1 00:00:00,000 --> 00:00:02,520 The following content is provided under a Creative 2 00:00:02,520 --> 00:00:03,970 Commons license. 3 00:00:03,970 --> 00:00:06,360 Your support will help MIT OpenCourseWare 4 00:00:06,360 --> 00:00:10,660 continue to offer high quality educational resources for free. 5 00:00:10,660 --> 00:00:13,350 To make a donation or view additional materials 6 00:00:13,350 --> 00:00:17,190 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:17,190 --> 00:00:18,326 at ocw.mit.edu. 8 00:00:25,410 --> 00:00:27,660 JEFFREY C. GROSSMAN: So today, what I 9 00:00:27,660 --> 00:00:34,590 want to do is, as requested and promised last week, 10 00:00:34,590 --> 00:00:37,770 today we'll spend some time just reviewing some of the things 11 00:00:37,770 --> 00:00:41,250 we've talked about up until now and some of the concepts 12 00:00:41,250 --> 00:00:45,600 that you might find questions around on the quiz. 13 00:00:45,600 --> 00:00:50,430 So maybe I'll ask you guys, just to make sure you understand 14 00:00:50,430 --> 00:00:53,430 each of the key concepts. 15 00:00:53,430 --> 00:00:55,110 I'll also, as part of this review, 16 00:00:55,110 --> 00:00:57,060 we'll look at a couple of questions, 17 00:00:57,060 --> 00:01:00,820 a couple more questions, from last year, from the quiz 18 00:01:00,820 --> 00:01:02,670 last year. 19 00:01:02,670 --> 00:01:06,782 You have a practice quiz and in solutions, 20 00:01:06,782 --> 00:01:08,490 and that would be a good idea to look at. 21 00:01:08,490 --> 00:01:10,800 Those are posted on Stellar, as well. 22 00:01:10,800 --> 00:01:13,440 That's not to say that that's exactly what you're 23 00:01:13,440 --> 00:01:14,110 going to get. 24 00:01:14,110 --> 00:01:19,120 But you might get-- in terms of topics, those are good ones. 25 00:01:19,120 --> 00:01:20,910 But what's not on the practice quiz 26 00:01:20,910 --> 00:01:24,060 is sort of any pictures of a density of states or a band 27 00:01:24,060 --> 00:01:26,170 structure. 28 00:01:26,170 --> 00:01:28,470 I can almost guarantee you you'll 29 00:01:28,470 --> 00:01:31,690 have sort of one of each of those on the real quiz. 30 00:01:31,690 --> 00:01:35,430 So you'll have a band structure that I'll 31 00:01:35,430 --> 00:01:37,920 ask you some questions about, as well as a DOS plot. 32 00:01:41,460 --> 00:01:44,880 So we're sort of supposed to be here. 33 00:01:44,880 --> 00:01:47,880 And I still hope to get to solar cells. 34 00:01:47,880 --> 00:01:54,090 And we have time, so we're going to talk about solar cells. 35 00:01:54,090 --> 00:01:55,980 But I know that, since the quiz is Thursday, 36 00:01:55,980 --> 00:01:57,522 we want to take a good chunk of today 37 00:01:57,522 --> 00:01:59,820 and just make sure that we have a good sense of what 38 00:01:59,820 --> 00:02:02,580 to expect and do a review. 39 00:02:02,580 --> 00:02:04,830 But I hope to get to our beginning 40 00:02:04,830 --> 00:02:08,009 of talking about modeling solar cells today, as well. 41 00:02:08,009 --> 00:02:10,530 And we'll pick up on that after the quiz. 42 00:02:10,530 --> 00:02:13,380 Are there any questions just about the quiz, which 43 00:02:13,380 --> 00:02:16,540 is Thursday? 44 00:02:16,540 --> 00:02:23,570 It's open book, open notes, no phones, PDAs. 45 00:02:23,570 --> 00:02:24,351 Yeah? 46 00:02:24,351 --> 00:02:26,460 AUDIENCE: How many questions can we expect? 47 00:02:26,460 --> 00:02:27,990 JEFFREY C. GROSSMAN: Somewhere-- 48 00:02:27,990 --> 00:02:31,005 definitely no more than 100, and-- 49 00:02:31,005 --> 00:02:33,242 [LAUGHS] I'm kidding. 50 00:02:38,610 --> 00:02:39,688 10-- I don't know. 51 00:02:39,688 --> 00:02:41,730 Does that sound about right, something like that? 52 00:02:46,170 --> 00:02:46,670 12. 53 00:02:50,410 --> 00:02:51,460 OK, so there we are. 54 00:02:51,460 --> 00:02:54,100 Now, I do want to, since Lynn already 55 00:02:54,100 --> 00:02:56,050 made a little announcement about part 2, 56 00:02:56,050 --> 00:02:59,145 I wanted to start today-- 57 00:02:59,145 --> 00:03:00,520 so that's what we're going to do. 58 00:03:00,520 --> 00:03:03,640 I wanted to just, even though I just postponed the piece 59 00:03:03,640 --> 00:03:11,130 that-- oh, I'm going to have an office hour tomorrow at 4:00. 60 00:03:11,130 --> 00:03:12,930 Is that what I said, 4:00 to 5:00? 61 00:03:12,930 --> 00:03:14,490 Or did I say 5:00 to 6:00? 62 00:03:14,490 --> 00:03:17,040 4:00 to 5:00, I think. 63 00:03:17,040 --> 00:03:20,290 But if anybody has questions, as always, send me an email. 64 00:03:20,290 --> 00:03:23,100 And I'm happy to answer electronically or set up 65 00:03:23,100 --> 00:03:29,010 a time to meet that works on your side. 66 00:03:29,010 --> 00:03:31,650 So that's very good. 67 00:03:31,650 --> 00:03:34,980 And how many of you have looked at problem 3? 68 00:03:34,980 --> 00:03:36,140 A couple of you, OK. 69 00:03:40,250 --> 00:03:43,820 So are there any questions that anybody has about problem 70 00:03:43,820 --> 00:03:45,450 3 right now who have looked at it? 71 00:03:45,450 --> 00:03:46,900 Go ahead. 72 00:03:46,900 --> 00:03:49,108 AUDIENCE: Well, in terms of-- 73 00:03:49,108 --> 00:03:51,253 how do you find maximum efficiency? 74 00:03:51,253 --> 00:03:52,920 JEFFREY C. GROSSMAN: All right, [LAUGHS] 75 00:03:52,920 --> 00:03:54,130 that's a good question. 76 00:03:54,130 --> 00:03:56,130 That's a really good question. 77 00:03:56,130 --> 00:03:58,937 Anything more specific? 78 00:03:58,937 --> 00:04:00,645 AUDIENCE: You know the maximum efficiency 79 00:04:00,645 --> 00:04:02,690 is going to be related to the energy going 80 00:04:02,690 --> 00:04:04,610 in versus going out. 81 00:04:04,610 --> 00:04:09,077 But how do you determine, I guess, the energy going out? 82 00:04:09,077 --> 00:04:10,160 JEFFREY C. GROSSMAN: Yeah. 83 00:04:10,160 --> 00:04:10,770 Yeah. 84 00:04:10,770 --> 00:04:14,810 OK, so let me talk a little bit about this problem to make sure 85 00:04:14,810 --> 00:04:18,709 that we kind of know where to go with it. 86 00:04:18,709 --> 00:04:21,620 And the key setup here is actually really 87 00:04:21,620 --> 00:04:22,880 part A, in a way. 88 00:04:22,880 --> 00:04:25,010 It seems pretty simple. 89 00:04:25,010 --> 00:04:27,350 But it's kind of the core piece of information 90 00:04:27,350 --> 00:04:29,330 that you need to understand. 91 00:04:29,330 --> 00:04:31,730 And I'm going to use this yellow chalk that's 92 00:04:31,730 --> 00:04:35,060 actually white to draw. 93 00:04:35,060 --> 00:04:38,400 Let's not forget what it is that we're talking about, 94 00:04:38,400 --> 00:04:43,100 which is basically an energy landscape. 95 00:04:43,100 --> 00:04:46,492 Remember, in capturing the sun's energy, 96 00:04:46,492 --> 00:04:48,200 what we're trying to-- what we're doing-- 97 00:04:48,200 --> 00:04:51,530 and in many energy technologies, what we're doing 98 00:04:51,530 --> 00:04:57,170 is we're pumping something up an energy hill. 99 00:04:57,170 --> 00:05:00,290 And in this case, we pump an electron. 100 00:05:00,290 --> 00:05:01,580 We shine light on it. 101 00:05:04,470 --> 00:05:09,270 And the molecule is in the trans state. 102 00:05:09,270 --> 00:05:13,920 And then it gets excited because the light, the electrons 103 00:05:13,920 --> 00:05:17,640 from the photons from the light, excite 104 00:05:17,640 --> 00:05:19,190 electrons in the molecule. 105 00:05:19,190 --> 00:05:21,240 So that's that pumping action that's happening. 106 00:05:21,240 --> 00:05:23,760 You're pumping electrons within this molecule 107 00:05:23,760 --> 00:05:25,590 up to a higher level. 108 00:05:25,590 --> 00:05:27,750 When you do that, the molecule is 109 00:05:27,750 --> 00:05:32,740 allowed to go to here just from that energy from the light. 110 00:05:32,740 --> 00:05:36,480 So the light's energy is being converted 111 00:05:36,480 --> 00:05:39,960 into creating electrons that are higher in energy. 112 00:05:39,960 --> 00:05:43,740 And that allows the molecule to go from this structure 113 00:05:43,740 --> 00:05:44,730 to this structure. 114 00:05:44,730 --> 00:05:48,870 And that's allowing you to store this much energy. 115 00:05:48,870 --> 00:05:52,920 So don't forget this picture as you think about this homework, 116 00:05:52,920 --> 00:05:57,630 because this homework is all about this picture. 117 00:05:57,630 --> 00:06:03,560 Now, who can tell me-- we talked about this in class 118 00:06:03,560 --> 00:06:07,220 already when we talked about this whole solar thermal fuel 119 00:06:07,220 --> 00:06:08,720 concept. 120 00:06:08,720 --> 00:06:12,350 Who can tell me why-- 121 00:06:12,350 --> 00:06:14,930 who can tell me the answer to part A? 122 00:06:14,930 --> 00:06:16,680 Let's just see if we can do that together. 123 00:06:19,910 --> 00:06:21,330 Yeah? 124 00:06:21,330 --> 00:06:27,040 AUDIENCE: Is it because there's a energy [INAUDIBLE] 125 00:06:27,040 --> 00:06:29,126 between the trans and the cis states that's 126 00:06:29,126 --> 00:06:31,960 higher than natural cis energy? 127 00:06:31,960 --> 00:06:34,450 JEFFREY C. GROSSMAN: OK, so here I'm going. 128 00:06:34,450 --> 00:06:38,560 I'm shining light, and I shined light of this energy-- 129 00:06:38,560 --> 00:06:40,300 or if you want to think about it as HC 130 00:06:40,300 --> 00:06:43,780 over lambda of that amount of energy, 131 00:06:43,780 --> 00:06:46,210 just going between wavelength and frequency. 132 00:06:46,210 --> 00:06:48,790 And I shined light on this trans state, 133 00:06:48,790 --> 00:06:54,740 and I only shined light with this amount of energy. 134 00:06:54,740 --> 00:06:59,350 Can it possibly be converted to here? 135 00:06:59,350 --> 00:07:03,490 It can't, because we can't-- 136 00:07:03,490 --> 00:07:05,515 now, some of you took 3.012, and you 137 00:07:05,515 --> 00:07:08,350 know we don't violate the laws of thermodynamics. 138 00:07:08,350 --> 00:07:10,380 Those are untouchable. 139 00:07:10,380 --> 00:07:12,930 You can't get something for nothing, right? 140 00:07:12,930 --> 00:07:18,870 So you're not going to get to store this much energy if you 141 00:07:18,870 --> 00:07:21,360 only put in this much. 142 00:07:21,360 --> 00:07:23,270 That kind of makes sense. 143 00:07:23,270 --> 00:07:26,040 You can't put it up on some shelf 144 00:07:26,040 --> 00:07:28,140 of energy, some chemical shelf, which 145 00:07:28,140 --> 00:07:30,810 is a way of thinking about this, if you haven't given 146 00:07:30,810 --> 00:07:32,730 it enough to get up there-- 147 00:07:32,730 --> 00:07:35,772 unless you use a lot of thermal vibrations, but that's not what 148 00:07:35,772 --> 00:07:36,480 we're doing here. 149 00:07:36,480 --> 00:07:37,590 You could use heat. 150 00:07:37,590 --> 00:07:42,260 But you can't get it with this input less than output. 151 00:07:42,260 --> 00:07:44,210 OK, so that's sort of what part A is asking. 152 00:07:44,210 --> 00:07:46,670 Does everybody see that? 153 00:07:46,670 --> 00:07:49,350 Now, here comes the fun part. 154 00:07:49,350 --> 00:07:53,680 But, you see, it's not just-- this is the molecule sort 155 00:07:53,680 --> 00:07:55,510 of going about its business. 156 00:07:55,510 --> 00:07:59,930 This is the happy-go-lucky molecule. 157 00:07:59,930 --> 00:08:01,510 But then we have the sun. 158 00:08:01,510 --> 00:08:02,290 We have this part. 159 00:08:02,290 --> 00:08:03,890 Where does this come from? 160 00:08:03,890 --> 00:08:06,400 Well, this is the sun, you see. 161 00:08:06,400 --> 00:08:09,790 And that has its thing that it does. 162 00:08:09,790 --> 00:08:14,710 And its thing that it does is it has intensity that 163 00:08:14,710 --> 00:08:18,280 comes in as a function of-- 164 00:08:18,280 --> 00:08:21,610 this has probably nothing to do with the real curve, 165 00:08:21,610 --> 00:08:25,910 but I draw the sun's intensity different every time I draw it. 166 00:08:25,910 --> 00:08:28,160 But this would be, say-- 167 00:08:28,160 --> 00:08:31,990 well, this could be energy or wavelength or frequency. 168 00:08:31,990 --> 00:08:34,049 Let's call it energy. 169 00:08:34,049 --> 00:08:38,280 And so you have a dependence of intensity of the sunlight that 170 00:08:38,280 --> 00:08:40,320 strikes the Earth or the atmosphere-- 171 00:08:40,320 --> 00:08:42,090 those are different-- 172 00:08:42,090 --> 00:08:45,390 on the energy that you get. 173 00:08:45,390 --> 00:08:47,790 So there's some energies of light 174 00:08:47,790 --> 00:08:51,090 that have a lot of intensity and some that have very little. 175 00:08:51,090 --> 00:08:54,060 Now, what's the key connection here between these two? 176 00:08:57,050 --> 00:08:57,890 Who remembers? 177 00:09:00,630 --> 00:09:03,090 Which is really what part 2 is about, 178 00:09:03,090 --> 00:09:05,730 question 2 is about-- what's the key connection here 179 00:09:05,730 --> 00:09:10,360 between this curve and this picture? 180 00:09:10,360 --> 00:09:11,330 Yeah? 181 00:09:11,330 --> 00:09:15,280 AUDIENCE: So only photons with a sufficient energy 182 00:09:15,280 --> 00:09:18,435 will be able to excite your molecule from the trans 183 00:09:18,435 --> 00:09:19,520 to cis states. 184 00:09:19,520 --> 00:09:22,420 So only some part of that curve with energy 185 00:09:22,420 --> 00:09:26,770 greater than or equal to delta H will be able to do that. 186 00:09:26,770 --> 00:09:30,100 So it can only capture that much of the sun's total energy? 187 00:09:30,100 --> 00:09:32,290 JEFFREY C. GROSSMAN: Yeah, exactly. 188 00:09:32,290 --> 00:09:34,090 And there's something else, too. 189 00:09:34,090 --> 00:09:37,750 But that's exactly what we need for a problem 3. 190 00:09:37,750 --> 00:09:39,970 That's exactly it. 191 00:09:39,970 --> 00:09:42,850 So what I've told you-- 192 00:09:42,850 --> 00:09:45,990 what we did already is we said, well, 193 00:09:45,990 --> 00:09:48,720 you can't get more energy out than you put in. 194 00:09:48,720 --> 00:09:52,170 So you've got to have at least delta 195 00:09:52,170 --> 00:10:03,850 H. Minimum of sun's energy is delta H. That's 196 00:10:03,850 --> 00:10:07,270 the absolute minimum you have to put into this to get delta H 197 00:10:07,270 --> 00:10:09,010 stored, right? 198 00:10:09,010 --> 00:10:11,510 Sorry, that's kind of hard to read. 199 00:10:11,510 --> 00:10:14,410 I'm not liking this yellow-colored white chalk, 200 00:10:14,410 --> 00:10:17,990 because it's too thick. 201 00:10:17,990 --> 00:10:21,750 So the minimum sun's energy is-- 202 00:10:21,750 --> 00:10:26,560 that's better-- is delta H. 203 00:10:26,560 --> 00:10:29,800 But you see, there's also now-- what happens is-- 204 00:10:29,800 --> 00:10:31,690 so let's say I can-- 205 00:10:34,550 --> 00:10:36,688 let's say that delta is somewhere here. 206 00:10:36,688 --> 00:10:37,230 I don't know. 207 00:10:37,230 --> 00:10:45,090 Call it one electron volt. well, what I've just said in part A 208 00:10:45,090 --> 00:10:49,800 is that anything below that, anything below one electron 209 00:10:49,800 --> 00:10:54,280 volt, cannot be used to store energy. 210 00:10:54,280 --> 00:10:58,500 So any sunlight energy that's below that is wasted. 211 00:10:58,500 --> 00:11:01,860 It's not going to do anything to charge that fuel, 212 00:11:01,860 --> 00:11:04,690 because it's below this amount. 213 00:11:04,690 --> 00:11:09,850 On the other hand, everything above that 214 00:11:09,850 --> 00:11:11,500 will charge the fuel. 215 00:11:17,770 --> 00:11:19,930 But now here's where the question of efficiency 216 00:11:19,930 --> 00:11:24,220 comes in, because is it really-- 217 00:11:24,220 --> 00:11:26,650 what would I really like to do here 218 00:11:26,650 --> 00:11:30,790 in terms of charging this fuel? 219 00:11:30,790 --> 00:11:34,600 Somebody tell me the difference between a photon of sunlight 220 00:11:34,600 --> 00:11:37,150 energy that's here, that charges the fuel, 221 00:11:37,150 --> 00:11:42,020 versus one that's out here that also charges the fuel. 222 00:11:42,020 --> 00:11:45,050 Somebody tell me what's different or similar 223 00:11:45,050 --> 00:11:49,190 between those two parts of the spectrum, both of which 224 00:11:49,190 --> 00:11:52,040 convert my fuel. 225 00:11:52,040 --> 00:11:52,690 Yeah? 226 00:11:52,690 --> 00:11:57,240 AUDIENCE: The one that's higher energy has less energy wasted, 227 00:11:57,240 --> 00:11:58,963 because delta H is constant. 228 00:11:58,963 --> 00:12:01,130 So once you get above it, the more above it you get, 229 00:12:01,130 --> 00:12:03,500 the less efficient it becomes. 230 00:12:03,500 --> 00:12:04,860 JEFFREY C. GROSSMAN: Exactly. 231 00:12:04,860 --> 00:12:05,720 Exactly. 232 00:12:05,720 --> 00:12:08,120 So I can charge the fuel now because, I said, 233 00:12:08,120 --> 00:12:11,000 I can't have less than how much I'm storing. 234 00:12:11,000 --> 00:12:13,550 That's a rule but I can charge you 235 00:12:13,550 --> 00:12:15,635 with anything above that except for one thing 236 00:12:15,635 --> 00:12:17,510 that I'm going to tell you about in a second. 237 00:12:17,510 --> 00:12:19,052 Or you're going to tell me, because I 238 00:12:19,052 --> 00:12:21,800 know somebody knows this. 239 00:12:21,800 --> 00:12:24,110 But if I use this amount of energy from the sun, 240 00:12:24,110 --> 00:12:26,090 well, I still only stored that. 241 00:12:26,090 --> 00:12:31,540 That's my delta H. So that means I wasted a whole lot. 242 00:12:31,540 --> 00:12:33,820 And that's what I want you to tell me. 243 00:12:33,820 --> 00:12:34,870 What's the efficiency? 244 00:12:38,650 --> 00:12:41,150 So if I'm all the way down here, you can say, well-- 245 00:12:41,150 --> 00:12:43,150 and this is what we talked about in the lecture. 246 00:12:43,150 --> 00:12:44,920 If I'm all the way down here, then I 247 00:12:44,920 --> 00:12:47,620 can absorb all this light and use it to convert. 248 00:12:47,620 --> 00:12:50,140 But light up here is really wasted. 249 00:12:50,140 --> 00:12:55,630 It's super wasted the further you get up in energy. 250 00:12:55,630 --> 00:12:57,760 So where is the sweet spot? 251 00:12:57,760 --> 00:13:00,340 There's going to be a sweet spot. 252 00:13:00,340 --> 00:13:03,160 That's what I want you to tell me in part B, OK? 253 00:13:03,160 --> 00:13:05,480 Now, there's something I'm not telling you 254 00:13:05,480 --> 00:13:07,930 which is really important here that's not 255 00:13:07,930 --> 00:13:10,985 part of that question. 256 00:13:10,985 --> 00:13:12,610 But there's something else that matters 257 00:13:12,610 --> 00:13:14,800 a lot that's part of part B-- 258 00:13:14,800 --> 00:13:16,570 number 2, question number 2. 259 00:13:16,570 --> 00:13:20,770 What have we not considered yet? 260 00:13:20,770 --> 00:13:23,410 And in particular, what about it? 261 00:13:23,410 --> 00:13:24,190 AUDIENCE: Gap. 262 00:13:24,190 --> 00:13:25,780 JEFFREY C. GROSSMAN: The band gap. 263 00:13:25,780 --> 00:13:28,420 The gap, or the gap of the molecule-- 264 00:13:28,420 --> 00:13:33,030 and you see, because that's the other component here. 265 00:13:33,030 --> 00:13:35,480 So these are-- problem 3 is talking 266 00:13:35,480 --> 00:13:39,650 about theoretical limits based on how much the molecule stores 267 00:13:39,650 --> 00:13:42,020 and how much sunlight shines on it. 268 00:13:42,020 --> 00:13:44,640 But there's this other thing that problem 2 talks about, 269 00:13:44,640 --> 00:13:47,330 which is the fact that the molecule will not absorb 270 00:13:47,330 --> 00:13:49,370 any light lower than its gap. 271 00:13:52,505 --> 00:13:53,880 And that's why those two problems 272 00:13:53,880 --> 00:13:56,650 are very I think complementary to one another. 273 00:13:56,650 --> 00:13:58,450 So all of that comes into play. 274 00:13:58,450 --> 00:14:00,330 So even if I say, well, it stores in EV, 275 00:14:00,330 --> 00:14:03,690 so theoretically, it could absorb all of this. 276 00:14:03,690 --> 00:14:08,910 Actually, if its gap is 2 EV, it's only absorbing this. 277 00:14:08,910 --> 00:14:13,550 But we're not talking about the gap in problem number 2, OK? 278 00:14:13,550 --> 00:14:14,050 All right. 279 00:14:17,660 --> 00:14:18,600 It's fun. 280 00:14:18,600 --> 00:14:19,430 This is fun, right? 281 00:14:19,430 --> 00:14:21,866 Any questions? 282 00:14:21,866 --> 00:14:26,430 We're integrating the sun. 283 00:14:26,430 --> 00:14:28,120 Any questions about that problem? 284 00:14:28,120 --> 00:14:28,620 Yeah? 285 00:14:28,620 --> 00:14:31,460 AUDIENCE: So to find the energy that's lost, do we just 286 00:14:31,460 --> 00:14:34,880 have to subtract the delta H energy from all 287 00:14:34,880 --> 00:14:40,930 of the high-energy states and integrate that new area? 288 00:14:40,930 --> 00:14:42,930 JEFFREY C. GROSSMAN: Yeah, it seems to me like-- 289 00:14:42,930 --> 00:14:48,030 so you figured out in the earlier problem 290 00:14:48,030 --> 00:14:51,420 how to figure out that, if you integrated this, 291 00:14:51,420 --> 00:14:53,940 you would get, like, how much of the sun's energy 292 00:14:53,940 --> 00:14:55,350 that molecule is absorbing. 293 00:14:55,350 --> 00:14:58,170 And you used the band gap as the cutoff. 294 00:14:58,170 --> 00:14:59,670 But now it seems like maybe you want 295 00:14:59,670 --> 00:15:03,420 to use delta H in a similar way, because you're 296 00:15:03,420 --> 00:15:06,390 looking at sort of a theoretical efficiency 297 00:15:06,390 --> 00:15:08,930 and ignoring the gap. 298 00:15:08,930 --> 00:15:11,510 Now, then, what is the efficiency? 299 00:15:11,510 --> 00:15:16,710 Well, it's how much energy that molecule 300 00:15:16,710 --> 00:15:18,060 can take in from the sun-- 301 00:15:23,230 --> 00:15:27,568 divided by that, the amount that is stored. 302 00:15:27,568 --> 00:15:30,120 Did I answer your question, or did I dance around it? 303 00:15:34,410 --> 00:15:35,207 Was that helpful? 304 00:15:35,207 --> 00:15:36,790 AUDIENCE: How do you, like, physically 305 00:15:36,790 --> 00:15:38,060 calculate that amount? 306 00:15:38,060 --> 00:15:40,560 JEFFREY C. GROSSMAN: Ah, but that's what you-- you chose it. 307 00:15:40,560 --> 00:15:41,352 You just picked it. 308 00:15:41,352 --> 00:15:43,110 You said, I'm going to say it stores 1 EV, 309 00:15:43,110 --> 00:15:44,152 because that was delta H. 310 00:15:44,152 --> 00:15:46,445 AUDIENCE: But if there's one of these per-- 311 00:15:46,445 --> 00:15:47,862 JEFFREY C. GROSSMAN: Per molecule. 312 00:15:47,862 --> 00:15:52,295 AUDIENCE: [INAUDIBLE] 313 00:15:52,295 --> 00:15:53,670 JEFFREY C. GROSSMAN: Per molecule 314 00:15:53,670 --> 00:15:57,720 is the way to think about it, right? 315 00:15:57,720 --> 00:16:01,950 And then there's-- so that's how much energy you're storing 316 00:16:01,950 --> 00:16:04,860 in each molecule, and then each molecule is getting how much 317 00:16:04,860 --> 00:16:08,370 energy from the sun? 318 00:16:08,370 --> 00:16:10,330 Right? 319 00:16:10,330 --> 00:16:12,320 And between those, you have an efficiency. 320 00:16:12,320 --> 00:16:14,260 It's basically 1 divided by the other. 321 00:16:23,083 --> 00:16:25,000 And you know which one to divide by the other, 322 00:16:25,000 --> 00:16:27,250 because if you divide it, and it's more than one, 323 00:16:27,250 --> 00:16:29,770 you should do it the other way. 324 00:16:29,770 --> 00:16:31,900 That's a hint. 325 00:16:31,900 --> 00:16:34,250 No, but seriously, are there-- 326 00:16:34,250 --> 00:16:36,720 did that make sense enough? 327 00:16:36,720 --> 00:16:37,620 OK. 328 00:16:37,620 --> 00:16:40,025 Now, question C is a little bit-- 329 00:16:40,025 --> 00:16:41,400 taking that a little bit further. 330 00:16:45,560 --> 00:16:49,664 But it's that same exact concept that-- 331 00:16:49,664 --> 00:16:52,820 yeah, OK. 332 00:16:52,820 --> 00:16:56,080 Any questions? 333 00:16:56,080 --> 00:16:56,948 Yeah? 334 00:16:56,948 --> 00:16:58,860 AUDIENCE: I'm just a little confused. 335 00:16:58,860 --> 00:17:01,240 So when we calculate the band gap, 336 00:17:01,240 --> 00:17:04,150 that's the amount of energy needed for it 337 00:17:04,150 --> 00:17:06,744 to absorb energy from the sun. 338 00:17:06,744 --> 00:17:07,869 JEFFREY C. GROSSMAN: Right. 339 00:17:07,869 --> 00:17:10,815 AUDIENCE: Then how does that relate to the delta H? 340 00:17:10,815 --> 00:17:11,770 Are those separate? 341 00:17:11,770 --> 00:17:13,359 JEFFREY C. GROSSMAN: Yeah, that's a great, great question. 342 00:17:13,359 --> 00:17:14,290 And that really is-- 343 00:17:19,069 --> 00:17:25,589 I want you to think about them separately for this problem. 344 00:17:25,589 --> 00:17:29,420 So they really are, of course, intertwined 345 00:17:29,420 --> 00:17:33,170 in fairly complicated ways. 346 00:17:33,170 --> 00:17:37,360 But here, what I want you to do is 347 00:17:37,360 --> 00:17:40,300 suppose you could just make the gap. 348 00:17:40,300 --> 00:17:43,768 At any delta H, you could just make it equal to delta H. 349 00:17:43,768 --> 00:17:45,310 That's really what you're doing here, 350 00:17:45,310 --> 00:17:48,760 because you're taking a kind of theoretical limit 351 00:17:48,760 --> 00:17:51,610 exercise in this. 352 00:17:51,610 --> 00:17:52,760 That's not the case. 353 00:17:52,760 --> 00:17:54,100 It's not as tunable as that. 354 00:17:54,100 --> 00:17:56,980 Although, you can tune the gap in these materials 355 00:17:56,980 --> 00:17:58,870 to quite an extent. 356 00:17:58,870 --> 00:18:02,650 But here I'm saying, suppose that the amount it absorbs 357 00:18:02,650 --> 00:18:07,990 is, in fact, set not by the gap but by this other constraint 358 00:18:07,990 --> 00:18:10,300 that is part A of this question, which 359 00:18:10,300 --> 00:18:12,550 is that you just can't convert it unless you 360 00:18:12,550 --> 00:18:13,850 have as much as delta H. 361 00:18:13,850 --> 00:18:17,740 That's just-- that there's no way around. 362 00:18:17,740 --> 00:18:19,000 You can't tune around that. 363 00:18:19,000 --> 00:18:19,720 That's just it. 364 00:18:19,720 --> 00:18:24,460 You can't get to here unless enough energy from the sun 365 00:18:24,460 --> 00:18:26,800 is this or more. 366 00:18:26,800 --> 00:18:28,630 So that's really ignoring the gap. 367 00:18:31,880 --> 00:18:35,710 But in reality, it's going to only absorb photons 368 00:18:35,710 --> 00:18:37,250 at the gap or higher. 369 00:18:37,250 --> 00:18:38,530 But if you found it-- 370 00:18:38,530 --> 00:18:43,210 now, if you were to happen to do 3B and get 371 00:18:43,210 --> 00:18:48,630 a maximum in a curve, let's suppose, 372 00:18:48,630 --> 00:18:51,940 and that maximum occurred at a certain delta H, 373 00:18:51,940 --> 00:18:54,940 then you might say, well, that's where I should try 374 00:18:54,940 --> 00:18:58,240 to get my gap to that point. 375 00:18:58,240 --> 00:18:59,755 That might be some guidance. 376 00:18:59,755 --> 00:19:01,880 Of course, that's not actually what you want to do. 377 00:19:01,880 --> 00:19:05,140 But as we ignore the gap, you can think about it that way. 378 00:19:05,140 --> 00:19:10,210 It provides some guidance into where you might look at-- 379 00:19:10,210 --> 00:19:13,240 these kinds of exercises in theoretical efficiencies 380 00:19:13,240 --> 00:19:16,930 can always be useful for those reasons. 381 00:19:16,930 --> 00:19:18,287 Does that answer your question? 382 00:19:18,287 --> 00:19:20,610 AUDIENCE: I think so. 383 00:19:20,610 --> 00:19:22,110 JEFFREY C. GROSSMAN: Definitely, I'm 384 00:19:22,110 --> 00:19:23,730 very happy to talk about this more. 385 00:19:23,730 --> 00:19:28,028 Office hours, tomorrow at 4:00 and also by request-- 386 00:19:28,028 --> 00:19:29,070 so just send me an email. 387 00:19:29,070 --> 00:19:32,460 Or if you-- I think a lot of you know, if you send me an email, 388 00:19:32,460 --> 00:19:35,260 I'll try to write back pretty quickly. 389 00:19:35,260 --> 00:19:38,280 So if you have questions, I'm happy to answer. 390 00:19:38,280 --> 00:19:41,280 Are we feeling good? 391 00:19:41,280 --> 00:19:41,780 Yeah. 392 00:19:44,540 --> 00:19:45,997 OK. 393 00:19:45,997 --> 00:19:48,330 Nope, we're not going to look at a recommendation letter 394 00:19:48,330 --> 00:19:48,900 together. 395 00:19:48,900 --> 00:19:52,072 [LAUGHTER] That wouldn't be appropriate. 396 00:19:52,072 --> 00:19:57,240 [LAUGHS] Wait a second. 397 00:19:57,240 --> 00:20:00,360 But there was-- yeah, let's get that out of there. 398 00:20:00,360 --> 00:20:04,330 And there was a-- 399 00:20:04,330 --> 00:20:07,730 aha, here we go. 400 00:20:07,730 --> 00:20:10,090 What did you do? 401 00:20:10,090 --> 00:20:13,940 Now, this is not this year's quiz. 402 00:20:13,940 --> 00:20:16,070 But this is last year's quiz. 403 00:20:16,070 --> 00:20:18,600 And I'll do this first, because then we can review. 404 00:20:18,600 --> 00:20:20,330 So here's a couple of questions from last year's quiz. 405 00:20:20,330 --> 00:20:21,650 Let's just focus on this one. 406 00:20:26,440 --> 00:20:29,380 Oh, what are basis functions, and how 407 00:20:29,380 --> 00:20:31,210 do if you have enough of them. 408 00:20:33,900 --> 00:20:36,440 Somebody answer that for me first. 409 00:20:36,440 --> 00:20:43,090 What are basis functions, and how do if you have Enough yeah 410 00:20:43,090 --> 00:20:45,550 AUDIENCE: So basis functions are a set 411 00:20:45,550 --> 00:20:48,250 of functions which you can take combinations 412 00:20:48,250 --> 00:20:51,520 of to create an approximation of what the exact function should 413 00:20:51,520 --> 00:20:52,330 be. 414 00:20:52,330 --> 00:20:54,490 And you know you have enough of them 415 00:20:54,490 --> 00:20:56,170 if whatever you're trying to calculate 416 00:20:56,170 --> 00:21:02,680 you use basis set and then a, I guess, more refined basis 417 00:21:02,680 --> 00:21:04,240 and do this a little bit. 418 00:21:04,240 --> 00:21:06,625 And it sort of converges to some value. 419 00:21:06,625 --> 00:21:07,750 JEFFREY C. GROSSMAN: Right. 420 00:21:07,750 --> 00:21:08,250 Exactly. 421 00:21:11,013 --> 00:21:12,680 There's a really important part of that. 422 00:21:12,680 --> 00:21:17,050 So that is-- basis functions are mathematical functions-- 423 00:21:17,050 --> 00:21:22,840 Gaussians, exponents, plane waves, wavelets. 424 00:21:22,840 --> 00:21:24,100 Don't use wavelets. 425 00:21:24,100 --> 00:21:25,450 But they're kind of funny. 426 00:21:25,450 --> 00:21:26,560 They're neat functions. 427 00:21:26,560 --> 00:21:28,730 But it can be anything. 428 00:21:28,730 --> 00:21:29,700 It's just a function. 429 00:21:33,310 --> 00:21:35,020 And you just use them. 430 00:21:35,020 --> 00:21:38,140 You use a series of them usually, a sequence of them 431 00:21:38,140 --> 00:21:41,560 that you add together, to make up the complexity that 432 00:21:41,560 --> 00:21:44,612 is psi, which is the wave function, 433 00:21:44,612 --> 00:21:46,570 the wave function that we're after in this part 434 00:21:46,570 --> 00:21:48,670 of the course. 435 00:21:48,670 --> 00:21:51,040 So it's just a representation, but it's one 436 00:21:51,040 --> 00:21:54,338 that you don't find in classical simulations 437 00:21:54,338 --> 00:21:55,630 that you did in the first part. 438 00:21:55,630 --> 00:21:56,710 But you do find it here. 439 00:21:56,710 --> 00:21:59,230 And it's really important to know when you're converged. 440 00:21:59,230 --> 00:22:00,340 And say that part again. 441 00:22:00,340 --> 00:22:02,770 When are you converged? 442 00:22:02,770 --> 00:22:06,100 AUDIENCE: When you use -- 443 00:22:06,100 --> 00:22:08,250 when you take whatever you're trying to calculate-- 444 00:22:08,250 --> 00:22:10,000 JEFFREY C. GROSSMAN: Ah, stop right there. 445 00:22:10,000 --> 00:22:13,210 That's it-- whatever you're trying to calculate. 446 00:22:13,210 --> 00:22:15,888 What are you trying to calculate? 447 00:22:15,888 --> 00:22:16,680 Give me an example. 448 00:22:19,482 --> 00:22:20,940 AUDIENCE: Total energy of a system. 449 00:22:20,940 --> 00:22:21,960 JEFFREY C. GROSSMAN: Total energy of the system. 450 00:22:21,960 --> 00:22:23,840 Now give me another example. 451 00:22:23,840 --> 00:22:25,200 AUDIENCE: HOMO-LUMO gap. 452 00:22:25,200 --> 00:22:26,820 JEFFREY C. GROSSMAN: HOMO-LUMO gap. 453 00:22:26,820 --> 00:22:27,360 I love it. 454 00:22:27,360 --> 00:22:29,260 We could go on like this, but I won't. 455 00:22:29,260 --> 00:22:32,310 But now, are the number of basis functions 456 00:22:32,310 --> 00:22:35,880 you need to converge the representation of your wave 457 00:22:35,880 --> 00:22:40,593 function the same for the total energy or the HOMO-LUMO gap? 458 00:22:40,593 --> 00:22:43,140 AUDIENCE: No. 459 00:22:43,140 --> 00:22:43,890 AUDIENCE: Depends. 460 00:22:43,890 --> 00:22:44,817 AUDIENCE: [INAUDIBLE] 461 00:22:44,817 --> 00:22:47,150 JEFFREY C. GROSSMAN: It depends is always a good answer. 462 00:22:47,150 --> 00:22:48,310 You can always write that. 463 00:22:48,310 --> 00:22:52,300 Don't put it for your name, but you can put it for-- 464 00:22:52,300 --> 00:22:53,110 well, I don't know. 465 00:22:53,110 --> 00:22:55,595 Maybe you do need the same number of functions 466 00:22:55,595 --> 00:22:56,470 for those properties. 467 00:22:56,470 --> 00:23:01,240 But you need to look at them on a property-by-property basis, 468 00:23:01,240 --> 00:23:03,490 no pun intended. 469 00:23:03,490 --> 00:23:05,150 OK? 470 00:23:05,150 --> 00:23:06,050 So very good. 471 00:23:06,050 --> 00:23:09,200 Now, without solving any equations, which electron 472 00:23:09,200 --> 00:23:11,840 do you think would require more basis functions to describe 473 00:23:11,840 --> 00:23:15,920 well the 2p electron in carbon or the 3p electron in silicon? 474 00:23:15,920 --> 00:23:18,010 Who can tell me what they think? 475 00:23:18,010 --> 00:23:18,510 Yeah? 476 00:23:18,510 --> 00:23:20,190 AUDIENCE: 3p electron in silicon. 477 00:23:20,190 --> 00:23:22,315 JEFFREY C. GROSSMAN: Well, you need-- now, hang on. 478 00:23:22,315 --> 00:23:24,840 You need more basis functions for 3p? 479 00:23:24,840 --> 00:23:26,850 Tell me why. 480 00:23:26,850 --> 00:23:30,633 AUDIENCE: [INAUDIBLE] more electron attraction. 481 00:23:30,633 --> 00:23:32,050 JEFFREY C. GROSSMAN: Well, what is 482 00:23:32,050 --> 00:23:35,330 it that makes you need more basis functions? 483 00:23:35,330 --> 00:23:38,880 What is it that makes you need more basis functions? 484 00:23:38,880 --> 00:23:39,380 Yeah? 485 00:23:39,380 --> 00:23:41,422 AUDIENCE: It's like a more complex wave function. 486 00:23:41,422 --> 00:23:44,390 JEFFREY C. GROSSMAN: OK, so if the function-- 487 00:23:50,838 --> 00:23:58,620 if the wave function looks like this versus, say, 488 00:23:58,620 --> 00:24:02,990 a wave function that looks like that, 489 00:24:02,990 --> 00:24:06,500 which one do you think I'm going to need more functions for? 490 00:24:06,500 --> 00:24:11,380 I'm going to need more basis functions for this one. 491 00:24:16,120 --> 00:24:17,120 Does everybody see that? 492 00:24:17,120 --> 00:24:20,490 Now, and then the question is, OK, so if you put that down, 493 00:24:20,490 --> 00:24:22,460 you're already doing really well, 494 00:24:22,460 --> 00:24:28,370 because on these questions, what I'm looking for isn't even-- 495 00:24:28,370 --> 00:24:33,650 if you didn't know the answer to what 2p carbon or 3p silicon, 496 00:24:33,650 --> 00:24:37,070 which one is more wiggly, but you knew that you needed 497 00:24:37,070 --> 00:24:39,410 to know that to answer the question, that's already-- 498 00:24:39,410 --> 00:24:45,060 that's, in my opinion, 4 out of 5 points, 499 00:24:45,060 --> 00:24:46,050 because that's the key. 500 00:24:46,050 --> 00:24:47,340 The key is what-- 501 00:24:47,340 --> 00:24:49,470 I'm trying to just get at the key things you 502 00:24:49,470 --> 00:24:52,110 need to know in computational quantum mechanics, some 503 00:24:52,110 --> 00:24:53,370 of the key ingredients. 504 00:24:53,370 --> 00:24:55,410 And that's the key is that you need more basis 505 00:24:55,410 --> 00:24:59,040 functions if the electrons function wiggles 506 00:24:59,040 --> 00:25:02,150 more or wiggles more quickly. 507 00:25:09,170 --> 00:25:10,950 AUDIENCE: But it's [INAUDIBLE]. 508 00:25:10,950 --> 00:25:12,867 JEFFREY C. GROSSMAN: What was more for carbon? 509 00:25:12,867 --> 00:25:14,670 AUDIENCE: [INAUDIBLE] 510 00:25:14,670 --> 00:25:16,662 JEFFREY C. GROSSMAN: Because the-- 511 00:25:16,662 --> 00:25:19,720 you see, it's what you said, actually. 512 00:25:19,720 --> 00:25:23,290 You have more screening in silicon. 513 00:25:23,290 --> 00:25:27,250 And so the outer electrons, they're further out, 514 00:25:27,250 --> 00:25:30,700 and they actually wiggle less. 515 00:25:30,700 --> 00:25:32,352 They're more smooth. 516 00:25:32,352 --> 00:25:33,310 That's not always true. 517 00:25:33,310 --> 00:25:35,143 But between silicon and carbon, that's true. 518 00:25:35,143 --> 00:25:37,240 I think I talked about that in lecture 2. 519 00:25:40,370 --> 00:25:43,650 And it's part of why carbon can make such strong bonds. 520 00:25:43,650 --> 00:25:46,310 So carbon has no p electrons in the core. 521 00:25:46,310 --> 00:25:47,330 Silicon does. 522 00:25:47,330 --> 00:25:49,170 So the screening is very different. 523 00:25:49,170 --> 00:25:52,250 A p electron in carbon sees no p electrons in the core. 524 00:25:52,250 --> 00:25:53,900 But a p electron in silicon does. 525 00:25:53,900 --> 00:25:55,790 It sees two p electrons in the core. 526 00:25:55,790 --> 00:25:57,950 So that screening, that shielding, 527 00:25:57,950 --> 00:25:59,930 makes a huge difference in the kind of bonding 528 00:25:59,930 --> 00:26:02,960 that these two atoms can do. 529 00:26:02,960 --> 00:26:05,180 That's why we're made of carbon and not silicon. 530 00:26:05,180 --> 00:26:07,340 But that's not the question. 531 00:26:07,340 --> 00:26:09,080 Now let's do another one. 532 00:26:09,080 --> 00:26:12,930 Materials are composed of nuclei and electrons. 533 00:26:12,930 --> 00:26:14,540 When the Kohn-Sham equation is solved, 534 00:26:14,540 --> 00:26:16,880 solutions only for electrons are obtained. 535 00:26:16,880 --> 00:26:19,430 Why do we not care about nuclei? 536 00:26:19,430 --> 00:26:21,230 Come on, that's a good one, right? 537 00:26:21,230 --> 00:26:22,460 Sam? 538 00:26:22,460 --> 00:26:24,710 AUDIENCE: So basically, nuclei are 1,000 times heavier 539 00:26:24,710 --> 00:26:25,400 than electrons. 540 00:26:25,400 --> 00:26:25,790 JEFFREY C. GROSSMAN: Right. 541 00:26:25,790 --> 00:26:27,373 AUDIENCE: But realistically, electrons 542 00:26:27,373 --> 00:26:29,840 are basically still [INAUDIBLE] motions in saying 543 00:26:29,840 --> 00:26:31,840 that electrons are [INAUDIBLE]. 544 00:26:34,380 --> 00:26:37,750 JEFFREY C. GROSSMAN: And do you remember what that's called? 545 00:26:37,750 --> 00:26:40,135 It's that guy's back, the tattoo. 546 00:26:40,135 --> 00:26:41,260 AUDIENCE: Born-Oppenheimer. 547 00:26:41,260 --> 00:26:41,990 JEFFREY C. GROSSMAN: Born-Oppenheimer. 548 00:26:41,990 --> 00:26:43,130 See, that's going to be it. 549 00:26:43,130 --> 00:26:45,850 You're always going to remember that guy's tattoo on his back, 550 00:26:45,850 --> 00:26:47,740 and you're going to think Born-Oppenheimer. 551 00:26:47,740 --> 00:26:48,975 It's effective. 552 00:26:51,555 --> 00:26:53,800 OK, and then we'll do one more. 553 00:26:56,590 --> 00:26:58,410 What does k-point sampling refer to? 554 00:26:58,410 --> 00:27:00,420 Below are the band structures computed 555 00:27:00,420 --> 00:27:01,830 for two different materials. 556 00:27:01,830 --> 00:27:04,350 Which requires more k-points to converge? 557 00:27:04,350 --> 00:27:07,800 And what I'm looking for here is not a long essay. 558 00:27:07,800 --> 00:27:12,130 It's really just a sentence to explain the reasoning. 559 00:27:12,130 --> 00:27:15,360 So somebody tell me which of these might need more k-points. 560 00:27:15,360 --> 00:27:18,060 Which band structure would need more k-points? 561 00:27:18,060 --> 00:27:18,720 I see this. 562 00:27:18,720 --> 00:27:19,410 Yes, why? 563 00:27:21,210 --> 00:27:22,585 AUDIENCE: There's more variation. 564 00:27:22,585 --> 00:27:25,200 There's more wiggles with it, so you need more points 565 00:27:25,200 --> 00:27:29,790 to get after [INAUDIBLE]. 566 00:27:29,790 --> 00:27:33,525 JEFFREY C. GROSSMAN: It's the same-- you see, these are-- 567 00:27:33,525 --> 00:27:38,870 this is also just a convergence question, OK? 568 00:27:38,870 --> 00:27:40,088 Did everybody see that? 569 00:27:40,088 --> 00:27:41,630 This is another convergence question. 570 00:27:41,630 --> 00:27:44,088 I mean, you're not going to just get convergence questions, 571 00:27:44,088 --> 00:27:45,650 but those two were. 572 00:27:48,570 --> 00:27:50,460 And then we did this one. 573 00:27:50,460 --> 00:27:52,190 Did everybody see this last time? 574 00:27:52,190 --> 00:27:53,100 OK. 575 00:27:53,100 --> 00:27:56,010 This is that band structure that you got, 576 00:27:56,010 --> 00:27:59,900 but your advisor spilled coffee on it, 577 00:27:59,900 --> 00:28:03,410 and this is the only copy you have. 578 00:28:03,410 --> 00:28:06,350 And so I'm not-- you won't have a coffee-spilled-- well, 579 00:28:06,350 --> 00:28:08,420 you might have a coffee-spilled band structure, 580 00:28:08,420 --> 00:28:11,690 because it's kind of a fun way to ask questions. 581 00:28:11,690 --> 00:28:15,170 But you'll definitely have a question about band structures. 582 00:28:18,123 --> 00:28:20,540 So make sure you kind of are comfortable with the concepts 583 00:28:20,540 --> 00:28:22,486 that I'm going to-- 584 00:28:22,486 --> 00:28:25,160 we'll review right now with band structures. 585 00:28:25,160 --> 00:28:27,860 So those are a couple of nice examples of the kinds 586 00:28:27,860 --> 00:28:29,315 of problems you might get. 587 00:28:29,315 --> 00:28:32,420 AUDIENCE: Yeah, you can see a coffee stain in the example. 588 00:28:32,420 --> 00:28:34,657 Don't [INAUDIBLE] because [INAUDIBLE] put in there. 589 00:28:34,657 --> 00:28:36,740 JEFFREY C. GROSSMAN: Yeah, we're going to actually 590 00:28:36,740 --> 00:28:38,580 use real coffee this time. 591 00:28:38,580 --> 00:28:44,350 [LAUGHTER] OK, good. 592 00:28:44,350 --> 00:28:47,860 So what we're going to do now-- 593 00:28:47,860 --> 00:28:48,690 so any questions? 594 00:28:48,690 --> 00:28:49,770 The questions are great. 595 00:28:49,770 --> 00:28:52,920 It's really helpful-- questions on the p set, questions 596 00:28:52,920 --> 00:28:57,220 on those questions? 597 00:28:57,220 --> 00:29:00,870 Questions on the questions? 598 00:29:00,870 --> 00:29:01,710 Questions about-- 599 00:29:01,710 --> 00:29:02,627 AUDIENCE: The Celtics. 600 00:29:02,627 --> 00:29:04,085 JEFFREY C. GROSSMAN: What was that? 601 00:29:04,085 --> 00:29:04,910 The Celtics? 602 00:29:04,910 --> 00:29:06,320 They're going to wrap it up. 603 00:29:06,320 --> 00:29:08,240 Yeah, tonight. 604 00:29:08,240 --> 00:29:16,670 Anyway, OK-- I just like sharing a little something like this 605 00:29:16,670 --> 00:29:17,570 each time. 606 00:29:17,570 --> 00:29:19,990 Has everybody seen this one? 607 00:29:19,990 --> 00:29:22,690 With great power comes great responsibility. 608 00:29:22,690 --> 00:29:24,520 Vision without action is a dream. 609 00:29:24,520 --> 00:29:26,695 Action without vision is a nightmare. 610 00:29:29,200 --> 00:29:30,970 This is my reminder. 611 00:29:30,970 --> 00:29:34,810 When you do calculations, this is what counts most. 612 00:29:37,570 --> 00:29:39,880 don't just start computing. 613 00:29:39,880 --> 00:29:41,130 Think about what you're doing. 614 00:29:43,860 --> 00:29:47,310 I'm going to take you through a little bit of a tour of some 615 00:29:47,310 --> 00:29:48,990 of the key concepts that I think would 616 00:29:48,990 --> 00:29:53,400 be important to know about that you might get questions on. 617 00:29:53,400 --> 00:29:54,960 You might get a question on-- 618 00:29:54,960 --> 00:29:57,570 and I think there's a practice quiz question or two 619 00:29:57,570 --> 00:30:00,240 on some of these-- 620 00:30:00,240 --> 00:30:05,430 concepts of what led to quantum mechanics, which we talked 621 00:30:05,430 --> 00:30:07,300 about in the first lecture. 622 00:30:07,300 --> 00:30:09,940 So why did we need a new physics? 623 00:30:09,940 --> 00:30:11,300 Why did we need something new? 624 00:30:16,160 --> 00:30:17,750 And the fact that you have-- 625 00:30:20,360 --> 00:30:27,080 as a result of a lot of research in that time, what came out 626 00:30:27,080 --> 00:30:32,190 of it was that matter has both wave and particle character. 627 00:30:32,190 --> 00:30:34,340 So we've talked about this experiment. 628 00:30:34,340 --> 00:30:35,910 We've talked about that experiment. 629 00:30:35,910 --> 00:30:37,640 So you would know if I asked a question 630 00:30:37,640 --> 00:30:41,750 about those experiments, maybe, one of them. 631 00:30:41,750 --> 00:30:48,850 And we found that that, actually, light 632 00:30:48,850 --> 00:30:52,960 can behave like a particle, and matter can behave like a wave. 633 00:30:52,960 --> 00:30:55,840 And it would have a wave vector k 634 00:30:55,840 --> 00:31:00,430 that's related to its momentum and a frequency. 635 00:31:00,430 --> 00:31:02,600 And that's kind of really cool. 636 00:31:02,600 --> 00:31:07,695 So if I asked you what the wavelength of a baseball was-- 637 00:31:07,695 --> 00:31:09,820 I think that might have been on the practice quiz-- 638 00:31:09,820 --> 00:31:14,980 then that's something you could compute, for example. 639 00:31:14,980 --> 00:31:18,190 I won't ask you that, but you kind of 640 00:31:18,190 --> 00:31:22,450 could compute the wavelength of something. 641 00:31:22,450 --> 00:31:23,680 And then that took us to-- 642 00:31:26,610 --> 00:31:30,220 well, OK, so you have to represent matter now 643 00:31:30,220 --> 00:31:31,570 with waves. 644 00:31:31,570 --> 00:31:36,040 So we're going to have this function to do that. 645 00:31:36,040 --> 00:31:37,720 So that took us to this function. 646 00:31:37,720 --> 00:31:39,580 We said there's going to be this function. 647 00:31:39,580 --> 00:31:40,870 It's a wave function. 648 00:31:40,870 --> 00:31:42,700 Well, that's a creative name. 649 00:31:42,700 --> 00:31:45,550 It's a function that represents waves. 650 00:31:45,550 --> 00:31:46,910 OK, that's good. 651 00:31:46,910 --> 00:31:49,270 And we also said-- 652 00:31:49,270 --> 00:31:51,340 we didn't really explain this much, but we said, 653 00:31:51,340 --> 00:31:52,810 but you can't-- 654 00:31:52,810 --> 00:31:55,960 we don't actually know much about the physical meaning 655 00:31:55,960 --> 00:31:57,190 of this function. 656 00:31:57,190 --> 00:31:59,650 But we do know that, when you square it, 657 00:31:59,650 --> 00:32:01,600 or since it's complex, you multiply it 658 00:32:01,600 --> 00:32:03,430 by its complex conjugate, that you 659 00:32:03,430 --> 00:32:08,140 get the density of this quantum mechanical particle. 660 00:32:08,140 --> 00:32:10,010 And we said, this is it. 661 00:32:10,010 --> 00:32:11,470 This is what we need. 662 00:32:11,470 --> 00:32:13,840 We need this function, because in quantum mechanics, 663 00:32:13,840 --> 00:32:18,910 that function tells you where electrons are, 664 00:32:18,910 --> 00:32:20,607 the probability density of electrons. 665 00:32:20,607 --> 00:32:21,940 And so that's the thing we need. 666 00:32:21,940 --> 00:32:23,357 Because if you know that, then you 667 00:32:23,357 --> 00:32:25,060 get all these other properties, see? 668 00:32:25,060 --> 00:32:29,390 Once you have this, that's what the DOS comes from. 669 00:32:29,390 --> 00:32:32,200 That's what the band structure comes from. 670 00:32:32,200 --> 00:32:35,710 It came from solving for that. 671 00:32:35,710 --> 00:32:38,710 And then the question is, well, what are you solving? 672 00:32:38,710 --> 00:32:41,490 And so what we needed there was the F 673 00:32:41,490 --> 00:32:44,040 equals MA of quantum mechanics. 674 00:32:44,040 --> 00:32:47,340 We needed the equation that governs the behavior 675 00:32:47,340 --> 00:32:51,020 of this wave function. 676 00:32:51,020 --> 00:32:53,190 And that's the Schrodinger equation. 677 00:32:53,190 --> 00:32:53,690 That's it. 678 00:32:58,180 --> 00:32:59,030 This is it, right? 679 00:32:59,030 --> 00:33:00,697 So do we have the function that we need, 680 00:33:00,697 --> 00:33:02,822 which when we solve it, we get all these properties 681 00:33:02,822 --> 00:33:04,240 that we really care about, that we 682 00:33:04,240 --> 00:33:06,220 can use to make solar cells and solar fuels 683 00:33:06,220 --> 00:33:08,860 and lots of other things? 684 00:33:08,860 --> 00:33:10,480 There is an equation we need to solve 685 00:33:10,480 --> 00:33:12,493 to get that wave function, and that equation 686 00:33:12,493 --> 00:33:13,660 is the Schrodinger equation. 687 00:33:13,660 --> 00:33:16,450 And we took time out, because we don't like time. 688 00:33:16,450 --> 00:33:18,440 It just complicates things. 689 00:33:18,440 --> 00:33:21,805 And so we did it for the stationary solution. 690 00:33:25,030 --> 00:33:28,720 And the Schrodinger equation is H psi equals E psi, 691 00:33:28,720 --> 00:33:30,860 where H is the total energy. 692 00:33:30,860 --> 00:33:35,140 So it's the kinetic energy plus the potential energy. 693 00:33:35,140 --> 00:33:38,470 And when you write these out, you 694 00:33:38,470 --> 00:33:43,570 write out the kinetic energy as this second derivative. 695 00:33:43,570 --> 00:33:46,840 And the potential-- well, that depends 696 00:33:46,840 --> 00:33:48,410 on what we're talking about. 697 00:33:48,410 --> 00:33:52,750 But if we're talking about, say, an electron in a hydrogen atom, 698 00:33:52,750 --> 00:33:55,690 then it's E squared over r. 699 00:33:55,690 --> 00:33:58,300 That's your potential, the potential that that 700 00:33:58,300 --> 00:33:59,650 charged particle feels. 701 00:34:02,490 --> 00:34:04,320 So that's a hydrogen atom. 702 00:34:04,320 --> 00:34:06,170 That's the electron in a hydrogen atom. 703 00:34:09,840 --> 00:34:12,270 I'm going through this quickly, because I think we are all 704 00:34:12,270 --> 00:34:13,260 feeling OK about this. 705 00:34:13,260 --> 00:34:16,409 But if anyone has questions, please raise your hand, please, 706 00:34:16,409 --> 00:34:19,290 because if you have a question, it's very likely 707 00:34:19,290 --> 00:34:22,969 someone else has the same question. 708 00:34:22,969 --> 00:34:26,250 Any questions? 709 00:34:26,250 --> 00:34:29,850 Now, you can solve this equation, actually, 710 00:34:29,850 --> 00:34:31,290 very easily. 711 00:34:31,290 --> 00:34:36,730 We did this, I think, in the second lecture, maybe. 712 00:34:36,730 --> 00:34:39,659 And you get solutions for that wave function. 713 00:34:39,659 --> 00:34:42,570 And we talked about how one of the key results 714 00:34:42,570 --> 00:34:46,139 here is that you get quantization 715 00:34:46,139 --> 00:34:47,880 of the energies of the wave function. 716 00:34:47,880 --> 00:34:50,400 And what that means is that the energies can only 717 00:34:50,400 --> 00:34:51,550 have certain values-- 718 00:34:51,550 --> 00:34:52,615 nothing in between. 719 00:34:52,615 --> 00:34:57,090 And we talked about the magic of that 720 00:34:57,090 --> 00:35:00,780 and how that explains these spectral lines that 721 00:35:00,780 --> 00:35:03,420 were observed long before. 722 00:35:03,420 --> 00:35:06,240 It finally explained those. 723 00:35:06,240 --> 00:35:08,810 So I don't know like calculating the energy differences here 724 00:35:08,810 --> 00:35:11,220 or how much energy it takes to allow electrons to move 725 00:35:11,220 --> 00:35:13,890 from one level to another-- 726 00:35:13,890 --> 00:35:15,840 that sounds like a good problem to me. 727 00:35:21,640 --> 00:35:23,420 and units, so forth. 728 00:35:23,420 --> 00:35:26,290 Now, the other piece of ingredient 729 00:35:26,290 --> 00:35:30,010 that was really important is that, actually, electrons-- 730 00:35:30,010 --> 00:35:33,790 they have this angular moment-- they have this spin. 731 00:35:33,790 --> 00:35:35,710 And it was observed by putting them-- 732 00:35:35,710 --> 00:35:39,600 shooting them through a big magnet and basically finding 733 00:35:39,600 --> 00:35:40,770 that-- 734 00:35:40,770 --> 00:35:41,520 what was observed? 735 00:35:41,520 --> 00:35:44,850 What was observed wasn't just that they had spin 736 00:35:44,850 --> 00:35:47,340 but that they only had one of two kinds of spin. 737 00:35:47,340 --> 00:35:49,055 So instead of getting a spread, you 738 00:35:49,055 --> 00:35:50,430 would think you would be applying 739 00:35:50,430 --> 00:35:53,700 a force on these electrons, which are magnetic, 740 00:35:53,700 --> 00:35:55,740 since they're spinning. 741 00:35:55,740 --> 00:35:56,700 But they're not. 742 00:35:56,700 --> 00:36:00,090 But that's how we like to think of them in our classical minds. 743 00:36:00,090 --> 00:36:02,250 You would think that you would get 744 00:36:02,250 --> 00:36:06,600 a nice continuous spread of force acting on them, causing 745 00:36:06,600 --> 00:36:07,710 them to separate. 746 00:36:07,710 --> 00:36:10,770 But instead, you only get two spots. 747 00:36:10,770 --> 00:36:12,930 That was really important, because they told us 748 00:36:12,930 --> 00:36:19,000 that these there's another kind of quantum mechanical number, 749 00:36:19,000 --> 00:36:22,500 which is the spin number, which can be up or down-- 750 00:36:22,500 --> 00:36:25,120 only up or down. 751 00:36:25,120 --> 00:36:29,020 And then you put that together, and you put together 752 00:36:29,020 --> 00:36:31,480 your solution for the Schrodinger equation, 753 00:36:31,480 --> 00:36:33,620 and voila. 754 00:36:33,620 --> 00:36:39,550 You get, essentially-- oh, you add on a little bit of Pauli. 755 00:36:39,550 --> 00:36:42,010 You put in some Pauli exclusions-- 756 00:36:42,010 --> 00:36:44,130 just a little bit. 757 00:36:44,130 --> 00:36:45,620 You don't want to over-Pauli-- 758 00:36:45,620 --> 00:36:48,320 anyway, never mind. 759 00:36:48,320 --> 00:36:51,050 Which it says that, OK, we got these quantum numbers-- 760 00:36:51,050 --> 00:36:54,260 you know, N, L, M, and now the spin. 761 00:36:54,260 --> 00:36:58,070 And no two electrons can have the same set, 762 00:36:58,070 --> 00:37:01,370 which results in the fact that you cannot put more than two 763 00:37:01,370 --> 00:37:03,085 electrons in one of these energy levels. 764 00:37:03,085 --> 00:37:04,460 And remember, these energy levels 765 00:37:04,460 --> 00:37:06,200 are kind of like the key ingredient 766 00:37:06,200 --> 00:37:09,237 we're after in this class. 767 00:37:09,237 --> 00:37:10,820 It's really one of the key ingredients 768 00:37:10,820 --> 00:37:13,520 we're after, where do those electrons want to sit, 769 00:37:13,520 --> 00:37:17,790 because it tells us so much about properties of materials 770 00:37:17,790 --> 00:37:20,780 that are interesting. 771 00:37:20,780 --> 00:37:23,750 Now, that really allows you to go to a description 772 00:37:23,750 --> 00:37:25,620 of the whole periodic table. 773 00:37:25,620 --> 00:37:29,090 The problem is that that was a description based 774 00:37:29,090 --> 00:37:32,590 on one electron and one proton. 775 00:37:32,590 --> 00:37:33,580 We solve for that. 776 00:37:33,580 --> 00:37:35,000 We could solve for that. 777 00:37:35,000 --> 00:37:37,348 And so we did, and we got the levels, 778 00:37:37,348 --> 00:37:38,390 and that was really neat. 779 00:37:38,390 --> 00:37:40,190 And then we had rules about how to fill them, 780 00:37:40,190 --> 00:37:41,240 and that was really neat. 781 00:37:41,240 --> 00:37:42,790 And then you can actually explain 782 00:37:42,790 --> 00:37:45,460 a lot of chemistry that way. 783 00:37:45,460 --> 00:37:49,150 You get your S and your P and your D orbitals, 784 00:37:49,150 --> 00:37:50,062 and you fill them. 785 00:37:50,062 --> 00:37:51,520 The problem is that, actually, when 786 00:37:51,520 --> 00:37:53,920 you have anything but hydrogen, you 787 00:37:53,920 --> 00:37:55,120 have more than one electron. 788 00:37:57,640 --> 00:38:02,620 and so that really requires going back to the Schrodinger 789 00:38:02,620 --> 00:38:06,460 equation and adding in the interactions between electrons 790 00:38:06,460 --> 00:38:10,560 that was not in the original hydrogen atom. 791 00:38:10,560 --> 00:38:12,300 And that's hard. 792 00:38:12,300 --> 00:38:15,890 That's the hard part, hard stuff. 793 00:38:15,890 --> 00:38:22,370 And so we turn to computation. 794 00:38:22,370 --> 00:38:24,260 That's really hard to do analytically, 795 00:38:24,260 --> 00:38:28,950 and it gets much, much worse the more electrons you have. 796 00:38:28,950 --> 00:38:31,270 any questions up to this point? 797 00:38:31,270 --> 00:38:32,600 All right. 798 00:38:32,600 --> 00:38:33,890 So how do we do that? 799 00:38:33,890 --> 00:38:36,820 Well, you've got to-- so we're using computation, 800 00:38:36,820 --> 00:38:38,620 but you can't just throw this onto a grid 801 00:38:38,620 --> 00:38:39,880 or throw this into MATLAB. 802 00:38:39,880 --> 00:38:42,860 It still isn't doable. 803 00:38:42,860 --> 00:38:45,010 And so there's sort of two branches 804 00:38:45,010 --> 00:38:48,310 in computational quantum mechanics, one that loosely 805 00:38:48,310 --> 00:38:51,130 is labeled quantum chemistry and the other kind of more 806 00:38:51,130 --> 00:38:53,770 solid-state physics, density functional theory. 807 00:38:53,770 --> 00:38:56,682 And both of them make approximations. 808 00:38:56,682 --> 00:38:58,390 And we talked about those approximations. 809 00:38:58,390 --> 00:39:02,140 And what they're approximating is the Schrodinger equation. 810 00:39:02,140 --> 00:39:03,880 They're simplifying it, because even as 811 00:39:03,880 --> 00:39:05,530 simple as that may look-- 812 00:39:05,530 --> 00:39:07,700 just throw that into MATLAB-- 813 00:39:07,700 --> 00:39:08,830 it doesn't happen. 814 00:39:08,830 --> 00:39:11,650 You can't solve it when you have more than a couple 815 00:39:11,650 --> 00:39:13,380 of electrons-- 816 00:39:13,380 --> 00:39:16,967 five electrons, I don't know, six. 817 00:39:16,967 --> 00:39:18,050 That won't be on the quiz. 818 00:39:18,050 --> 00:39:18,980 [LAUGHS] 819 00:39:18,980 --> 00:39:21,080 But you just can't solve it exactly on a computer 820 00:39:21,080 --> 00:39:22,910 unless you have the age of the universe. 821 00:39:22,910 --> 00:39:25,190 And even then, it's too hard. 822 00:39:25,190 --> 00:39:27,080 So we've got to simplify this equation. 823 00:39:27,080 --> 00:39:30,590 And mostly in the quantum chemistry world, what you do 824 00:39:30,590 --> 00:39:33,330 is you simplify this. 825 00:39:33,330 --> 00:39:36,020 We talked about using basis sets, basis functions 826 00:39:36,020 --> 00:39:36,830 to represent this. 827 00:39:36,830 --> 00:39:40,810 Well, you can restrict the degrees of freedom 828 00:39:40,810 --> 00:39:44,400 in that function, as well. 829 00:39:44,400 --> 00:39:46,900 And that makes that equation much easier. 830 00:39:46,900 --> 00:39:49,910 And the other thing you can do is you can actually change-- 831 00:39:49,910 --> 00:39:51,960 so that's changing this part, and the other thing 832 00:39:51,960 --> 00:39:54,120 is you could change this part. 833 00:39:54,120 --> 00:39:59,400 And that's what physicists mostly did, and now everyone 834 00:39:59,400 --> 00:40:01,720 holds hands and sings "Kumbaya," and everyone's happy. 835 00:40:01,720 --> 00:40:05,580 Back then, there was a lot of two fields, 836 00:40:05,580 --> 00:40:07,950 physicists versus chemists, and all that. 837 00:40:07,950 --> 00:40:11,670 But we're all happy together now. 838 00:40:11,670 --> 00:40:13,800 So chemists do density functional theory. 839 00:40:13,800 --> 00:40:18,400 Physicists don't mind wave function-based methods, 840 00:40:18,400 --> 00:40:20,780 as they're called. 841 00:40:20,780 --> 00:40:24,490 The result-- and this was one of my red flag 842 00:40:24,490 --> 00:40:27,160 key results here is that what you've 843 00:40:27,160 --> 00:40:31,890 done when you do this is you have taken a problem that 844 00:40:31,890 --> 00:40:33,945 involved all of these interactions-- remember, 845 00:40:33,945 --> 00:40:37,170 1 over r 1, 2 meant taking into account 846 00:40:37,170 --> 00:40:40,410 the interaction between electron 1 and electron 2. 847 00:40:40,410 --> 00:40:42,420 And that just gets really painful and hard. 848 00:40:42,420 --> 00:40:45,960 And so what you've done in both categories 849 00:40:45,960 --> 00:40:49,080 is you've completely changed the picture into what's 850 00:40:49,080 --> 00:40:50,290 called a mean field picture. 851 00:40:50,290 --> 00:40:53,430 So each electron is only now really solved 852 00:40:53,430 --> 00:40:58,290 in the context of an average field of the other electrons. 853 00:40:58,290 --> 00:41:00,090 That's the simplification key. 854 00:41:00,090 --> 00:41:01,950 That's the key simplification. 855 00:41:01,950 --> 00:41:04,470 So the mean field methods are really 856 00:41:04,470 --> 00:41:06,600 what enable us to do computational quantum 857 00:41:06,600 --> 00:41:08,745 mechanics for large systems. 858 00:41:13,160 --> 00:41:16,880 I don't really think I need to review this 859 00:41:16,880 --> 00:41:19,580 too much, because I did just review this, I think, 860 00:41:19,580 --> 00:41:21,710 a week ago. 861 00:41:21,710 --> 00:41:24,890 But the density is a nice thing to work with, 862 00:41:24,890 --> 00:41:27,860 because unlike the function with sort of-- if you wanted a grid 863 00:41:27,860 --> 00:41:29,540 to represent each-- 864 00:41:29,540 --> 00:41:34,610 a grid of points, even as the number of atoms in the system 865 00:41:34,610 --> 00:41:39,075 grows, the density grid is just the same. 866 00:41:39,075 --> 00:41:41,450 So the number of points you need to represent the density 867 00:41:41,450 --> 00:41:43,075 is constant, while the number of points 868 00:41:43,075 --> 00:41:46,230 you would need to represent psi grows exponentially. 869 00:41:46,230 --> 00:41:52,340 So it's a really hard problem in the context of scaling 870 00:41:52,340 --> 00:41:54,830 with size for the wave function, but the density 871 00:41:54,830 --> 00:41:59,072 offers this really nice scaling. 872 00:41:59,072 --> 00:42:01,030 And so that's what density functional theory is 873 00:42:01,030 --> 00:42:03,610 is it's a method that relates-- 874 00:42:03,610 --> 00:42:08,830 it shows that the density can be related to the wave function. 875 00:42:08,830 --> 00:42:10,570 And then you just work with the density, 876 00:42:10,570 --> 00:42:12,160 and you throw out the wave function. 877 00:42:12,160 --> 00:42:14,980 You bring it back in later, but that's basically 878 00:42:14,980 --> 00:42:16,990 what the theory does. 879 00:42:16,990 --> 00:42:19,190 The problem is that it pushes out-- 880 00:42:19,190 --> 00:42:26,880 it has this sort of term that you talked about in lecture 3 881 00:42:26,880 --> 00:42:32,420 or 4 that you have to kind of approximate, this exchange 882 00:42:32,420 --> 00:42:35,690 correlation potential. 883 00:42:35,690 --> 00:42:38,510 We talked about that. 884 00:42:38,510 --> 00:42:42,530 And the exchange correlation potential-- let's get to that-- 885 00:42:42,530 --> 00:42:43,730 is not known. 886 00:42:43,730 --> 00:42:46,190 If you knew it, it would be, actually, an exact method. 887 00:42:46,190 --> 00:42:48,240 But it's not, and so you make approximations. 888 00:42:48,240 --> 00:42:50,240 And these are actually two of the approximations 889 00:42:50,240 --> 00:42:55,910 that you have as options in the NanoLab tools. 890 00:42:55,910 --> 00:43:02,270 Now, what these approximations are is not part of this class. 891 00:43:02,270 --> 00:43:09,170 That gets into kind of more complicated equations 892 00:43:09,170 --> 00:43:11,520 that we would have to cover that I don't want to do. 893 00:43:11,520 --> 00:43:14,150 But what I want you to pull out from this 894 00:43:14,150 --> 00:43:22,690 is that we are not solving the Schrodinger equation exactly. 895 00:43:22,690 --> 00:43:24,750 We are making approximations. 896 00:43:24,750 --> 00:43:27,580 And those approximations need to be checked. 897 00:43:27,580 --> 00:43:32,050 So you see, there's two kinds of convergence here. 898 00:43:32,050 --> 00:43:33,760 That's the key, right? 899 00:43:33,760 --> 00:43:37,780 And this is where I come with responsibility. 900 00:43:37,780 --> 00:43:44,600 One kind of convergence is k-points, basis sets. 901 00:43:44,600 --> 00:43:48,710 But another kind of convergence is, where are you 902 00:43:48,710 --> 00:43:51,110 in accuracy space? 903 00:43:51,110 --> 00:43:52,500 Where are you? 904 00:43:52,500 --> 00:43:55,430 Do you know? 905 00:43:55,430 --> 00:43:57,380 Because you are making approximations. 906 00:43:57,380 --> 00:43:59,900 When you pull down that option on the toolkit 907 00:43:59,900 --> 00:44:02,690 to say GGA or LDA, what you're doing is you're 908 00:44:02,690 --> 00:44:04,790 changing the form of this. 909 00:44:04,790 --> 00:44:06,620 Which one is right? 910 00:44:06,620 --> 00:44:09,470 You're still not solving the equations exactly. 911 00:44:09,470 --> 00:44:13,262 So how do if you're right? 912 00:44:13,262 --> 00:44:14,720 Throw that out there as a question. 913 00:44:17,480 --> 00:44:19,245 AUDIENCE: Find an experimentalist. 914 00:44:19,245 --> 00:44:21,120 JEFFREY C. GROSSMAN: Find an experimentalist. 915 00:44:21,120 --> 00:44:23,668 Bother them. 916 00:44:23,668 --> 00:44:25,020 Say, can you measure this? 917 00:44:25,020 --> 00:44:27,570 And they say, no, are you crazy? 918 00:44:27,570 --> 00:44:31,140 My advisor just told me to work 90 hours a week 919 00:44:31,140 --> 00:44:32,530 on something else. 920 00:44:32,530 --> 00:44:35,280 So then what do you do, because it's not in the literature? 921 00:44:35,280 --> 00:44:35,985 Yeah? 922 00:44:35,985 --> 00:44:38,027 AUDIENCE: Try a bunch of different approximations 923 00:44:38,027 --> 00:44:39,270 and see if any of them agree. 924 00:44:39,270 --> 00:44:40,980 JEFFREY C. GROSSMAN: See if any of them agree. 925 00:44:40,980 --> 00:44:43,200 Let's suppose half of them agree, and half of them 926 00:44:43,200 --> 00:44:45,100 disagree. 927 00:44:45,100 --> 00:44:48,230 Say I had 10 functionals to choose from. 928 00:44:48,230 --> 00:44:49,610 What else could you do? 929 00:44:49,610 --> 00:44:50,630 Or are you done? 930 00:44:50,630 --> 00:44:52,280 Is that good enough? 931 00:44:52,280 --> 00:44:53,983 AUDIENCE: Maybe run one more. 932 00:44:53,983 --> 00:44:55,400 JEFFREY C. GROSSMAN: Run one more. 933 00:44:55,400 --> 00:44:56,480 AUDIENCE: The tiebreaker. 934 00:44:56,480 --> 00:44:58,022 JEFFREY C. GROSSMAN: The tiebreaker-- 935 00:44:58,022 --> 00:44:58,554 I love it. 936 00:44:58,554 --> 00:45:01,280 [LAUGHTER] 937 00:45:01,280 --> 00:45:04,280 Sadly, there are papers in the literature that kind of 938 00:45:04,280 --> 00:45:06,440 take that approach. 939 00:45:06,440 --> 00:45:08,600 It's a little too loosey-goosey. 940 00:45:08,600 --> 00:45:09,920 But it was a good idea. 941 00:45:09,920 --> 00:45:10,760 OK, what else? 942 00:45:10,760 --> 00:45:12,050 Well, is it good enough? 943 00:45:12,050 --> 00:45:15,185 I mean, if I had 10 functionals-- 944 00:45:15,185 --> 00:45:17,060 by the way, there are hundreds of functionals 945 00:45:17,060 --> 00:45:19,060 now to choose from in density functional theory. 946 00:45:19,060 --> 00:45:22,100 If I had 10, and half of them agreed, 947 00:45:22,100 --> 00:45:24,580 but the other half didn't, what do I do? 948 00:45:27,484 --> 00:45:29,910 AUDIENCE: Apply quantum chemistry. 949 00:45:29,910 --> 00:45:32,452 JEFFREY C. GROSSMAN: OK, why? 950 00:45:32,452 --> 00:45:34,400 AUDIENCE: It's a whole different theory. 951 00:45:34,400 --> 00:45:36,692 JEFFREY C. GROSSMAN: Whole different theory-- good, OK. 952 00:45:36,692 --> 00:45:38,651 Go to a different theory for quantum mechanics. 953 00:45:38,651 --> 00:45:40,375 See what that agrees with. 954 00:45:40,375 --> 00:45:42,910 But see, that may have its own whole-- 955 00:45:42,910 --> 00:45:47,680 it does have its own whole world of approximations. 956 00:45:47,680 --> 00:45:49,870 But that's the right-- 957 00:45:49,870 --> 00:45:52,960 that's sort of the right way to think about it, because there 958 00:45:52,960 --> 00:45:54,940 are theories that are more accurate and less 959 00:45:54,940 --> 00:45:57,220 accurate in how they solve for-- 960 00:45:57,220 --> 00:45:59,390 how they simplify the Schrodinger equation. 961 00:45:59,390 --> 00:46:01,320 So you can try to go to more accurate, or what 962 00:46:01,320 --> 00:46:03,070 are known to be better accurate, theories. 963 00:46:03,070 --> 00:46:05,750 Now, there's one other thing to do. 964 00:46:05,750 --> 00:46:10,090 I told you that, in this particular case, 965 00:46:10,090 --> 00:46:14,380 it's a solar fuel that you just calculated. 966 00:46:14,380 --> 00:46:20,100 You think it's going to be revolutionary 967 00:46:20,100 --> 00:46:22,200 but only by one functional. 968 00:46:22,200 --> 00:46:25,228 The other functional says it's really bad. 969 00:46:25,228 --> 00:46:26,520 You went to an experimentalist. 970 00:46:26,520 --> 00:46:27,690 They said no. 971 00:46:27,690 --> 00:46:29,310 And you can't do higher-level theory. 972 00:46:31,840 --> 00:46:34,089 Anything else you can do? 973 00:46:34,089 --> 00:46:35,510 AUDIENCE: Take a poll? 974 00:46:35,510 --> 00:46:38,456 JEFFREY C. GROSSMAN: Take a poll [LAUGHS] of your group members? 975 00:46:38,456 --> 00:46:41,160 [LAUGHS] That's good. 976 00:46:41,160 --> 00:46:45,290 I like that-- computational people, people computing. 977 00:46:45,290 --> 00:46:46,320 What else? 978 00:46:46,320 --> 00:46:47,803 AUDIENCE: Request more funding. 979 00:46:47,803 --> 00:46:49,220 JEFFREY C. GROSSMAN: What is that? 980 00:46:49,220 --> 00:46:50,720 AUDIENCE: I said, request more funding. 981 00:46:50,720 --> 00:46:52,512 JEFFREY C. GROSSMAN: Request more funding-- 982 00:46:52,512 --> 00:46:55,190 you're talking like a professor. 983 00:46:55,190 --> 00:46:56,330 [LAUGHTER] 984 00:46:56,330 --> 00:46:56,870 What else? 985 00:46:56,870 --> 00:46:57,800 Anything else? 986 00:46:57,800 --> 00:46:59,390 There is something else you can do. 987 00:46:59,390 --> 00:47:00,170 So the key is-- 988 00:47:00,170 --> 00:47:03,760 I said that the experiment for that fuel hasn't been done. 989 00:47:03,760 --> 00:47:04,260 But-- 990 00:47:04,260 --> 00:47:05,830 AUDIENCE: Try a different fuel. 991 00:47:05,830 --> 00:47:07,210 JEFFREY C. GROSSMAN: OK. 992 00:47:07,210 --> 00:47:11,050 Use the same level theory on a system 993 00:47:11,050 --> 00:47:13,960 that has been done that's related, 994 00:47:13,960 --> 00:47:17,630 that's closely related. 995 00:47:17,630 --> 00:47:21,310 While I modified azobenzenes and make a good fuel, 996 00:47:21,310 --> 00:47:22,660 that hasn't been made yet. 997 00:47:22,660 --> 00:47:24,280 But azobenzene has. 998 00:47:24,280 --> 00:47:26,410 Did my theory work well for all of the data 999 00:47:26,410 --> 00:47:28,630 I can get my hands on that's relevant to what I'm 1000 00:47:28,630 --> 00:47:31,760 simulating for that material? 1001 00:47:31,760 --> 00:47:33,940 This is validation. 1002 00:47:33,940 --> 00:47:34,990 This is validation. 1003 00:47:34,990 --> 00:47:37,060 It's not the same as convergence. 1004 00:47:37,060 --> 00:47:39,280 I said there's sort of two kinds of convergence. 1005 00:47:39,280 --> 00:47:40,930 This kind is called validation, and it 1006 00:47:40,930 --> 00:47:43,330 is critical in computation. 1007 00:47:43,330 --> 00:47:46,730 It is a critical part of computation. 1008 00:47:46,730 --> 00:47:49,130 Please don't go away from this class 1009 00:47:49,130 --> 00:47:53,010 without remembering that part. 1010 00:47:53,010 --> 00:47:54,480 Know where you are. 1011 00:47:54,480 --> 00:47:56,670 Test your calculations. 1012 00:47:56,670 --> 00:47:59,150 Be confident in them because you validated them. 1013 00:48:01,960 --> 00:48:05,830 Too much computation goes on that doesn't have that, 1014 00:48:05,830 --> 00:48:07,780 and it's a lot of wasted time-- 1015 00:48:07,780 --> 00:48:10,590 [LAUGHS] computer time, but also people time. 1016 00:48:13,460 --> 00:48:17,240 Now, so we can get a lot of properties. 1017 00:48:17,240 --> 00:48:19,103 We can get properties of-- 1018 00:48:19,103 --> 00:48:21,020 I've talked about lots of different properties 1019 00:48:21,020 --> 00:48:21,860 you can get. 1020 00:48:21,860 --> 00:48:25,220 I won't ask you anything on the test about properties 1021 00:48:25,220 --> 00:48:29,840 we haven't actually really talked about in class, OK? 1022 00:48:29,840 --> 00:48:33,080 But you can calculate a lot of things. 1023 00:48:33,080 --> 00:48:34,370 We just talked about this. 1024 00:48:34,370 --> 00:48:37,863 The one thing-- OK, did you exit the scf at the right loop? 1025 00:48:37,863 --> 00:48:40,280 Don't worry about that, because the code just sort of does 1026 00:48:40,280 --> 00:48:41,240 that for you. 1027 00:48:41,240 --> 00:48:42,413 Was my basis big enough? 1028 00:48:42,413 --> 00:48:43,580 We talked about that, right? 1029 00:48:43,580 --> 00:48:47,060 Convergence for molecules-- was my box big enough? 1030 00:48:47,060 --> 00:48:50,368 Now, why do I have a box for molecules? 1031 00:48:50,368 --> 00:48:51,410 What does that even mean? 1032 00:48:54,180 --> 00:48:54,944 Yeah? 1033 00:48:54,944 --> 00:48:57,569 AUDIENCE: So you're going to use plane waves as your basic set, 1034 00:48:57,569 --> 00:48:58,740 and they're periodic. 1035 00:48:58,740 --> 00:49:00,828 And a real molecule's not going to be periodic. 1036 00:49:00,828 --> 00:49:03,280 So you don't want to have it see itself. 1037 00:49:03,280 --> 00:49:04,860 So you need a really big box. 1038 00:49:04,860 --> 00:49:06,440 JEFFREY C. GROSSMAN: Yeah, exactly. 1039 00:49:06,440 --> 00:49:07,440 Exactly. 1040 00:49:07,440 --> 00:49:08,790 So if I have-- 1041 00:49:08,790 --> 00:49:13,668 so a lot of these codes, especially plane-wave codes, 1042 00:49:13,668 --> 00:49:15,210 were originally developed for solids. 1043 00:49:15,210 --> 00:49:18,210 But they work fine for molecules. 1044 00:49:18,210 --> 00:49:20,130 Actually SIESTA's not even a plane-wave code. 1045 00:49:20,130 --> 00:49:22,070 It uses a different kind of basis. 1046 00:49:22,070 --> 00:49:27,480 It uses a more Gaussian-like, localized functions basis. 1047 00:49:27,480 --> 00:49:30,240 But it's still a periodic box. 1048 00:49:30,240 --> 00:49:32,880 It's based on a periodic box. 1049 00:49:32,880 --> 00:49:39,340 So that means that when you input something like an atom, 1050 00:49:39,340 --> 00:49:44,330 if I want to simulate that one atom, then 1051 00:49:44,330 --> 00:49:53,360 I need to make sure that I leave enough space so that it's not 1052 00:49:53,360 --> 00:49:58,210 going to feel its periodic image in all directions. 1053 00:49:58,210 --> 00:50:01,280 So for a new molecule, is my box big enough means leaving 1054 00:50:01,280 --> 00:50:03,950 vacuum between the molecules. 1055 00:50:08,790 --> 00:50:10,950 And then we talked about solids. 1056 00:50:10,950 --> 00:50:13,458 And that's certainly fair game for the quiz, 1057 00:50:13,458 --> 00:50:15,000 even though we haven't had a homework 1058 00:50:15,000 --> 00:50:17,738 problem on the solar cells, certainly I 1059 00:50:17,738 --> 00:50:18,780 wouldn't talk about that. 1060 00:50:18,780 --> 00:50:21,360 I won't talk about solar cells on the quiz. 1061 00:50:21,360 --> 00:50:23,700 Or I should rephrase that. 1062 00:50:23,700 --> 00:50:26,023 [LAUGHS] I won't ask you questions 1063 00:50:26,023 --> 00:50:27,690 that we haven't talked about in lecture. 1064 00:50:30,970 --> 00:50:35,680 But the band structure of a solar cell-- well, 1065 00:50:35,680 --> 00:50:38,450 band structures we've talked about a lot, right? 1066 00:50:43,300 --> 00:50:48,170 Now, the way we built up our solids part 1067 00:50:48,170 --> 00:50:50,510 is we said, well, OK, now we're talking 1068 00:50:50,510 --> 00:50:53,780 not about some molecule that can have some shape 1069 00:50:53,780 --> 00:50:55,520 and then gets repeated like this. 1070 00:50:55,520 --> 00:50:58,140 But we're actually talking now about a crystal 1071 00:50:58,140 --> 00:50:59,730 that goes on forever and ever. 1072 00:50:59,730 --> 00:51:03,290 And so it needs to have a kind of lattice. 1073 00:51:03,290 --> 00:51:07,790 And we talked about how you can define that, 1074 00:51:07,790 --> 00:51:11,480 just like we defined it in class, 1075 00:51:11,480 --> 00:51:13,460 and you've seen it in other classes. 1076 00:51:13,460 --> 00:51:16,040 You define it in a computer. 1077 00:51:16,040 --> 00:51:18,230 And then we talked about the inverse lattice, 1078 00:51:18,230 --> 00:51:20,220 and I'm not going to go through this again. 1079 00:51:20,220 --> 00:51:21,680 But we built this up. 1080 00:51:21,680 --> 00:51:23,480 Why did we build up the inverse lattice, 1081 00:51:23,480 --> 00:51:24,620 the understanding of that? 1082 00:51:28,345 --> 00:51:30,163 Where does that come in? 1083 00:51:30,163 --> 00:51:32,080 Why do you need to know about inverse lattice? 1084 00:51:32,080 --> 00:51:33,272 Yeah? 1085 00:51:33,272 --> 00:51:34,855 AUDIENCE: Because that's how we define 1086 00:51:34,855 --> 00:51:36,740 the Brillouin zone, which is where 1087 00:51:36,740 --> 00:51:38,597 we define the k-space vectors. 1088 00:51:38,597 --> 00:51:39,680 JEFFREY C. GROSSMAN: Good. 1089 00:51:39,680 --> 00:51:42,752 OK, and why does k-space matter? 1090 00:51:42,752 --> 00:51:45,980 AUDIENCE: [INAUDIBLE] associated with [INAUDIBLE] 1091 00:51:45,980 --> 00:51:48,830 JEFFREY C. GROSSMAN: Yeah, so that's exactly-- 1092 00:51:48,830 --> 00:51:51,920 the inverse lattice is the reciprocal lattice 1093 00:51:51,920 --> 00:51:55,130 of our real lattice. 1094 00:51:55,130 --> 00:51:57,140 It's really important in crystallography, 1095 00:51:57,140 --> 00:52:00,050 so I think a lot of you have seen this. 1096 00:52:00,050 --> 00:52:02,697 And you can define by just drawing these perpendiculars 1097 00:52:02,697 --> 00:52:05,030 to the nearest neighbors you defined the first Brillouin 1098 00:52:05,030 --> 00:52:12,240 zone, which is where the energy levels, those precious energy 1099 00:52:12,240 --> 00:52:16,410 levels of this molecule that I want-- 1100 00:52:16,410 --> 00:52:21,090 that first Brillouin zone is where in the inverse lattice-- 1101 00:52:21,090 --> 00:52:33,900 see, this now becomes inverse space, also known as k-space. 1102 00:52:33,900 --> 00:52:37,230 That becomes a degree of freedom. 1103 00:52:37,230 --> 00:52:40,480 And so that makes these guys move. 1104 00:52:40,480 --> 00:52:42,600 They can even move and cross one another. 1105 00:52:46,300 --> 00:52:47,950 And that is the difference between 1106 00:52:47,950 --> 00:52:50,530 a solid computational quantum mechanics on a solid-- 1107 00:52:50,530 --> 00:52:53,830 what you can get out in a molecule. 1108 00:52:53,830 --> 00:52:56,320 And the Brillouin zone is the playground 1109 00:52:56,320 --> 00:52:59,530 of this space that matters. 1110 00:52:59,530 --> 00:53:02,500 Because as we showed from Bloch's theorem, 1111 00:53:02,500 --> 00:53:05,620 if you go outside of the Brillouin zone, 1112 00:53:05,620 --> 00:53:09,410 you can just wrap it and get back exactly to where you work. 1113 00:53:09,410 --> 00:53:12,860 So your function and your energies won't change. 1114 00:53:12,860 --> 00:53:16,010 So all that matters is to know and understand and compute, 1115 00:53:16,010 --> 00:53:18,770 which is what the code does, the variation inside this Brillouin 1116 00:53:18,770 --> 00:53:19,270 zone. 1117 00:53:19,270 --> 00:53:21,250 That's why we defined it, because we just 1118 00:53:21,250 --> 00:53:23,140 don't need any other zone. 1119 00:53:25,770 --> 00:53:30,130 And we got here by looking at periodic potential, 1120 00:53:30,130 --> 00:53:34,940 and the result of solving the Schrodinger equation 1121 00:53:34,940 --> 00:53:37,310 in the presence of a periodic potential 1122 00:53:37,310 --> 00:53:40,280 is that you get this new constraint on the wave 1123 00:53:40,280 --> 00:53:41,900 function. 1124 00:53:41,900 --> 00:53:47,150 And the key here is that-- 1125 00:53:47,150 --> 00:53:51,440 OK, so this is just saying you can go one lattice vector away 1126 00:53:51,440 --> 00:53:52,873 and get back to same thing. 1127 00:53:52,873 --> 00:53:55,040 That's why I just said about only the Brillouin zone 1128 00:53:55,040 --> 00:53:56,270 mattering. 1129 00:53:56,270 --> 00:54:00,800 But the key result of Bloch's theorem is not here. 1130 00:54:00,800 --> 00:54:02,210 Ha. 1131 00:54:02,210 --> 00:54:04,370 But the key results of Bloch's theorem 1132 00:54:04,370 --> 00:54:07,370 is that you have this k in the first place. 1133 00:54:07,370 --> 00:54:11,240 The key result is that you have a new index. 1134 00:54:11,240 --> 00:54:14,600 Just like the quantum numbers came out of the hydrogen atom, 1135 00:54:14,600 --> 00:54:17,520 you have a new index that can vary. 1136 00:54:17,520 --> 00:54:19,420 And as it varies, it changes your levels. 1137 00:54:19,420 --> 00:54:21,170 And we spent some time talking about this. 1138 00:54:21,170 --> 00:54:25,560 So please let me know if you have any questions about this. 1139 00:54:25,560 --> 00:54:27,312 I just talked right into the mic. 1140 00:54:27,312 --> 00:54:29,860 [LAUGHS] (LOUDER) Let me know if you have any-- oh, sorry. 1141 00:54:29,860 --> 00:54:35,930 [LAUGHS] Does everybody understand that? 1142 00:54:35,930 --> 00:54:40,520 By putting-- by mapping quantum mechanics and all 1143 00:54:40,520 --> 00:54:44,270 of our machinery, Schrodinger equation, 1144 00:54:44,270 --> 00:54:46,950 approximations to it-- 1145 00:54:46,950 --> 00:54:49,430 but remember, H psi equals E psi. 1146 00:54:49,430 --> 00:54:51,380 H has v. 1147 00:54:51,380 --> 00:54:55,220 And by having v be the same everywhere in space, 1148 00:54:55,220 --> 00:54:58,340 we got this new degree of freedom, 1149 00:54:58,340 --> 00:55:02,360 this new thing that's critical. 1150 00:55:02,360 --> 00:55:06,950 And this new thing is what makes a band structure. 1151 00:55:06,950 --> 00:55:12,690 So if I showed you a band structure like this, 1152 00:55:12,690 --> 00:55:15,714 what am I simulating? 1153 00:55:15,714 --> 00:55:20,983 AUDIENCE: [INAUDIBLE] 1154 00:55:20,983 --> 00:55:22,400 JEFFREY C. GROSSMAN: What is that? 1155 00:55:22,400 --> 00:55:23,400 Forget these other ones. 1156 00:55:23,400 --> 00:55:25,506 Just look at those. 1157 00:55:25,506 --> 00:55:28,880 AUDIENCE: It's a molecule. 1158 00:55:28,880 --> 00:55:34,690 JEFFREY C. GROSSMAN: Yeah, it's a non-periodic system, right? 1159 00:55:34,690 --> 00:55:41,012 If the bands are flat, you don't have this variation in k-space. 1160 00:55:41,012 --> 00:55:42,970 And if you don't have the variation in k-space, 1161 00:55:42,970 --> 00:55:46,510 well, at least to within what the system can feel, 1162 00:55:46,510 --> 00:55:47,620 it's not a crystal. 1163 00:55:47,620 --> 00:55:51,100 It's not a periodically repeating potential. 1164 00:55:51,100 --> 00:55:54,730 It may be, or it may be really close. 1165 00:55:54,730 --> 00:55:59,110 What if you had a molecular crystal, which exist? 1166 00:55:59,110 --> 00:56:00,910 There are many molecular crystals. 1167 00:56:00,910 --> 00:56:02,890 But they're really far spaced apart. 1168 00:56:02,890 --> 00:56:05,140 These molecules are weakly interacting. 1169 00:56:05,140 --> 00:56:08,192 Well, you might get, then, something-- you 1170 00:56:08,192 --> 00:56:10,150 might just start to see this-- and we've played 1171 00:56:10,150 --> 00:56:11,500 with this in the computer. 1172 00:56:11,500 --> 00:56:15,490 You might just start to see some little wiggles, 1173 00:56:15,490 --> 00:56:19,840 feeling that effective the variation in k-space. 1174 00:56:19,840 --> 00:56:23,980 But you won't see very much. 1175 00:56:23,980 --> 00:56:27,160 And then as the interactions, or as the potential 1176 00:56:27,160 --> 00:56:31,810 that's periodic, gets stronger, well, then this variation 1177 00:56:31,810 --> 00:56:32,590 can get very high. 1178 00:56:38,257 --> 00:56:39,590 Any questions about any of that? 1179 00:56:42,430 --> 00:56:45,430 So that's kind of the key point there. 1180 00:56:45,430 --> 00:56:47,620 And we talked about the kinds of things you can get. 1181 00:56:47,620 --> 00:56:51,220 And we also talked about how-- 1182 00:56:51,220 --> 00:56:52,780 so this is density functional theory. 1183 00:56:52,780 --> 00:56:56,560 We talked about how, when you solve for the band structure, 1184 00:56:56,560 --> 00:56:59,680 you first converge the density. 1185 00:56:59,680 --> 00:57:01,555 That's a separate calculation. 1186 00:57:04,810 --> 00:57:06,760 And then what am I doing here? 1187 00:57:06,760 --> 00:57:08,440 How do I get this? 1188 00:57:08,440 --> 00:57:09,970 The third point is sort of silly. 1189 00:57:09,970 --> 00:57:11,450 You plot. 1190 00:57:11,450 --> 00:57:13,370 But point 2, what am I doing? 1191 00:57:13,370 --> 00:57:14,690 Somebody explain point 2. 1192 00:57:21,020 --> 00:57:21,740 Yeah? 1193 00:57:21,740 --> 00:57:22,820 AUDIENCE: You go in the Brillouin zone, 1194 00:57:22,820 --> 00:57:24,820 and you look at the different points in k-space. 1195 00:57:24,820 --> 00:57:26,450 And then, using those points, you 1196 00:57:26,450 --> 00:57:29,257 define potential for band gaps. 1197 00:57:29,257 --> 00:57:30,340 JEFFREY C. GROSSMAN: Yeah. 1198 00:57:30,340 --> 00:57:32,980 Well, you find-- yeah, you find the band gaps. 1199 00:57:32,980 --> 00:57:37,450 You find the energy levels at each point. 1200 00:57:37,450 --> 00:57:42,380 But as we said, as you just said, 1201 00:57:42,380 --> 00:57:46,040 you're doing this for lines in the Brillouin zone. 1202 00:57:46,040 --> 00:57:48,530 How do you choose which lines? 1203 00:57:48,530 --> 00:57:49,627 AUDIENCE: Your choice. 1204 00:57:49,627 --> 00:57:50,960 JEFFREY C. GROSSMAN: My choice-- 1205 00:57:50,960 --> 00:57:51,920 but I need to choose. 1206 00:57:54,728 --> 00:57:55,590 Sam? 1207 00:57:55,590 --> 00:57:57,600 AUDIENCE: You pick the high-symmetry region. 1208 00:57:57,600 --> 00:58:00,270 JEFFREY C. GROSSMAN: Yeah, it's the high-symmetry parts, right? 1209 00:58:00,270 --> 00:58:02,550 We talked about that. 1210 00:58:02,550 --> 00:58:03,300 Because why? 1211 00:58:05,920 --> 00:58:07,450 AUDIENCE: Nature likes symmetries. 1212 00:58:07,450 --> 00:58:08,560 JEFFREY C. GROSSMAN: Well, that's a good answer. 1213 00:58:08,560 --> 00:58:10,102 [LAUGHS] That's always a good answer. 1214 00:58:10,102 --> 00:58:11,350 Nature does like symmetry. 1215 00:58:11,350 --> 00:58:14,330 It's a beautiful thing. 1216 00:58:14,330 --> 00:58:16,490 But is that really why that's what 1217 00:58:16,490 --> 00:58:18,440 I do for my band structure? 1218 00:58:18,440 --> 00:58:20,446 What does that mean? 1219 00:58:20,446 --> 00:58:23,115 AUDIENCE: After reaction occurs, [INAUDIBLE].. 1220 00:58:23,115 --> 00:58:24,490 JEFFREY C. GROSSMAN: Pretty much. 1221 00:58:24,490 --> 00:58:28,900 That's where the variation that could happen in the energy 1222 00:58:28,900 --> 00:58:31,360 levels is going to happen. 1223 00:58:31,360 --> 00:58:33,790 And that's what you want to capture, right? 1224 00:58:33,790 --> 00:58:38,530 So a band structure is a simple two-dimensional way 1225 00:58:38,530 --> 00:58:44,110 of cruising through this kind of complex three-dimensional 1226 00:58:44,110 --> 00:58:47,530 Brillouin zone where things are varying any point I go. 1227 00:58:47,530 --> 00:58:50,020 But if I go just along the high-symmetry points, 1228 00:58:50,020 --> 00:58:55,530 then I get the variation that's usually most important. 1229 00:58:55,530 --> 00:58:57,490 And then we talked about how you fill these up 1230 00:58:57,490 --> 00:58:58,323 to the Fermi energy. 1231 00:59:01,100 --> 00:59:04,538 Is the for energy always at 0? 1232 00:59:04,538 --> 00:59:06,026 AUDIENCE: [INAUDIBLE] 1233 00:59:06,026 --> 00:59:07,020 AUDIENCE: No. 1234 00:59:07,020 --> 00:59:08,530 JEFFREY C. GROSSMAN: Yeah. 1235 00:59:08,530 --> 00:59:13,330 So if I didn't tell you where the Fermi energy is, and I 1236 00:59:13,330 --> 00:59:16,900 asked you to tell me if it's a metal or an insulator, 1237 00:59:16,900 --> 00:59:18,760 could you? 1238 00:59:18,760 --> 00:59:20,115 Would it even be possible? 1239 00:59:25,410 --> 00:59:26,460 Why or why not? 1240 00:59:29,870 --> 00:59:30,370 Yeah? 1241 00:59:30,370 --> 00:59:31,670 AUDIENCE: Because then we'd see whether or not 1242 00:59:31,670 --> 00:59:33,172 the bands are constant, right? 1243 00:59:33,172 --> 00:59:35,880 And if they're constant, then we know it's going to [INAUDIBLE].. 1244 00:59:35,880 --> 00:59:37,255 JEFFREY C. GROSSMAN: Yeah, and so 1245 00:59:37,255 --> 00:59:38,790 if I leave that piece of information 1246 00:59:38,790 --> 00:59:43,210 out, which I did last year, and I give you 1247 00:59:43,210 --> 00:59:49,910 a band structure that looks like this, 1248 00:59:49,910 --> 00:59:52,310 and then let's say you have bands up here, 1249 00:59:52,310 --> 00:59:54,530 well, everybody is really excited 1250 00:59:54,530 --> 00:59:56,780 to call this an insulator. 1251 00:59:56,780 --> 00:59:58,070 I'm excited to do it. 1252 00:59:58,070 --> 01:00:01,020 I can hardly hold back. 1253 01:00:01,020 --> 01:00:02,330 This is an insulator. 1254 01:00:02,330 --> 01:00:03,350 But hang on. 1255 01:00:03,350 --> 01:00:05,870 If I didn't tell you where the Fermi energy is, what 1256 01:00:05,870 --> 01:00:08,092 if the Fermi energy is here? 1257 01:00:08,092 --> 01:00:09,550 You got to have all the information 1258 01:00:09,550 --> 01:00:12,160 to answer the questions, right? 1259 01:00:12,160 --> 01:00:14,080 So know what information you need 1260 01:00:14,080 --> 01:00:17,470 if you're asked a question about a metal insulator. 1261 01:00:17,470 --> 01:00:19,450 And you know-- yeah? 1262 01:00:19,450 --> 01:00:22,652 AUDIENCE: Why do we typically begin with the energy at 0? 1263 01:00:22,652 --> 01:00:24,640 What would be a case where we vary it? 1264 01:00:24,640 --> 01:00:29,164 JEFFREY C. GROSSMAN: It's only because it's sort of a-- 1265 01:00:29,164 --> 01:00:34,344 there's no good reason except that it's convenient. 1266 01:00:34,344 --> 01:00:36,579 AUDIENCE: OK, so usually it's just static? 1267 01:00:36,579 --> 01:00:39,079 JEFFREY C. GROSSMAN: It's just nice to shift them so they're 1268 01:00:39,079 --> 01:00:40,780 always at the same place. 1269 01:00:40,780 --> 01:00:42,840 And then we can compare things more easily. 1270 01:00:48,490 --> 01:00:50,680 Why is this definitely going to be a metal if I have 1271 01:00:50,680 --> 01:00:51,970 an odd number of electrons? 1272 01:01:02,420 --> 01:01:04,803 OK, there's a little discussion there. 1273 01:01:04,803 --> 01:01:06,470 I want to know what you guys are saying. 1274 01:01:06,470 --> 01:01:07,345 AUDIENCE: Confirming. 1275 01:01:07,345 --> 01:01:09,470 JEFFREY C. GROSSMAN: Confirming, OK. 1276 01:01:09,470 --> 01:01:13,320 You're validating-- I love it-- using the group consensus. 1277 01:01:13,320 --> 01:01:15,452 Crowdsourcing is very powerful. 1278 01:01:15,452 --> 01:01:16,910 Anyway, don't use it for computing. 1279 01:01:16,910 --> 01:01:20,030 AUDIENCE: [INAUDIBLE] if there's not enough electrons, then 1280 01:01:20,030 --> 01:01:21,310 a band's only half filled. 1281 01:01:21,310 --> 01:01:23,378 The Fermi energy has to be in that band. 1282 01:01:23,378 --> 01:01:24,420 JEFFREY C. GROSSMAN: Why? 1283 01:01:24,420 --> 01:01:25,310 That's exactly right. 1284 01:01:25,310 --> 01:01:25,810 Why? 1285 01:01:25,810 --> 01:01:28,430 AUDIENCE: The Fermi energy is where you fill up until it's-- 1286 01:01:28,430 --> 01:01:29,900 JEFFREY C. GROSSMAN: That's it. 1287 01:01:29,900 --> 01:01:31,130 Did everybody get that? 1288 01:01:31,130 --> 01:01:34,790 Fermi energy is the energy that you fill the electrons to. 1289 01:01:34,790 --> 01:01:38,840 So if you have an odd number of electrons, well, 1290 01:01:38,840 --> 01:01:41,286 how many electrons go in each one of these bands? 1291 01:01:41,286 --> 01:01:41,869 AUDIENCE: Two. 1292 01:01:41,869 --> 01:01:42,911 JEFFREY C. GROSSMAN: Two. 1293 01:01:42,911 --> 01:01:45,220 So if I have an odd number of electrons, one of them 1294 01:01:45,220 --> 01:01:46,810 is only going to be half filled. 1295 01:01:46,810 --> 01:01:50,380 That means my Fermi energy has to cut it. 1296 01:01:50,380 --> 01:01:52,840 It's got to cut it somewhere, which 1297 01:01:52,840 --> 01:01:55,600 means I have a band crossing the Fermi energy, which 1298 01:01:55,600 --> 01:01:58,740 means it's a metal-- 1299 01:01:58,740 --> 01:01:59,330 has to be. 1300 01:02:02,770 --> 01:02:04,840 You can think about the same for an atom, 1301 01:02:04,840 --> 01:02:06,880 except that atoms are metals. 1302 01:02:06,880 --> 01:02:08,690 But most atoms have that case. 1303 01:02:08,690 --> 01:02:11,590 They have half or partially filled levels. 1304 01:02:11,590 --> 01:02:15,610 You don't fill all the p electrons in carbon 1305 01:02:15,610 --> 01:02:18,130 but we don't think of the carbon atom as a metal, 1306 01:02:18,130 --> 01:02:20,425 because atoms and molecules don't really 1307 01:02:20,425 --> 01:02:21,550 have this kind of behavior. 1308 01:02:25,570 --> 01:02:26,910 But it's the same idea. 1309 01:02:26,910 --> 01:02:28,250 You're partially filling levels. 1310 01:02:32,270 --> 01:02:35,600 We talked about-- how are we feeling about 1311 01:02:35,600 --> 01:02:38,720 direct versus indirect gaps? 1312 01:02:38,720 --> 01:02:39,500 Good? 1313 01:02:39,500 --> 01:02:40,820 OK, we talked about that. 1314 01:02:40,820 --> 01:02:44,270 Yeah, liking that-- that could be a good question. 1315 01:02:44,270 --> 01:02:49,280 And we talked about other things that you can calculate-- 1316 01:02:49,280 --> 01:02:51,440 vibrational properties. 1317 01:02:51,440 --> 01:02:54,830 We did talk about magnetization, right? 1318 01:02:54,830 --> 01:02:56,090 Now, this is not-- 1319 01:02:56,090 --> 01:03:01,850 sorry, this is actually from a different code we used to use. 1320 01:03:01,850 --> 01:03:03,230 So just ignore this. 1321 01:03:03,230 --> 01:03:06,440 We used to use a different code than SIESTA. 1322 01:03:06,440 --> 01:03:08,260 And that was the input for it. 1323 01:03:11,150 --> 01:03:14,900 And this is showing that you can do calculations 1324 01:03:14,900 --> 01:03:20,960 of, say, different phases of a magnetic material like iron. 1325 01:03:20,960 --> 01:03:24,290 And how would I calculate the magnetization 1326 01:03:24,290 --> 01:03:26,810 of those materials? 1327 01:03:26,810 --> 01:03:33,080 This was in lecture something, some number of days ago. 1328 01:03:33,080 --> 01:03:33,730 Yeah? 1329 01:03:33,730 --> 01:03:36,476 AUDIENCE: I guess you could put on and apply the magnetic field 1330 01:03:36,476 --> 01:03:38,350 and then see where [INAUDIBLE] is. 1331 01:03:38,350 --> 01:03:40,100 JEFFREY C. GROSSMAN: You absolutely could, 1332 01:03:40,100 --> 01:03:41,960 and that would be really hard. 1333 01:03:41,960 --> 01:03:43,670 But you could do that, actually. 1334 01:03:43,670 --> 01:03:44,660 And we do do that. 1335 01:03:44,660 --> 01:03:49,470 But that's a hard calculation. 1336 01:03:49,470 --> 01:03:52,950 What is the magnetization of material what's it due to, 1337 01:03:52,950 --> 01:03:54,630 anyway? 1338 01:03:54,630 --> 01:03:56,320 What part of the materials is due to? 1339 01:03:56,320 --> 01:03:57,162 Yeah? 1340 01:03:57,162 --> 01:03:58,954 AUDIENCE: A difference in density and space 1341 01:03:58,954 --> 01:04:00,470 between the spin up and spin down. 1342 01:04:00,470 --> 01:04:01,553 JEFFREY C. GROSSMAN: Yeah. 1343 01:04:01,553 --> 01:04:03,560 Yeah, it's due to electrons. 1344 01:04:03,560 --> 01:04:08,000 It's due to the spin of the electrons. 1345 01:04:08,000 --> 01:04:11,700 That's what gave us the Stern-Gerlach experiments. 1346 01:04:11,700 --> 01:04:15,740 It was the magnetization possible 1347 01:04:15,740 --> 01:04:18,860 of the spins of the electrons. 1348 01:04:18,860 --> 01:04:20,690 It was the fact that a magnetic field 1349 01:04:20,690 --> 01:04:23,820 could exert a force on those. 1350 01:04:23,820 --> 01:04:29,160 Now, we said that, in your material, 1351 01:04:29,160 --> 01:04:32,790 you have spin up electrons and spin down 1352 01:04:32,790 --> 01:04:35,760 electrons, the precious things that were computing 1353 01:04:35,760 --> 01:04:39,000 this whole second half. 1354 01:04:39,000 --> 01:04:41,100 And you fill those up. 1355 01:04:41,100 --> 01:04:42,330 And you fill them up. 1356 01:04:42,330 --> 01:04:44,190 According to the Pauli exclusion principle, 1357 01:04:44,190 --> 01:04:46,700 you fill the levels up with these electrons, right? 1358 01:04:49,870 --> 01:04:53,350 But when you get to a solid or, even in atoms, 1359 01:04:53,350 --> 01:04:55,210 you don't always necessarily have 1360 01:04:55,210 --> 01:04:58,720 the same up and down electrons. 1361 01:04:58,720 --> 01:05:01,630 You can have differences. 1362 01:05:01,630 --> 01:05:04,180 And when you have differences between them, 1363 01:05:04,180 --> 01:05:08,340 you can have a net magnetic moment. 1364 01:05:08,340 --> 01:05:12,950 And we talked about that before. 1365 01:05:12,950 --> 01:05:16,533 And then we said, well, OK, if I had an atom, 1366 01:05:16,533 --> 01:05:18,200 then you can have a net magnetic moment. 1367 01:05:18,200 --> 01:05:20,720 Just count the number of up electrons minus the number 1368 01:05:20,720 --> 01:05:21,930 of down electrons. 1369 01:05:21,930 --> 01:05:27,740 But in a solid, in a crystal, you now 1370 01:05:27,740 --> 01:05:30,290 have these electrons in these bands. 1371 01:05:30,290 --> 01:05:31,740 You need to use something else. 1372 01:05:31,740 --> 01:05:34,280 And that's where you need to use the density of states. 1373 01:05:38,110 --> 01:05:41,740 And so if you have sort of the density of states-- 1374 01:05:41,740 --> 01:05:44,590 now, remember-- versus, say, energy, 1375 01:05:44,590 --> 01:05:46,090 and this is something you're all now 1376 01:05:46,090 --> 01:05:50,140 familiar with from the homework, but we talked about this, also, 1377 01:05:50,140 --> 01:05:54,490 how it relates to magnetism, and that, in the SIESTA tool, 1378 01:05:54,490 --> 01:05:58,250 you could plot, for example, the spin up electrons. 1379 01:05:58,250 --> 01:06:02,660 So let's say these are the spin up electrons. 1380 01:06:02,660 --> 01:06:06,032 And then you can plot the spin down electrons. 1381 01:06:06,032 --> 01:06:07,990 And that's a little hard to see because there's 1382 01:06:07,990 --> 01:06:10,360 three curves with one color. 1383 01:06:10,360 --> 01:06:13,900 But the main point is that the up electrons and down electrons 1384 01:06:13,900 --> 01:06:16,480 could be very different in where they 1385 01:06:16,480 --> 01:06:19,390 are in energy, which translates into what where the peaks are 1386 01:06:19,390 --> 01:06:19,990 in the DOS. 1387 01:06:24,560 --> 01:06:31,640 Now, you see, what matters, though, 1388 01:06:31,640 --> 01:06:34,942 is not the difference across the whole DOS curve. 1389 01:06:34,942 --> 01:06:35,900 What's going to matter? 1390 01:06:39,590 --> 01:06:42,080 It's not the whole DOS that matters. 1391 01:06:42,080 --> 01:06:43,710 It's only part of it. 1392 01:06:43,710 --> 01:06:45,860 Which part? 1393 01:06:45,860 --> 01:06:53,390 Yeah, it's the part up until the Fermi level. 1394 01:06:53,390 --> 01:06:56,905 What are the differences in where I filled electrons? 1395 01:06:56,905 --> 01:06:58,280 Between the ones that would be up 1396 01:06:58,280 --> 01:07:02,150 and the ones that would be down, right? 1397 01:07:02,150 --> 01:07:05,960 Now, and that got us to talking about this spin-polarized thing 1398 01:07:05,960 --> 01:07:07,920 that we talked about last time. 1399 01:07:10,490 --> 01:07:13,880 And that's a little button on your simulation tool 1400 01:07:13,880 --> 01:07:15,470 that you can check or uncheck. 1401 01:07:15,470 --> 01:07:20,430 So if something is spin-polarized, 1402 01:07:20,430 --> 01:07:24,270 it allows the up and down electrons to be different, 1403 01:07:24,270 --> 01:07:26,310 to have different energies. 1404 01:07:26,310 --> 01:07:30,660 So I just I just told you that difference is 1405 01:07:30,660 --> 01:07:31,950 what gives you magnetization. 1406 01:07:31,950 --> 01:07:37,110 So if you don't allow it to be spin-polarized, 1407 01:07:37,110 --> 01:07:39,250 then you won't get magnetization, right? 1408 01:07:39,250 --> 01:07:39,750 Yeah? 1409 01:07:39,750 --> 01:07:41,482 AUDIENCE: Isn't there a spin up and spin 1410 01:07:41,482 --> 01:07:47,410 down electron in every energy state [INAUDIBLE] that are all 1411 01:07:47,410 --> 01:07:48,660 going to have the same energy? 1412 01:07:48,660 --> 01:07:50,535 JEFFREY C. GROSSMAN: Ah, very good question-- 1413 01:07:50,535 --> 01:08:00,463 and that is exactly what spin-polarized does. 1414 01:08:00,463 --> 01:08:02,380 You see, so this is what you're talking about. 1415 01:08:02,380 --> 01:08:08,890 You're saying, well, isn't this just in one level? 1416 01:08:08,890 --> 01:08:11,470 But it actually, it turns out, that that's 1417 01:08:11,470 --> 01:08:16,300 what's called a restricted-- 1418 01:08:16,300 --> 01:08:18,100 you can say restricted closed shell 1419 01:08:18,100 --> 01:08:19,750 or restricted open shell-- 1420 01:08:19,750 --> 01:08:24,100 formalism that is valid for many, many materials 1421 01:08:24,100 --> 01:08:27,470 and molecules, where in fact, there's no difference. 1422 01:08:27,470 --> 01:08:31,000 But in reality-- in reality-- 1423 01:08:31,000 --> 01:08:32,950 even when it's restricted, you still 1424 01:08:32,950 --> 01:08:38,290 should write these as a sort of one spin channel and another. 1425 01:08:38,290 --> 01:08:41,590 You could call it alpha is spin up, and beta is is spin down. 1426 01:08:41,590 --> 01:08:43,930 And each one of those has its own set 1427 01:08:43,930 --> 01:08:46,899 of orbitals and wave functions. 1428 01:08:46,899 --> 01:08:50,620 So in reality, that's what you solve for. 1429 01:08:50,620 --> 01:08:52,840 Now, in many materials, it turns out alpha 1430 01:08:52,840 --> 01:08:56,890 and beta electrons do have the exact same energy level, 1431 01:08:56,890 --> 01:08:57,729 but not always. 1432 01:08:57,729 --> 01:09:02,800 And actually, in exactly what you were talking about, 1433 01:09:02,800 --> 01:09:04,630 when I apply a magnetic field even 1434 01:09:04,630 --> 01:09:07,120 to a material that's not very magnetic, 1435 01:09:07,120 --> 01:09:11,050 you can cause big shifts in these. 1436 01:09:11,050 --> 01:09:13,760 You can-- depends. 1437 01:09:13,760 --> 01:09:14,970 That depends on the material. 1438 01:09:14,970 --> 01:09:17,770 But when you apply external perturbations to the system, 1439 01:09:17,770 --> 01:09:20,950 you can split these so that actually you 1440 01:09:20,950 --> 01:09:27,359 do have this picture where the energy of the spin up channel 1441 01:09:27,359 --> 01:09:32,700 for that energy level is different than the spin 1442 01:09:32,700 --> 01:09:33,250 down channel. 1443 01:09:33,250 --> 01:09:35,700 And that's exactly what spin-polarized does. 1444 01:09:35,700 --> 01:09:38,310 It allows those energies to be different. 1445 01:09:38,310 --> 01:09:45,390 Without that, you can't really study magnetism correctly. 1446 01:09:48,010 --> 01:09:49,490 That's a good question. 1447 01:09:49,490 --> 01:09:52,630 OK, and so we talked about some other things. 1448 01:09:52,630 --> 01:09:57,820 We did talk about how you could calculate electrical 1449 01:09:57,820 --> 01:10:00,910 conductivity-- so that's fair game-- 1450 01:10:00,910 --> 01:10:02,500 from the band structure. 1451 01:10:02,500 --> 01:10:07,390 There's an equation in the lecture from last week on that. 1452 01:10:07,390 --> 01:10:09,250 We didn't talk about thermal conductivity. 1453 01:10:09,250 --> 01:10:13,822 We've talked about optical properties and magnetization. 1454 01:10:13,822 --> 01:10:15,280 That looks like it's just repeating 1455 01:10:15,280 --> 01:10:21,250 the first and fourth bullet, which is interesting to me. 1456 01:10:21,250 --> 01:10:22,960 But these are the kinds of things 1457 01:10:22,960 --> 01:10:26,470 we can calculate using the band structure in the DOS, which 1458 01:10:26,470 --> 01:10:30,552 is what we've focused on a lot in the last three, 1459 01:10:30,552 --> 01:10:31,135 four lectures. 1460 01:10:34,010 --> 01:10:37,460 So that's certainly I would think you should know about, 1461 01:10:37,460 --> 01:10:41,660 how to get some of the key properties 1462 01:10:41,660 --> 01:10:45,303 from the band structure in DOS in these first four, 1463 01:10:45,303 --> 01:10:47,220 excluding thermal, which we didn't talk about. 1464 01:10:57,450 --> 01:11:02,140 And with the convergence questions, 1465 01:11:02,140 --> 01:11:04,450 we got to have a convergence question, right? 1466 01:11:04,450 --> 01:11:06,280 You just-- you got to. 1467 01:11:06,280 --> 01:11:11,360 You would feel cheated if you didn't have one, right? 1468 01:11:11,360 --> 01:11:14,690 And I don't want you to have that feeling. 1469 01:11:14,690 --> 01:11:16,910 When you have a solid, k-points now 1470 01:11:16,910 --> 01:11:19,880 becomes a convergence parameter. 1471 01:11:19,880 --> 01:11:22,910 So that's kind of our review. 1472 01:11:22,910 --> 01:11:24,660 Any questions? 1473 01:11:24,660 --> 01:11:26,040 Any questions about that at all? 1474 01:11:32,100 --> 01:11:36,727 Any thoughts or comments? 1475 01:11:36,727 --> 01:11:37,560 Any other questions? 1476 01:11:37,560 --> 01:11:38,190 We're good? 1477 01:11:38,190 --> 01:11:40,660 Any questions about the quiz? 1478 01:11:43,960 --> 01:11:48,775 OK, let me just take five minutes to do a little stuff, 1479 01:11:48,775 --> 01:11:50,650 get it out of the way, so that after the quiz 1480 01:11:50,650 --> 01:11:52,790 we can dive into-- 1481 01:11:52,790 --> 01:11:55,180 or do you guys just kind of want to-- 1482 01:11:55,180 --> 01:11:57,130 maybe we stop here, huh? 1483 01:11:57,130 --> 01:11:58,850 Should we stop here? 1484 01:11:58,850 --> 01:12:05,220 Except five minutes on solar right before quiz. 1485 01:12:05,220 --> 01:12:06,117 Yeah. 1486 01:12:06,117 --> 01:12:06,950 I'll tell you what-- 1487 01:12:06,950 --> 01:12:11,360 I'll do my little energy slides, and then we'll start solar. 1488 01:12:11,360 --> 01:12:14,750 Because this isn't really solar, but it's related. 1489 01:12:14,750 --> 01:12:16,780 And I don't think I showed these before. 1490 01:12:16,780 --> 01:12:18,780 Did I show these before when I was 1491 01:12:18,780 --> 01:12:20,880 motivating research and energy? 1492 01:12:20,880 --> 01:12:22,470 I really like this. 1493 01:12:22,470 --> 01:12:25,400 We talk a lot about global warming. 1494 01:12:29,070 --> 01:12:33,900 And I think that's a really important topic. 1495 01:12:33,900 --> 01:12:39,510 And there's some really great work and, unfortunately, 1496 01:12:39,510 --> 01:12:44,442 not enough understanding, I think, on-- 1497 01:12:44,442 --> 01:12:46,935 [LAUGHS] I don't even know where to begin. 1498 01:12:46,935 --> 01:12:49,530 You know the polls show that half of this country 1499 01:12:49,530 --> 01:12:55,290 still doesn't think that there's any evidence that it's 1500 01:12:55,290 --> 01:12:56,550 anthropogenically linked. 1501 01:12:56,550 --> 01:13:01,680 But anyway-- OK, so let's say we don't talk about that. 1502 01:13:01,680 --> 01:13:07,140 And we ignore these sort of really hard scientific facts. 1503 01:13:07,140 --> 01:13:10,290 There are other reasons other reasons to think 1504 01:13:10,290 --> 01:13:11,730 about renewable energy. 1505 01:13:15,240 --> 01:13:16,232 And I like this one. 1506 01:13:16,232 --> 01:13:18,690 I don't know how many of you have seen something like this, 1507 01:13:18,690 --> 01:13:21,310 but this is-- the United Nations puts this out. 1508 01:13:21,310 --> 01:13:23,590 This is the Human Development Index. 1509 01:13:23,590 --> 01:13:27,060 What's that Mean I feel pretty developed. 1510 01:13:27,060 --> 01:13:30,540 I mean, does that just mean I can go to Starbucks 1511 01:13:30,540 --> 01:13:32,580 and get a latte when I want? 1512 01:13:32,580 --> 01:13:36,840 No, this means health care, education. 1513 01:13:36,840 --> 01:13:39,210 It means I can read. 1514 01:13:39,210 --> 01:13:41,940 It means I could maybe have a light on at night to read. 1515 01:13:41,940 --> 01:13:46,170 But it's primarily some sort of key indices 1516 01:13:46,170 --> 01:13:49,590 that talk about sort of the well-being of a person. 1517 01:13:49,590 --> 01:13:54,390 And that, you can see, is incredibly strongly correlated 1518 01:13:54,390 --> 01:13:57,750 with how much energy a country gets. 1519 01:13:57,750 --> 01:14:00,780 So this is the amount of per-capita electricity use. 1520 01:14:00,780 --> 01:14:03,090 And that's this Human Development-- it's basically 1521 01:14:03,090 --> 01:14:05,140 a well-being index. 1522 01:14:05,140 --> 01:14:08,520 As you can see, some people get surprised that Canada beats us. 1523 01:14:08,520 --> 01:14:09,570 So how do they beat us? 1524 01:14:09,570 --> 01:14:10,670 AUDIENCE: It's cold. 1525 01:14:10,670 --> 01:14:12,140 JEFFREY C. GROSSMAN: It's cold. 1526 01:14:12,140 --> 01:14:16,520 It's really cold up there, right? 1527 01:14:16,520 --> 01:14:19,550 But you can just see the strong correlation. 1528 01:14:23,740 --> 01:14:26,230 The question is, when they-- 1529 01:14:26,230 --> 01:14:29,230 see, there's enough fossil fuels for everybody 1530 01:14:29,230 --> 01:14:35,450 here, probably, certainly if you go with coal. 1531 01:14:35,450 --> 01:14:37,522 There's a whole lot of energy in fossil fuels, 1532 01:14:37,522 --> 01:14:39,730 and we could lift a lot of these people up the curve. 1533 01:14:39,730 --> 01:14:41,970 The question is, is that really how we want to do it? 1534 01:14:44,690 --> 01:14:46,760 Now, the other point I want to make-- 1535 01:14:46,760 --> 01:14:49,022 and this will be the other intro point. 1536 01:14:49,022 --> 01:14:50,480 Just so you have in your minds when 1537 01:14:50,480 --> 01:14:52,100 you're talking to people about energy, 1538 01:14:52,100 --> 01:14:56,220 it's not just about global warming. 1539 01:14:56,220 --> 01:15:00,540 And this was a great experiment that was run accidentally 1540 01:15:00,540 --> 01:15:03,300 when 256 power plants went offline 1541 01:15:03,300 --> 01:15:04,950 in the Eastern corridor. 1542 01:15:04,950 --> 01:15:07,770 This is one of these stories where one plant goes off 1543 01:15:07,770 --> 01:15:10,110 because a mouse chewed through a wire or something, 1544 01:15:10,110 --> 01:15:13,740 and then the whole country feels it. 1545 01:15:13,740 --> 01:15:15,570 But it was a great test bed, because they 1546 01:15:15,570 --> 01:15:17,640 were offline for quite a lot. 1547 01:15:17,640 --> 01:15:19,260 All these things shut down. 1548 01:15:19,260 --> 01:15:21,070 Everything had to shut down. 1549 01:15:21,070 --> 01:15:23,760 And so people took planes up and did testing 1550 01:15:23,760 --> 01:15:27,620 and published these results of the air quality. 1551 01:15:27,620 --> 01:15:30,230 And it's incredible to look at the data. 1552 01:15:30,230 --> 01:15:32,690 You look at all kinds of stuff that 1553 01:15:32,690 --> 01:15:35,750 affect what we breathe, what we see, how we live, 1554 01:15:35,750 --> 01:15:37,610 who has asthma. 1555 01:15:37,610 --> 01:15:40,790 A lot of that stuff goes down instantly. 1556 01:15:40,790 --> 01:15:44,120 So there are different reasons than just global warming. 1557 01:15:46,830 --> 01:15:48,050 And I like this map. 1558 01:15:48,050 --> 01:15:49,592 I don't know if I showed this to you. 1559 01:15:49,592 --> 01:15:54,270 But this is how much we consume scaled by consumption. 1560 01:15:54,270 --> 01:15:56,950 This is the country, the world map. 1561 01:15:56,950 --> 01:15:58,490 [LAUGHTER] 1562 01:15:58,490 --> 01:16:02,650 We're pretty big-- pretty big. 1563 01:16:02,650 --> 01:16:05,330 There are some places that are pretty small. 1564 01:16:05,330 --> 01:16:07,790 OK, so you scale it by country. 1565 01:16:11,510 --> 01:16:14,540 I mean, one question that comes up and gets 1566 01:16:14,540 --> 01:16:22,220 modified is, how much energy do we really need, or power? 1567 01:16:22,220 --> 01:16:26,390 In 2002, we burned energy at a rate of 3 and 1/2 terawatts. 1568 01:16:26,390 --> 01:16:28,010 What's it going to be in 2050? 1569 01:16:28,010 --> 01:16:29,810 Well, if you make some assumptions 1570 01:16:29,810 --> 01:16:35,120 about how many people there are, and if everybody used energy 1571 01:16:35,120 --> 01:16:38,330 like us, which is really inefficiently, 1572 01:16:38,330 --> 01:16:42,450 then we need 100 terawatts in 2050. 1573 01:16:42,450 --> 01:16:44,890 We only have 13 now, 14 now. 1574 01:16:44,890 --> 01:16:46,170 We need a whole lot. 1575 01:16:46,170 --> 01:16:49,480 And we like to think that people are going to be more efficient, 1576 01:16:49,480 --> 01:16:51,210 and so that becomes the target-- 1577 01:16:51,210 --> 01:16:54,110 30 terawatts, 30 to 50 terawatts is what we're going to need. 1578 01:16:54,110 --> 01:16:55,110 How do we generate that? 1579 01:16:55,110 --> 01:16:58,890 Well, this is-- and this is all just, again, 1580 01:16:58,890 --> 01:17:01,770 building up to solar, which we'll start next week. 1581 01:17:01,770 --> 01:17:06,220 This is how we've generated it so far. 1582 01:17:06,220 --> 01:17:09,790 We burned a lot of wood, and that was kind of dirty. 1583 01:17:09,790 --> 01:17:12,400 So we burned coal, and that was really dirty. 1584 01:17:12,400 --> 01:17:15,430 But there's so much coal, and it's so cheap. 1585 01:17:15,430 --> 01:17:16,660 [LAUGHTER] 1586 01:17:16,660 --> 01:17:19,430 And then we found oil, which is this magnificent energy 1587 01:17:19,430 --> 01:17:19,930 carrier. 1588 01:17:19,930 --> 01:17:22,000 It's a solar resource. 1589 01:17:22,000 --> 01:17:25,680 All these are solar resources, by the way, including hydro. 1590 01:17:31,930 --> 01:17:37,990 Now, natural gas, with fracking-- this 1591 01:17:37,990 --> 01:17:40,900 is going to go-- from this it's going to go like this 1592 01:17:40,900 --> 01:17:44,920 and just sort of take over this chart. 1593 01:17:44,920 --> 01:17:47,530 Fracking in the last few years has done more for energy 1594 01:17:47,530 --> 01:17:51,110 than anything has in many decades. 1595 01:17:51,110 --> 01:17:53,460 But that's not that's not what I'm talking about. 1596 01:17:53,460 --> 01:17:55,360 I'm talking about this green sliver, 1597 01:17:55,360 --> 01:17:58,540 which is where I like to sit. 1598 01:17:58,540 --> 01:18:03,130 And we separate out hydro, because at least on-shore hydro 1599 01:18:03,130 --> 01:18:07,427 is fairly tapped out. 1600 01:18:07,427 --> 01:18:09,010 And then you've got that green sliver. 1601 01:18:09,010 --> 01:18:14,035 And the thing is that, if you look at global warming 1602 01:18:14,035 --> 01:18:16,000 curves, CO2 emissions, people talk 1603 01:18:16,000 --> 01:18:18,790 about wanting half of all the energy 1604 01:18:18,790 --> 01:18:21,340 to come from that green sliver by 2050. 1605 01:18:21,340 --> 01:18:22,630 So you back the numbers out. 1606 01:18:22,630 --> 01:18:25,117 We need 30 terawatts in 2050. 1607 01:18:25,117 --> 01:18:27,700 That's how much the world needs if we're really good at how we 1608 01:18:27,700 --> 01:18:30,940 use it, 100 if we're like us. 1609 01:18:30,940 --> 01:18:34,000 And you want half of that to come from a green sliver, which 1610 01:18:34,000 --> 01:18:35,560 isn't really expanding much. 1611 01:18:35,560 --> 01:18:38,570 And notice, it's sitting on a slope like this. 1612 01:18:38,570 --> 01:18:40,270 This slope is still-- 1613 01:18:40,270 --> 01:18:43,707 could go even much higher much faster. 1614 01:18:43,707 --> 01:18:45,040 This is a really tall challenge. 1615 01:18:45,040 --> 01:18:50,350 This is the challenge that I like to think about, 1616 01:18:50,350 --> 01:18:51,730 is how can we actually do that. 1617 01:18:51,730 --> 01:18:54,700 And solar PV, I think, is-- 1618 01:18:54,700 --> 01:18:58,150 and I'll end on this side, and so we'll 1619 01:18:58,150 --> 01:19:02,320 start we'll pick up from here on the technology part 1620 01:19:02,320 --> 01:19:05,170 and the science part next week. 1621 01:19:05,170 --> 01:19:09,492 We use about 15 terawatts today. 1622 01:19:09,492 --> 01:19:11,450 Does anybody know how much we get from the sun? 1623 01:19:11,450 --> 01:19:13,060 I think I did talk about that. 1624 01:19:13,060 --> 01:19:16,300 What's the number we get from the sun? 1625 01:19:16,300 --> 01:19:19,092 We use 15 terawatts a year. 1626 01:19:19,092 --> 01:19:20,800 How much do we get from the sun per year? 1627 01:19:23,686 --> 01:19:25,610 AUDIENCE: [INAUDIBLE] 1628 01:19:25,610 --> 01:19:28,290 JEFFREY C. GROSSMAN: 40,000-- roughly 40,000. 1629 01:19:28,290 --> 01:19:33,050 There's just is a whole lot of energy that comes with the sun. 1630 01:19:33,050 --> 01:19:34,940 The energy released by an earthquake 1631 01:19:34,940 --> 01:19:37,580 we get from the sun in a second. 1632 01:19:37,580 --> 01:19:38,870 You probably heard this. 1633 01:19:38,870 --> 01:19:41,000 Every year, we get that amount of energy 1634 01:19:41,000 --> 01:19:42,860 in an hour from the sun. 1635 01:19:42,860 --> 01:19:43,972 Here's what I like-- 1636 01:19:43,972 --> 01:19:44,930 you may not have heard. 1637 01:19:44,930 --> 01:19:47,990 The total resource of oil, including 1638 01:19:47,990 --> 01:19:50,810 the 2 trillion barrels we've used, 1639 01:19:50,810 --> 01:19:54,980 roughly, and the trillion more that we're going to use, 1640 01:19:54,980 --> 01:19:56,930 for sure-- 1641 01:19:56,930 --> 01:19:59,330 that amount of energy resource you 1642 01:19:59,330 --> 01:20:02,186 get from the sun in two days. 1643 01:20:02,186 --> 01:20:05,660 It's an incredible resource, right? 1644 01:20:05,660 --> 01:20:08,720 But apart from just painting a barrel black 1645 01:20:08,720 --> 01:20:11,930 and heating water with it, we really don't use it much. 1646 01:20:11,930 --> 01:20:14,480 And even there, we don't use it much at all. 1647 01:20:14,480 --> 01:20:20,900 Solar photovoltaics is an extremely appealing way 1648 01:20:20,900 --> 01:20:22,700 of trying to capture this resource 1649 01:20:22,700 --> 01:20:26,150 and really change that green sliver. 1650 01:20:26,150 --> 01:20:29,150 And so that's what I want to talk about next, 1651 01:20:29,150 --> 01:20:30,290 after the quiz. 1652 01:20:30,290 --> 01:20:35,400 OK, so see you all Thursday, office hours tomorrow. 1653 01:20:35,400 --> 01:20:38,530 Any questions at all, please send me an email.