37,570 So this thing, the expectation value, the Hamiltonian 613 00:39:37,570 --> 00:39:40,930 for the molecule as opposed to the overall system 614 00:39:40,930 --> 00:39:43,240 is time dependent. 615 00:39:43,240 --> 00:39:47,530 We're used to the Hamiltonian being time independent. 616 00:39:47,530 --> 00:39:49,840 There can be dynamics because you 617 00:39:49,840 --> 00:39:52,345 excite a coherent superposition of states. 618 00:39:56,080 --> 00:40:01,030 So for condensed-phase systems, the Hamiltonian or energy 619 00:40:01,030 --> 00:40:04,570 is not conserved in the molecule. 620 00:40:04,570 --> 00:40:06,010 But of course thermodynamics says 621 00:40:06,010 --> 00:40:08,240 if you have an isolated system it's conserved. 622 00:40:08,240 --> 00:40:10,180 That's irrelevant because we always 623 00:40:10,180 --> 00:40:15,625 want to look at something more interesting than a bulk sample. 624 00:40:18,190 --> 00:40:25,430 Now I want to talk about dynamics 625 00:40:25,430 --> 00:40:30,180 that is more subtle than the naive stuff-- 626 00:40:30,180 --> 00:40:35,360 so subtle dynamics. 627 00:40:42,560 --> 00:40:47,469 Well, let's have no collisions. 628 00:40:47,469 --> 00:40:49,010 Well, we can do that in the gas phase 629 00:40:49,010 --> 00:40:50,218 if the pressure's low enough. 630 00:40:53,060 --> 00:40:58,320 No breaking of molecules. 631 00:41:01,170 --> 00:41:03,660 So if there is no predissociation or 632 00:41:03,660 --> 00:41:05,170 autoionization-- 633 00:41:05,170 --> 00:41:07,880 so we can restrict ourselves to a low enough energy 634 00:41:07,880 --> 00:41:09,000 that things don't break. 635 00:41:23,980 --> 00:41:27,120 Now this is subtle. 636 00:41:27,120 --> 00:41:32,010 Molecules will fluoresce, and populations in excited states 637 00:41:32,010 --> 00:41:33,480 will decay. 638 00:41:33,480 --> 00:41:40,890 And as a rule, the fluorescence lifetime, 639 00:41:40,890 --> 00:41:50,430 if it's truly only fluorescence and not other dynamics, 640 00:41:50,430 --> 00:41:52,740 the lifetime is longer than 10 nanoseconds. 641 00:41:55,580 --> 00:42:00,790 So if we're looking at times shorter than 10 nanoseconds 642 00:42:00,790 --> 00:42:04,290 we can say there's no fluorescence. 643 00:42:04,290 --> 00:42:06,560 We're going to ignore that. 644 00:42:06,560 --> 00:42:11,110 That's OK because there still can be dynamics. 645 00:42:11,110 --> 00:42:22,496 So simplest case, two-level quantum beats, 646 00:42:22,496 --> 00:42:23,870 and you know about quantum beats. 647 00:42:23,870 --> 00:42:27,440 You've already looked at them in various problems. 648 00:42:27,440 --> 00:42:30,560 And so you have a system where you have a ground state 649 00:42:30,560 --> 00:42:33,610 and you have two excited states, and one of them is bright 650 00:42:33,610 --> 00:42:35,110 and one of them is dark with respect 651 00:42:35,110 --> 00:42:37,640 to transitions from this state. 652 00:42:37,640 --> 00:42:39,550 But there is an interaction between them, 653 00:42:39,550 --> 00:42:43,220 and so they're mixed character and with a short pulse. 654 00:42:43,220 --> 00:42:45,620 You prepare a coherent superposition 655 00:42:45,620 --> 00:42:46,700 of two eigenstates. 656 00:42:51,290 --> 00:42:53,270 The intensity of the fluorescence 657 00:42:53,270 --> 00:42:56,630 oscillates, and it isolates at the frequency difference 658 00:42:56,630 --> 00:42:58,830 of these two levels. 659 00:42:58,830 --> 00:43:02,850 And the modulation depth of the fluorescence 660 00:43:02,850 --> 00:43:06,660 tells you something about what is the coupling matrix 661 00:43:06,660 --> 00:43:09,420 element between these two states relative to the energy 662 00:43:09,420 --> 00:43:11,430 difference between them? 663 00:43:11,430 --> 00:43:13,470 So there's a lot of information in there, 664 00:43:13,470 --> 00:43:17,150 and so this is something that can happen faster 665 00:43:17,150 --> 00:43:19,640 than the spontaneous fluorescence. 666 00:43:19,640 --> 00:43:22,100 One is observing it in the spontaneous fluorescence, 667 00:43:22,100 --> 00:43:28,850 but the whole point is you're looking at some dynamics that 668 00:43:28,850 --> 00:43:32,744 is encoded in eigenstates. 669 00:43:32,744 --> 00:43:33,910 And that's one of my mottos. 670 00:43:37,650 --> 00:43:40,950 We know how to write all the theory for this. 671 00:43:46,780 --> 00:43:52,870 We have something that looks broad, 672 00:43:52,870 --> 00:43:58,350 but in reality it's a whole bunch of eigenstates. 673 00:44:01,390 --> 00:44:04,960 And the pattern of these eigenstates 674 00:44:04,960 --> 00:44:08,470 is telling you what the dynamics is. 675 00:44:08,470 --> 00:44:10,930 Now normally we think of dynamics 676 00:44:10,930 --> 00:44:13,900 as the width of something. 677 00:44:13,900 --> 00:44:17,470 And this collection of eigenstates behaving 678 00:44:17,470 --> 00:44:21,920 in some coherent way has a width, 679 00:44:21,920 --> 00:44:23,700 but that's only the beginning. 680 00:44:23,700 --> 00:44:31,100 What was the thing that gave intensity to these eigenstates? 681 00:44:31,100 --> 00:44:38,220 What was the zero-order state, and what 682 00:44:38,220 --> 00:44:43,320 was the coupling matrix element between the bright state 683 00:44:43,320 --> 00:44:47,330 and the dark state, and what are the rules for these? 684 00:44:47,330 --> 00:44:50,300 And so if you can resolve these eigenstates, 685 00:44:50,300 --> 00:44:55,490 you learn about much more detailed picture of dynamics 686 00:44:55,490 --> 00:44:58,540 than just saying, well, dynamics is a width. 687 00:44:58,540 --> 00:45:02,020 If you're below the energy where molecules can break, 688 00:45:02,020 --> 00:45:02,770 there is no width. 689 00:45:06,240 --> 00:45:08,700 But if you do a crappy experiment, 690 00:45:08,700 --> 00:45:12,690 you don't resolve stuff and it looks broad. 691 00:45:12,690 --> 00:45:15,420 Now, sometimes the molecule sets the standard 692 00:45:15,420 --> 00:45:19,980 for what's a real experiment by having its density of states 693 00:45:19,980 --> 00:45:22,830 so large you couldn't resolve it even if you had the best 694 00:45:22,830 --> 00:45:26,340 experiment in the world. 695 00:45:26,340 --> 00:45:30,530 But there's still the idea that inside this broad thing 696 00:45:30,530 --> 00:45:33,650 there is some interpretable dynamics. 697 00:45:33,650 --> 00:45:34,440 That's my goal. 698 00:45:42,330 --> 00:45:44,710 Well, one kind of interpretable dynamics 699 00:45:44,710 --> 00:45:49,240 is, OK, so you have some excited state and some ground state, 700 00:45:49,240 --> 00:45:54,990 and there's a range of vibrational levels 701 00:45:54,990 --> 00:45:57,180 that you can excite. 702 00:45:57,180 --> 00:45:59,650 And if you have a short pulse, you 703 00:45:59,650 --> 00:46:01,780 make a coherent superposition of all 704 00:46:01,780 --> 00:46:04,000 of those vibrational levels. 705 00:46:04,000 --> 00:46:08,710 And then what you have is some wave packet which has got 706 00:46:08,710 --> 00:46:12,640 an energy, sort of the average of these. 707 00:46:12,640 --> 00:46:18,100 And the wave packet starts out at a turning point 708 00:46:18,100 --> 00:46:21,850 because you started out with essentially zero momentum. 709 00:46:21,850 --> 00:46:24,290 And the wave packet moves, and it goes back and forth 710 00:46:24,290 --> 00:46:26,220 and back and forth. 711 00:46:26,220 --> 00:46:29,280 And it's telling you what the vibrational frequency 712 00:46:29,280 --> 00:46:32,470 of that mode is. 713 00:46:32,470 --> 00:46:40,240 And so you can then observe the fluorescence from this evolving 714 00:46:40,240 --> 00:46:43,810 wave packet, or you can monitor this evolving wave packet 715 00:46:43,810 --> 00:46:46,450 either by looking at fluorescence back 716 00:46:46,450 --> 00:46:48,630 to where you started. 717 00:46:48,630 --> 00:46:50,130 And so when it's over here, it can't 718 00:46:50,130 --> 00:46:51,930 fluoresce to where you started. 719 00:46:51,930 --> 00:46:54,657 When it's over here where it was born, it can. 720 00:46:54,657 --> 00:46:56,490 And so the fluorescence is going to be doing 721 00:46:56,490 --> 00:46:58,440 a kind of quantum beating. 722 00:46:58,440 --> 00:47:01,650 You could also use some kind of pump-probe experiment 723 00:47:01,650 --> 00:47:03,810 where you say, I'm going to look at the wave packet 724 00:47:03,810 --> 00:47:06,300 when it's here because I have a transition 725 00:47:06,300 --> 00:47:08,220 to another electronic state. 726 00:47:08,220 --> 00:47:11,970 And so the vertical excitation is at that energy, 727 00:47:11,970 --> 00:47:15,070 and so I wait for the wave packet to get to a point. 728 00:47:15,070 --> 00:47:24,005 And so you have a periodic motion. 729 00:47:26,660 --> 00:47:34,950 And you have dephasing because this wave packet is built out 730 00:47:34,950 --> 00:47:38,580 of vibrational levels which are not harmonic so 731 00:47:38,580 --> 00:47:41,490 that there is some dispersion of the vibrational frequencies 732 00:47:41,490 --> 00:47:43,220 around the average. 733 00:47:43,220 --> 00:47:48,300 As a result, that causes this thing to dephase. 734 00:47:48,300 --> 00:47:55,320 And its dephasing time could look like a width, 735 00:47:55,320 --> 00:47:58,350 but it's actually a particular mechanism. 736 00:47:58,350 --> 00:48:00,570 And then there are other things that can happen, 737 00:48:00,570 --> 00:48:02,070 and I love this. 738 00:48:02,070 --> 00:48:05,340 So we've got a few minutes. 739 00:48:05,340 --> 00:48:08,394 So suppose we have two electronic states that 740 00:48:08,394 --> 00:48:10,560 are crossing, and you're starting out in this level. 741 00:48:10,560 --> 00:48:11,518 You made a wave packet. 742 00:48:13,950 --> 00:48:18,720 So this is going back and forth, and every half 743 00:48:18,720 --> 00:48:21,619 oscillation it goes through this critical region. 744 00:48:21,619 --> 00:48:22,410 What's that region? 745 00:48:26,380 --> 00:48:28,620 What's special about that region? 746 00:48:28,620 --> 00:48:30,429 Come on. 747 00:48:30,429 --> 00:48:31,330 AUDIENCE: [INAUDIBLE] 748 00:48:31,330 --> 00:48:32,330 ROBERT FIELD: I'm sorry? 749 00:48:32,330 --> 00:48:34,160 AUDIENCE: [INAUDIBLE] 750 00:48:34,160 --> 00:48:37,480 ROBERT FIELD: Not if this is a bounce state. 751 00:48:37,480 --> 00:48:38,440 That's a good try. 752 00:48:38,440 --> 00:48:41,860 That is, in fact, if this were a repulsive state, 753 00:48:41,860 --> 00:48:44,130 then predissociation would occur when 754 00:48:44,130 --> 00:48:45,850 it cross through the region. 755 00:48:45,850 --> 00:48:48,350 This is the stationary phase region. 756 00:48:48,350 --> 00:48:53,350 This is where the momentum on the two potential curves 757 00:48:53,350 --> 00:48:56,320 is the same. 758 00:48:56,320 --> 00:49:01,410 And so the molecule can make up its mind which potential curve 759 00:49:01,410 --> 00:49:06,470 it wants to leave on because there's no impulse that causes 760 00:49:06,470 --> 00:49:09,810 a change in its momentum, and it just 761 00:49:09,810 --> 00:49:11,280 makes a decision which one. 762 00:49:13,890 --> 00:49:20,580 And so when that happens, if you're following the dynamics, 763 00:49:20,580 --> 00:49:24,600 you have a series of beats. 764 00:49:24,600 --> 00:49:27,200 And I'm just sketching them as a stick, 765 00:49:27,200 --> 00:49:29,820 but really, they have width. 766 00:49:29,820 --> 00:49:32,250 And then at some later type you start 767 00:49:32,250 --> 00:49:36,900 seeing a new family of oscillations 768 00:49:36,900 --> 00:49:41,370 because now you've got some amplitude on this other state, 769 00:49:41,370 --> 00:49:45,080 and it has a different frequency. 770 00:49:45,080 --> 00:49:48,500 But the important thing-- and I should stop here-- 771 00:49:48,500 --> 00:49:53,230 is that the only time the molecule 772 00:49:53,230 --> 00:49:55,720 has to change its mind between one state 773 00:49:55,720 --> 00:49:57,850 and another is when it's crossing 774 00:49:57,850 --> 00:50:01,130 through this stationary phase region. 775 00:50:01,130 --> 00:50:02,890 So it's a complicated thing, but it's 776 00:50:02,890 --> 00:50:07,670 isolating a particular region where the curves cross. 777 00:50:07,670 --> 00:50:09,850 And where the curves cross, instead 778 00:50:09,850 --> 00:50:12,160 of having crossing curves, you could 779 00:50:12,160 --> 00:50:15,530 have something like this and something like that. 780 00:50:15,530 --> 00:50:19,310 Now we're back to Mr. Landau and Mr. Zener. 781 00:50:19,310 --> 00:50:23,060 And so if there's a curve crossing, depending 782 00:50:23,060 --> 00:50:25,460 on how far above the curve crossing, 783 00:50:25,460 --> 00:50:28,900 it tells you how fast you're going through it. 784 00:50:28,900 --> 00:50:31,630 See, there's all sorts of wonderful stuff here, 785 00:50:31,630 --> 00:50:36,850 which is not the trivial dynamics that-- 786 00:50:36,850 --> 00:50:40,000 this is the only way you get broadening is the molecule 787 00:50:40,000 --> 00:50:42,160 breaks. 788 00:50:42,160 --> 00:50:46,280 And the fluorescence is usually so slow-- 789 00:50:46,280 --> 00:50:47,510 10 nanoseconds is slow-- 790 00:50:50,040 --> 00:50:52,770 that you don't see any broadening because 10 791 00:50:52,770 --> 00:50:55,440 nanoseconds corresponds to a pretty high resolution, 792 00:50:55,440 --> 00:50:58,480 and most people aren't looking at that kind of resolution. 793 00:50:58,480 --> 00:51:03,200 And so we have quantum beats which 794 00:51:03,200 --> 00:51:08,060 then can show beautiful dynamics in a way 795 00:51:08,060 --> 00:51:11,730 that if you're prepared to build a model and to say, well, 796 00:51:11,730 --> 00:51:14,060 we could have this case and this case-- 797 00:51:14,060 --> 00:51:15,780 this is the chemists' case. 798 00:51:15,780 --> 00:51:18,860 We have quantum chemists' case-- 799 00:51:18,860 --> 00:51:20,728 you can interpret everything. 800 00:51:23,660 --> 00:51:27,320 This is very much related to what Mr. Zewail does. 801 00:51:27,320 --> 00:51:32,630 And I will spend a significant amount of time 802 00:51:32,630 --> 00:51:36,150 on Monday talking about the Zewail experiments 803 00:51:36,150 --> 00:51:39,480 and how the whole point of his experiments 804 00:51:39,480 --> 00:51:44,045 are not just saying, OK, I excite the molecule 805 00:51:44,045 --> 00:51:45,350 and it breaks. 806 00:51:45,350 --> 00:51:48,240 It breaks in this much time. 807 00:51:48,240 --> 00:51:49,940 Well, that's a useful question, but what 808 00:51:49,940 --> 00:51:51,240 did it do before it broke? 809 00:51:54,320 --> 00:51:57,870 One particular bond breaks, but what about the motions 810 00:51:57,870 --> 00:52:00,690 of the other bonds? 811 00:52:00,690 --> 00:52:03,390 Or maybe you're talking about breaking 812 00:52:03,390 --> 00:52:06,180 in a particular normal mode. 813 00:52:06,180 --> 00:52:11,610 Does the molecule arrange itself to be broken? 814 00:52:11,610 --> 00:52:14,520 Or once it's excited it goes downhill 815 00:52:14,520 --> 00:52:19,050 to the graveyard in a particular path, 816 00:52:19,050 --> 00:52:22,170 but there are wonderful things you 817 00:52:22,170 --> 00:52:26,430 can do by asking, what is the mechanism by which the molecule 818 00:52:26,430 --> 00:52:27,660 breaks? 819 00:52:27,660 --> 00:52:31,710 And by varying how you excite the molecule, 820 00:52:31,710 --> 00:52:35,580 you're looking at different aspects of that mechanism. 821 00:52:35,580 --> 00:52:40,690 Now Zewail sold this really hard, and it worked. 822 00:52:40,690 --> 00:52:43,980 And so I'll leave that for Monday.