1 00:00:16,500 --> 00:00:22,039 And speaking of VSEPR, that's what we did last lecture. 2 00:00:22,039 --> 00:00:23,741 We're going to move on today. 3 00:00:23,741 --> 00:00:26,276 But I want to just clarify something about VSEPR. 4 00:00:28,879 --> 00:00:31,448 When I was talking about this I tried 5 00:00:31,448 --> 00:00:33,617 to put two different concepts in the same place. 6 00:00:33,617 --> 00:00:36,286 And I put something in the table that shouldn't have been there. 7 00:00:36,286 --> 00:00:38,188 And people corrected me. 8 00:00:38,188 --> 00:00:41,892 I want to be sure that there is no confusion around this. 9 00:00:41,892 --> 00:00:48,298 So what we had was a case of formaldehyde. 10 00:00:48,298 --> 00:00:54,071 And we had the case of SO2. 11 00:01:00,044 --> 00:01:04,848 And I want to be really clear about this. 12 00:01:04,848 --> 00:01:07,918 Both of these molecules, when you're 13 00:01:07,918 --> 00:01:15,292 thinking about VSEPR, the number of electron domain count-- 14 00:01:15,292 --> 00:01:15,793 Right. 15 00:01:15,793 --> 00:01:17,628 Remember, that's how we start. 16 00:01:17,628 --> 00:01:24,435 The number of electron domains is the same for both of them. 17 00:01:24,435 --> 00:01:28,605 And we did this on Wednesday. 18 00:01:28,605 --> 00:01:29,106 Right. 19 00:01:29,106 --> 00:01:31,608 And if the number of electron domains is the same, 20 00:01:31,608 --> 00:01:35,946 then the electron domain geometry is trigonal planar. 21 00:01:35,946 --> 00:01:37,314 Right. 22 00:01:37,314 --> 00:01:38,549 OK. 23 00:01:38,549 --> 00:01:47,591 But I was also telling you about repulsion order 24 00:01:47,591 --> 00:01:49,960 at the same time. 25 00:01:49,960 --> 00:01:53,097 And so I put the wrong thing in the table. 26 00:01:53,097 --> 00:01:53,997 And then I erased it. 27 00:01:53,997 --> 00:01:55,732 And I just want to be sure we're clear 28 00:01:55,732 --> 00:01:57,801 and we don't get bent out of shape about it. 29 00:01:57,801 --> 00:01:58,502 [LAUGHTER] 30 00:01:58,502 --> 00:01:59,002 Stop. 31 00:01:59,002 --> 00:01:59,503 [CLAPPING] 32 00:01:59,503 --> 00:02:00,370 Get out of here. 33 00:02:00,370 --> 00:02:01,438 Stop. 34 00:02:01,438 --> 00:02:02,005 Stop it. 35 00:02:02,005 --> 00:02:02,506 All right. 36 00:02:02,506 --> 00:02:03,907 All right. 37 00:02:03,907 --> 00:02:05,576 I'm going to still be here. 38 00:02:05,576 --> 00:02:06,710 I'm going to be here. 39 00:02:06,710 --> 00:02:07,377 All right. 40 00:02:07,377 --> 00:02:09,713 So like here, right, the shape. 41 00:02:13,684 --> 00:02:21,925 Remember, what the table was about 42 00:02:21,925 --> 00:02:26,163 was the number of lone pairs. 43 00:02:26,163 --> 00:02:27,164 OK. 44 00:02:27,164 --> 00:02:28,532 The number of lone pairs. 45 00:02:28,532 --> 00:02:30,634 And so if I've got the three binding 46 00:02:30,634 --> 00:02:33,270 pairs and no lone pairs, then it's 47 00:02:33,270 --> 00:02:35,439 going to be a trigonal planar shape. 48 00:02:35,439 --> 00:02:38,742 So that is trigonal planar. 49 00:02:38,742 --> 00:02:42,478 And over here I've got two bonding pairs 50 00:02:42,478 --> 00:02:44,548 and one lone pair. 51 00:02:44,548 --> 00:02:47,284 And so this shape is called bent. 52 00:02:47,284 --> 00:02:49,553 Now, what I did is I used that word. 53 00:02:49,553 --> 00:02:51,221 Aw, why? 54 00:02:51,221 --> 00:02:51,788 I don't know. 55 00:02:51,788 --> 00:02:53,290 But you make mistakes. 56 00:02:53,290 --> 00:02:56,160 When you're in the arena, you keep going. 57 00:02:56,160 --> 00:02:58,262 And if you make a mistake, you admit it. 58 00:02:58,262 --> 00:03:00,197 You leave it all there. 59 00:03:00,197 --> 00:03:00,964 You do your best. 60 00:03:00,964 --> 00:03:01,732 Forget the rest. 61 00:03:01,732 --> 00:03:03,634 That's all you can ever do. 62 00:03:03,634 --> 00:03:05,135 Now, here's the thing. 63 00:03:05,135 --> 00:03:06,470 I said bent. 64 00:03:06,470 --> 00:03:07,538 I said the word bent. 65 00:03:07,538 --> 00:03:09,339 And what I was talking about was how 66 00:03:09,339 --> 00:03:12,643 that bends a little bit because of the repulsion order. 67 00:03:12,643 --> 00:03:13,177 Yeah. 68 00:03:13,177 --> 00:03:15,512 But that shape is not bent. 69 00:03:15,512 --> 00:03:17,214 I want to be real clear about that. 70 00:03:17,214 --> 00:03:19,049 That shape is trigonal planer. 71 00:03:19,049 --> 00:03:21,418 And it's a little bit distorted. 72 00:03:21,418 --> 00:03:23,453 OK. 73 00:03:23,453 --> 00:03:26,456 This shape is bent. 74 00:03:26,456 --> 00:03:30,427 That shape is bent, because it's got a lone pair. 75 00:03:30,427 --> 00:03:33,463 Remember, the shape is about where the atoms are. 76 00:03:33,463 --> 00:03:37,201 But it's also a little bit distorted. 77 00:03:37,201 --> 00:03:38,235 Right? 78 00:03:38,235 --> 00:03:43,240 Because the lone pair pushes on those guys a little bit more. 79 00:03:43,240 --> 00:03:43,807 All right. 80 00:03:43,807 --> 00:03:44,308 OK. 81 00:03:44,308 --> 00:03:48,712 So those are the two concepts that I was saying all at once. 82 00:03:48,712 --> 00:03:50,614 And I want to make sure we understand them. 83 00:03:50,614 --> 00:03:52,349 There's trigonal planar. 84 00:03:52,349 --> 00:03:53,350 there's bent. 85 00:03:53,350 --> 00:03:54,751 And then there's repulsion order, 86 00:03:54,751 --> 00:03:58,188 which talks about little changes in the angle from those parent 87 00:03:58,188 --> 00:03:58,755 shapes. 88 00:03:58,755 --> 00:03:59,256 OK. 89 00:03:59,256 --> 00:04:00,023 Good. 90 00:04:00,023 --> 00:04:00,524 All right. 91 00:04:00,524 --> 00:04:02,926 Now, onto today. 92 00:04:02,926 --> 00:04:03,994 Now, here's the thing. 93 00:04:03,994 --> 00:04:08,799 Now, in all of this stuff with Lewis, 94 00:04:08,799 --> 00:04:12,002 it's a really good way to think about molecules. 95 00:04:12,002 --> 00:04:16,373 But this tells me that there's electrons on the bond. 96 00:04:16,373 --> 00:04:17,808 It tells me that there's electrons 97 00:04:17,808 --> 00:04:21,111 really localized in the region between the atoms. 98 00:04:21,111 --> 00:04:25,082 But see, the thing is, how much is it localized? 99 00:04:25,082 --> 00:04:26,650 How much is it really? 100 00:04:26,650 --> 00:04:31,221 Are these electrons-- if I were to draw the two electrons, are 101 00:04:31,221 --> 00:04:34,424 those dots right there? 102 00:04:34,424 --> 00:04:38,428 It doesn't really tell me more information than that. 103 00:04:38,428 --> 00:04:42,099 But if we remember the picture-- let's see if I can pull. 104 00:04:42,099 --> 00:04:42,599 Yep. 105 00:04:42,599 --> 00:04:43,467 There it is. 106 00:04:43,467 --> 00:04:45,869 There's a picture I showed you when we first 107 00:04:45,869 --> 00:04:47,838 talked about covalent bonds. 108 00:04:47,838 --> 00:04:49,606 Sharing is caring. 109 00:04:49,606 --> 00:04:50,907 Remember what happens. 110 00:04:50,907 --> 00:04:52,042 I've got the two protons. 111 00:04:52,042 --> 00:04:53,143 And we talked about these. 112 00:04:53,143 --> 00:04:54,444 A repulsion. 113 00:04:54,444 --> 00:04:55,579 And then the two electrons. 114 00:04:55,579 --> 00:04:56,680 Repulsion. 115 00:04:56,680 --> 00:04:58,282 And then I drew for you the fact that, 116 00:04:58,282 --> 00:04:59,549 but they can come together. 117 00:04:59,549 --> 00:05:01,018 And they can be like, you know what? 118 00:05:01,018 --> 00:05:03,420 You can use my proton for a little of your attraction. 119 00:05:03,420 --> 00:05:05,355 And hey, can I use your-- 120 00:05:05,355 --> 00:05:06,223 And they share it. 121 00:05:06,223 --> 00:05:08,825 And each electron sees both of them. 122 00:05:08,825 --> 00:05:12,663 And this is where those electrons are. 123 00:05:12,663 --> 00:05:13,363 But look at that. 124 00:05:13,363 --> 00:05:15,232 The proton is there and there. 125 00:05:15,232 --> 00:05:18,468 And the electron is in this probability cloud 126 00:05:18,468 --> 00:05:19,703 around both of them. 127 00:05:19,703 --> 00:05:24,741 That's the molecular orbital. 128 00:05:24,741 --> 00:05:26,443 And Lewis can't tell us about that. 129 00:05:26,443 --> 00:05:27,544 So we need something else. 130 00:05:27,544 --> 00:05:29,446 And that's what today's topic is about. 131 00:05:29,446 --> 00:05:32,115 Today we're going to talk about something called 132 00:05:32,115 --> 00:05:35,886 molecular orbital theory that gives us a sense of how 133 00:05:35,886 --> 00:05:40,991 these atomic orbitals overlap. 134 00:05:40,991 --> 00:05:45,696 It gives us a much better and a deeper description 135 00:05:45,696 --> 00:05:48,899 with more details about these covalent bonds. 136 00:05:48,899 --> 00:05:49,499 OK. 137 00:05:49,499 --> 00:05:50,000 All right. 138 00:05:50,000 --> 00:05:55,672 Now, so let's write a few things about molecular orbital theory. 139 00:05:55,672 --> 00:05:58,241 Molecular orbital. 140 00:05:58,241 --> 00:06:03,146 And what we're going to do is say, MO, and Molecular Orbital 141 00:06:03,146 --> 00:06:03,647 theory. 142 00:06:03,647 --> 00:06:06,149 So we'll keep a list of some important things. 143 00:06:06,149 --> 00:06:06,650 All right. 144 00:06:06,650 --> 00:06:08,719 Well, first of all, the first thing 145 00:06:08,719 --> 00:06:17,494 is that atomic orbitals, or, as we may call them, 146 00:06:17,494 --> 00:06:25,902 AOs, are the basis for-- 147 00:06:25,902 --> 00:06:28,438 watch this efficiency, the MOs. 148 00:06:28,438 --> 00:06:29,773 I didn't have to write it again. 149 00:06:29,773 --> 00:06:30,607 Right? 150 00:06:30,607 --> 00:06:31,108 OK. 151 00:06:31,108 --> 00:06:32,075 So what does that mean? 152 00:06:32,075 --> 00:06:36,813 Well, it means that I'm going to construct the MOs from the AOs. 153 00:06:36,813 --> 00:06:38,181 Now, the AOs are the things we've 154 00:06:38,181 --> 00:06:39,816 been playing with and making. 155 00:06:39,816 --> 00:06:40,317 Right? 156 00:06:40,317 --> 00:06:41,952 We solved the Schrodinger equation. 157 00:06:41,952 --> 00:06:49,726 So the MOs are going to be linear combinations. 158 00:06:49,726 --> 00:06:50,227 All right. 159 00:06:50,227 --> 00:06:56,332 Combinations of the AOs. 160 00:06:56,332 --> 00:07:02,773 And that's why you might see this, in fact, called 161 00:07:02,773 --> 00:07:04,307 LCAO theory. 162 00:07:04,307 --> 00:07:05,308 LCAO. 163 00:07:05,308 --> 00:07:08,612 Linear Combination of Atomic Orbitals. 164 00:07:08,612 --> 00:07:10,180 OK. 165 00:07:10,180 --> 00:07:19,589 And in particular, sum and difference of orbitals 166 00:07:19,589 --> 00:07:20,424 is what we're about. 167 00:07:20,424 --> 00:07:25,095 Because this is like what we talked about before. 168 00:07:25,095 --> 00:07:26,963 These are waves. 169 00:07:26,963 --> 00:07:27,464 Right. 170 00:07:27,464 --> 00:07:28,832 These are waves. 171 00:07:28,832 --> 00:07:34,638 Waves can either constructively or destructively interfere. 172 00:07:34,638 --> 00:07:37,407 And that's what we're going to explore in MO theory. 173 00:07:37,407 --> 00:07:41,845 By adding or subtracting these wave functions, 174 00:07:41,845 --> 00:07:46,016 these orbitals, these atomic orbitals. 175 00:07:46,016 --> 00:07:47,082 So that's enough to start. 176 00:07:47,082 --> 00:07:47,784 Let's see. 177 00:07:47,784 --> 00:07:49,953 So look, basis. 178 00:07:49,953 --> 00:07:52,522 A basis is nothing more than the things 179 00:07:52,522 --> 00:07:55,292 that I'm going to use to represent the things that I 180 00:07:55,292 --> 00:07:56,659 want. 181 00:07:56,659 --> 00:07:57,159 Right. 182 00:07:57,159 --> 00:07:59,596 And the things that I want are these molecular orbitals. 183 00:07:59,596 --> 00:08:01,898 And the things that I'm going to use to represent those 184 00:08:01,898 --> 00:08:06,503 are these, these beautiful atomic orbitals 185 00:08:06,503 --> 00:08:09,606 that we spent a lot of time understanding and developing. 186 00:08:09,606 --> 00:08:15,412 We'll start with the simplest case, which is-- 187 00:08:15,412 --> 00:08:17,147 I think I have-- 188 00:08:17,147 --> 00:08:18,448 oh, I even highlighted it. 189 00:08:18,448 --> 00:08:21,685 And I said, let's first make molecular orbitals 190 00:08:21,685 --> 00:08:25,722 using combinations of the S orbital. 191 00:08:25,722 --> 00:08:26,790 That's the S orbital. 192 00:08:26,790 --> 00:08:28,892 That's the 1s orbital up there. 193 00:08:28,892 --> 00:08:32,962 Remember, by the way, blue and orange 194 00:08:32,962 --> 00:08:34,798 is just the sign of the wave. 195 00:08:34,798 --> 00:08:35,432 Right. 196 00:08:35,432 --> 00:08:37,467 This is not a charge. 197 00:08:37,467 --> 00:08:40,135 Please don't make that confusion. 198 00:08:40,135 --> 00:08:41,337 These are just waves. 199 00:08:41,337 --> 00:08:41,837 Right. 200 00:08:41,837 --> 00:08:43,440 Waves. 201 00:08:43,440 --> 00:08:45,809 And let's go back and see it. 202 00:08:45,809 --> 00:08:48,144 The p orbital has a plus and a minus. 203 00:08:48,144 --> 00:08:49,412 It's a wave. 204 00:08:49,412 --> 00:08:50,380 All right. 205 00:08:50,380 --> 00:08:52,582 And the 2s orbital has that too. 206 00:08:52,582 --> 00:08:55,151 And then you square it, and you get the probabilities. 207 00:08:55,151 --> 00:08:56,520 Right? 208 00:08:56,520 --> 00:08:57,354 OK. 209 00:08:57,354 --> 00:09:00,490 So we'll start with 1s where it's all just one sign. 210 00:09:00,490 --> 00:09:02,559 And I can add it. 211 00:09:02,559 --> 00:09:05,462 I can add an S and another S. Or I can subtract it. 212 00:09:05,462 --> 00:09:06,329 So let's do that. 213 00:09:06,329 --> 00:09:06,830 Right. 214 00:09:06,830 --> 00:09:08,498 So we'll do that over here. 215 00:09:08,498 --> 00:09:08,999 All right. 216 00:09:13,203 --> 00:09:21,478 So if I take a 1s orbital, and I add it to another 1s orbital, 217 00:09:21,478 --> 00:09:24,848 well, you can see, as I bring these close together, 218 00:09:24,848 --> 00:09:26,983 if they have the same sign, these are waves. 219 00:09:26,983 --> 00:09:29,319 So if the waves are both positive, 220 00:09:29,319 --> 00:09:32,956 and I bring them together, they can constructively interfere. 221 00:09:32,956 --> 00:09:35,592 So as I bring them closer and closer, 222 00:09:35,592 --> 00:09:37,294 well, I might actually get the picture 223 00:09:37,294 --> 00:09:38,628 that I showed you, right? 224 00:09:38,628 --> 00:09:42,165 I might actually get something that looks like this. 225 00:09:45,068 --> 00:09:45,735 OK. 226 00:09:45,735 --> 00:09:47,470 I might actually get something like this. 227 00:09:47,470 --> 00:09:55,545 Now, if I subtracted them, then as I bring these orbitals 228 00:09:55,545 --> 00:10:00,550 closer together, well, they're going to cancel each other. 229 00:10:00,550 --> 00:10:03,820 And you can see right here, if I bring these orbitals-- 230 00:10:03,820 --> 00:10:06,423 by the way, which are coming from two different atoms. 231 00:10:06,423 --> 00:10:06,923 Right. 232 00:10:06,923 --> 00:10:11,828 The whole point is we're talking about molecules, molecular. 233 00:10:11,828 --> 00:10:13,897 So if I bring them together now like this, 234 00:10:13,897 --> 00:10:17,367 but I'm subtracting these orbitals, 235 00:10:17,367 --> 00:10:19,469 then you can see that right at the interface, right 236 00:10:19,469 --> 00:10:22,205 between them, it's always zero. 237 00:10:22,205 --> 00:10:24,074 Because I've just subtracted the same amount. 238 00:10:24,074 --> 00:10:25,976 No matter how close they get, it's zero. 239 00:10:25,976 --> 00:10:27,477 That's a node. 240 00:10:27,477 --> 00:10:27,978 Right. 241 00:10:27,978 --> 00:10:29,846 And, in fact, what you're going to get 242 00:10:29,846 --> 00:10:31,982 is something that looks like this. 243 00:10:35,251 --> 00:10:40,023 Now, so what I've done is I have added and subtracted 244 00:10:40,023 --> 00:10:42,525 the same AO. 245 00:10:42,525 --> 00:10:44,861 And I've created two MOs. 246 00:10:44,861 --> 00:10:46,596 So these are my MOs. 247 00:10:46,596 --> 00:10:49,132 And these are my starting AOs. 248 00:10:49,132 --> 00:10:53,503 That's about the simplest thing you can do in MO theory. 249 00:10:53,503 --> 00:10:55,238 So I'm using these as a basis. 250 00:10:55,238 --> 00:10:58,942 Now, there's something very important, which is that-- 251 00:10:58,942 --> 00:11:01,111 I kind of already alluded to this-- 252 00:11:01,111 --> 00:11:04,547 these are two atoms coming together to make a bond. 253 00:11:04,547 --> 00:11:07,117 This is the bonding axis. 254 00:11:07,117 --> 00:11:08,318 This is the bonding axis. 255 00:11:08,318 --> 00:11:08,985 OK. 256 00:11:08,985 --> 00:11:15,425 Now, if an orbital, if an MO is symmetric, 257 00:11:15,425 --> 00:11:24,634 so if it has cylindrical symmetry about that bonding 258 00:11:24,634 --> 00:11:36,680 axis, then it's called a sigma orbital. 259 00:11:36,680 --> 00:11:37,847 It's called a sigma orbital. 260 00:11:37,847 --> 00:11:40,383 That's the MO. 261 00:11:40,383 --> 00:11:42,452 Sigma is a notation. 262 00:11:42,452 --> 00:11:44,621 A sigma orbital is one that has symmetry 263 00:11:44,621 --> 00:11:51,094 around the internuclear axis, the two-- 264 00:11:51,094 --> 00:11:54,497 Does Pauli exclusion not apply to that? 265 00:11:54,497 --> 00:11:58,201 We're coming to that very soon. 266 00:11:58,201 --> 00:11:59,703 Because these are just the orbitals. 267 00:11:59,703 --> 00:12:01,037 I got to do something with them. 268 00:12:01,037 --> 00:12:02,238 It's just like over here. 269 00:12:02,238 --> 00:12:03,339 I made all these orbitals. 270 00:12:03,339 --> 00:12:06,743 But then I had to fill them. 271 00:12:06,743 --> 00:12:08,978 That got me excited. 272 00:12:08,978 --> 00:12:11,681 But you can see right here. 273 00:12:11,681 --> 00:12:17,454 When I add them up there's charge in between. 274 00:12:17,454 --> 00:12:19,956 So this looks like it's going to have a bond. 275 00:12:24,394 --> 00:12:26,863 That's a bonding MO. 276 00:12:26,863 --> 00:12:30,333 But if I subtracted them, this doesn't look very happy 277 00:12:30,333 --> 00:12:33,269 in terms of electrons being in between 278 00:12:33,269 --> 00:12:35,672 and the caring is sharing principle of a covalent bond. 279 00:12:35,672 --> 00:12:36,873 Right. 280 00:12:36,873 --> 00:12:39,776 So if I were to put an electron in this MO, 281 00:12:39,776 --> 00:12:40,844 it doesn't look bonding. 282 00:12:40,844 --> 00:12:42,445 In fact, it looks-- 283 00:12:42,445 --> 00:12:43,346 Non-bonding. 284 00:12:43,346 --> 00:12:45,548 Or antibonding. 285 00:12:45,548 --> 00:12:47,383 It's actually not quite non-binding. 286 00:12:47,383 --> 00:12:48,651 We'll get to that later. 287 00:12:48,651 --> 00:12:51,755 This would be antibonding. 288 00:12:51,755 --> 00:12:53,156 Why? 289 00:12:53,156 --> 00:12:57,127 Because there's not even a chance of electron 290 00:12:57,127 --> 00:12:58,795 density in between. 291 00:12:58,795 --> 00:13:01,998 That's your starting principle of the relationship. 292 00:13:01,998 --> 00:13:02,799 Let's try to share. 293 00:13:02,799 --> 00:13:06,803 Oh, by the way, right half way, no chance. 294 00:13:06,803 --> 00:13:08,371 That's not a very good way to start. 295 00:13:08,371 --> 00:13:10,807 And you can see why this is antibonding. 296 00:13:10,807 --> 00:13:12,542 It's the opposite. 297 00:13:12,542 --> 00:13:14,577 You're actually pushing charge away from the bond 298 00:13:14,577 --> 00:13:17,714 if you're an electron in that orbital. 299 00:13:17,714 --> 00:13:19,415 So that's an antibonding orbital. 300 00:13:19,415 --> 00:13:21,551 Now we get to the question. 301 00:13:21,551 --> 00:13:23,019 What do you do with these orbitals? 302 00:13:23,019 --> 00:13:25,088 Well, you make them. 303 00:13:25,088 --> 00:13:28,992 I made these with 1s. 304 00:13:28,992 --> 00:13:32,962 And the way that we typically draw this is we 305 00:13:32,962 --> 00:13:35,932 go back to the same picture that we've 306 00:13:35,932 --> 00:13:41,171 been working with, 1s here and 1s here. 307 00:13:41,171 --> 00:13:42,739 And I brought those orbitals together, 308 00:13:42,739 --> 00:13:47,710 and I formed one that lowered the energy of the system, 309 00:13:47,710 --> 00:13:51,347 and another that actually raised the energy of the system, 310 00:13:51,347 --> 00:13:53,449 because the electrons are repelling. 311 00:13:53,449 --> 00:13:55,552 They're actually less bonding. 312 00:13:55,552 --> 00:13:56,786 They're antibonding. 313 00:13:56,786 --> 00:13:57,287 All right. 314 00:14:00,924 --> 00:14:04,127 So these are my MOs. 315 00:14:04,127 --> 00:14:05,728 Those are my AOs. 316 00:14:05,728 --> 00:14:06,229 Right. 317 00:14:06,229 --> 00:14:07,730 AO, AO. 318 00:14:07,730 --> 00:14:11,868 And now, this is called a sigma orbital. 319 00:14:11,868 --> 00:14:14,437 And the way we refer to the antibonding orbital 320 00:14:14,437 --> 00:14:17,040 is with a little star. 321 00:14:17,040 --> 00:14:20,276 They're both sigma because they both satisfy that. 322 00:14:20,276 --> 00:14:20,777 Right. 323 00:14:20,777 --> 00:14:23,213 They're both sigma cause they both have 324 00:14:23,213 --> 00:14:26,916 symmetry around the inter nuclear bonding axis. 325 00:14:26,916 --> 00:14:28,251 But now, see, OK. 326 00:14:28,251 --> 00:14:29,018 So that's good. 327 00:14:32,555 --> 00:14:33,923 But now let's fill them. 328 00:14:33,923 --> 00:14:35,191 Let's fill them. 329 00:14:35,191 --> 00:14:39,429 Because now let's write down the rules. 330 00:14:39,429 --> 00:14:41,364 And then we'll fill them for some examples. 331 00:14:41,364 --> 00:14:41,998 OK. 332 00:14:41,998 --> 00:14:44,868 So I'm going to keep going on my MO theory list. 333 00:14:44,868 --> 00:14:45,368 Right. 334 00:14:45,368 --> 00:14:49,105 As you can see, when I do it this way, the number of MOs 335 00:14:49,105 --> 00:14:56,713 equals the number of AOs used to create them. 336 00:14:56,713 --> 00:14:59,515 So that's one thing that we can see right away. 337 00:14:59,515 --> 00:15:00,383 Right. 338 00:15:00,383 --> 00:15:01,751 I used two AOs. 339 00:15:01,751 --> 00:15:02,919 I added and subtracted them. 340 00:15:02,919 --> 00:15:03,987 I got two MOs. 341 00:15:03,987 --> 00:15:05,088 That's good. 342 00:15:05,088 --> 00:15:16,499 Well, another thing is, each MO will be just like an AO. 343 00:15:16,499 --> 00:15:17,934 It makes a lot of sense. 344 00:15:17,934 --> 00:15:20,436 I had room for two electrons here. 345 00:15:20,436 --> 00:15:21,838 I had room for two electrons here. 346 00:15:21,838 --> 00:15:24,040 I got to have room for four. 347 00:15:24,040 --> 00:15:24,874 Two here. 348 00:15:24,874 --> 00:15:25,942 Two here. 349 00:15:25,942 --> 00:15:26,442 Right. 350 00:15:26,442 --> 00:15:33,349 So each MO has a max of two electrons. 351 00:15:33,349 --> 00:15:39,555 And they must obey Pauli, just like in AOs. 352 00:15:39,555 --> 00:15:41,124 They must obey Pauli. 353 00:15:41,124 --> 00:15:42,725 You can't mess with quantum mechanics. 354 00:15:42,725 --> 00:15:43,226 Uh-uh. 355 00:15:45,395 --> 00:15:46,396 They're still electrons. 356 00:15:46,396 --> 00:15:48,564 They're still quantum mechanical. 357 00:15:48,564 --> 00:15:49,165 All right. 358 00:15:49,165 --> 00:15:52,869 You're just making their wave function more sophisticated. 359 00:15:52,869 --> 00:15:54,737 But they still have to follow the Schrodinger 360 00:15:54,737 --> 00:15:57,573 equation and the principles of quantum mechanics. 361 00:15:57,573 --> 00:15:59,542 And so, finally, what we're going to do 362 00:15:59,542 --> 00:16:01,077 is we're going to fill them. 363 00:16:01,077 --> 00:16:08,284 So we're going to fill the MOs with electrons, starting 364 00:16:08,284 --> 00:16:09,953 with the lowest energy, just like we did 365 00:16:09,953 --> 00:16:14,857 for atoms, lowest energy first. 366 00:16:14,857 --> 00:16:16,125 OK. 367 00:16:16,125 --> 00:16:17,360 And one more thing. 368 00:16:17,360 --> 00:16:22,932 Just like we did with atoms is we're going to obey Hund. 369 00:16:22,932 --> 00:16:23,766 Hund. 370 00:16:23,766 --> 00:16:25,868 Hund's rule, which tells you about how 371 00:16:25,868 --> 00:16:27,937 to fill degenerate orbitals. 372 00:16:27,937 --> 00:16:30,974 Well, we're going to have degenerate orbitals here too. 373 00:16:30,974 --> 00:16:31,708 We don't yet. 374 00:16:31,708 --> 00:16:32,508 But we will. 375 00:16:32,508 --> 00:16:33,676 So we're going to fill them. 376 00:16:33,676 --> 00:16:36,746 So let's fill them for the very simplest cases. 377 00:16:36,746 --> 00:16:37,246 OK. 378 00:16:37,246 --> 00:16:39,549 So we'll do some cases together. 379 00:16:39,549 --> 00:16:41,584 And we'll see how that goes. 380 00:16:41,584 --> 00:16:42,085 All right. 381 00:16:42,085 --> 00:16:45,788 So what I'm going to do are four cases just so we can compare. 382 00:16:45,788 --> 00:16:48,658 So first, we're going to do H2 plus. 383 00:16:48,658 --> 00:16:49,158 OK. 384 00:16:49,158 --> 00:16:50,860 That's the first one. 385 00:16:50,860 --> 00:16:57,266 And here, what we have is the same graph. 386 00:16:57,266 --> 00:17:00,003 But now, over here I actually can label it now. 387 00:17:00,003 --> 00:17:01,537 This was just an orbital. 388 00:17:01,537 --> 00:17:02,638 But now, gazuntite. 389 00:17:02,638 --> 00:17:04,640 Now, I'll say, OK. 390 00:17:04,640 --> 00:17:12,080 Well, this would be like H and H plus. 391 00:17:12,080 --> 00:17:12,582 OK. 392 00:17:12,582 --> 00:17:18,121 These are my MOs, sigma, sigma star, 1s, 1s. 393 00:17:18,121 --> 00:17:20,823 Oh, boy. 394 00:17:20,823 --> 00:17:23,626 So if that's H and that's H plus, 395 00:17:23,626 --> 00:17:25,828 and they're coming together to make H2 plus-- that's 396 00:17:25,828 --> 00:17:26,963 what's in the middle there. 397 00:17:26,963 --> 00:17:28,330 That's the molecule. 398 00:17:28,330 --> 00:17:29,065 All right. 399 00:17:29,065 --> 00:17:33,036 Well, then I also can now fill in the starting AOs. 400 00:17:33,036 --> 00:17:33,870 So let's do that. 401 00:17:36,406 --> 00:17:37,206 That's it. 402 00:17:37,206 --> 00:17:41,344 Because somebody had to lose an electron to start with. 403 00:17:41,344 --> 00:17:43,913 So now, when these come together, you fill. 404 00:17:43,913 --> 00:17:45,982 You obey the Pauli exclusion. 405 00:17:45,982 --> 00:17:47,984 You fill it from the lowest energy first. 406 00:17:47,984 --> 00:17:50,086 You say, well, I only got one electron. 407 00:17:50,086 --> 00:17:51,721 There it is. 408 00:17:51,721 --> 00:17:56,659 That's my MO diagram populated by electrons. 409 00:17:56,659 --> 00:17:58,561 OK. 410 00:17:58,561 --> 00:18:00,963 Now, there's a principle that comes out of this. 411 00:18:00,963 --> 00:18:04,767 There's a way of understanding bond strength now. 412 00:18:04,767 --> 00:18:06,636 There's a way of understanding bond strength. 413 00:18:06,636 --> 00:18:09,539 And that is a very important concept. 414 00:18:09,539 --> 00:18:13,176 Now, let's put it here in our list. 415 00:18:13,176 --> 00:18:14,277 OK. 416 00:18:14,277 --> 00:18:16,045 And it's a concept called bond order. 417 00:18:18,648 --> 00:18:21,517 Now, this one I really want to write BO. 418 00:18:21,517 --> 00:18:24,253 But I don't know if that's a good idea. 419 00:18:27,356 --> 00:18:28,591 I got Laura on that one. 420 00:18:28,591 --> 00:18:29,725 OK. 421 00:18:29,725 --> 00:18:31,861 And there's a definition for this. 422 00:18:31,861 --> 00:18:37,900 It's going to equal 1/2 of the number of electrons 423 00:18:37,900 --> 00:18:48,010 in a bonding orbital, minus the number of electrons 424 00:18:48,010 --> 00:18:53,883 in an antibonding orbital. 425 00:18:53,883 --> 00:18:54,383 Sorry. 426 00:18:54,383 --> 00:18:57,954 This is a little bit small here. 427 00:18:57,954 --> 00:19:00,456 But we'll do a bunch of them so you can see what this means. 428 00:19:00,456 --> 00:19:00,957 Right. 429 00:19:00,957 --> 00:19:03,593 So now, the bond order is important because the bond 430 00:19:03,593 --> 00:19:21,244 order of a molecule, if it's higher than a stronger bond, 431 00:19:21,244 --> 00:19:29,285 and it has to be greater than zero for stability. 432 00:19:29,285 --> 00:19:31,754 Let's see how that works. 433 00:19:31,754 --> 00:19:35,391 And we'll see this intuitively as well as we fill these up. 434 00:19:35,391 --> 00:19:35,892 Right. 435 00:19:35,892 --> 00:19:38,461 So if I count the bond order here-- oh, I'm going to do it. 436 00:19:38,461 --> 00:19:40,163 I don't feel like writing it out. 437 00:19:40,163 --> 00:19:46,869 The BO on this one is 1/2 times 1 minus 0, which equals 1/2. 438 00:19:46,869 --> 00:19:47,370 OK. 439 00:19:47,370 --> 00:19:48,404 Good. 440 00:19:48,404 --> 00:19:49,238 It's 1/2. 441 00:19:49,238 --> 00:19:50,873 Well, it's greater than 0. 442 00:19:50,873 --> 00:19:53,576 So right away I know that the H2 plus molecule is probably 443 00:19:53,576 --> 00:19:54,110 stable. 444 00:19:54,110 --> 00:19:54,977 That's good. 445 00:19:54,977 --> 00:19:57,480 But let's go to some more examples now. 446 00:19:57,480 --> 00:19:59,549 Let's do a few more. 447 00:19:59,549 --> 00:20:01,017 All right. 448 00:20:01,017 --> 00:20:03,219 Now we're going to work our way to H2. 449 00:20:03,219 --> 00:20:05,388 And in this case, energy is always 450 00:20:05,388 --> 00:20:07,690 going up in these diagrams. 451 00:20:07,690 --> 00:20:11,827 Now, each of these H atoms is bringing an electron. 452 00:20:11,827 --> 00:20:13,930 There's no charge to the system. 453 00:20:13,930 --> 00:20:20,836 And so now different quantum numbers. 454 00:20:20,836 --> 00:20:21,337 Pauli. 455 00:20:24,740 --> 00:20:26,342 But same sigma. 456 00:20:26,342 --> 00:20:26,943 Right. 457 00:20:26,943 --> 00:20:29,078 And so now that's the H2. 458 00:20:29,078 --> 00:20:33,583 Now, the bond order here is equal to 1. 459 00:20:33,583 --> 00:20:34,850 Right? 460 00:20:34,850 --> 00:20:38,387 I didn't have any electrons in an antibonding orbital. 461 00:20:38,387 --> 00:20:38,888 All right. 462 00:20:38,888 --> 00:20:40,022 But you know what's coming. 463 00:20:40,022 --> 00:20:42,692 I'm going to do He2 plus next. 464 00:20:42,692 --> 00:20:51,534 And let's just put it here for comparison in real time. 465 00:20:51,534 --> 00:20:57,773 If I were He2, each of these would be the AO occupation 466 00:20:57,773 --> 00:20:59,875 of an He atom. 467 00:20:59,875 --> 00:21:00,376 Right? 468 00:21:05,548 --> 00:21:10,419 But since I'm He2 plus, one of them is missing an electron. 469 00:21:10,419 --> 00:21:12,121 So this is what you're going to see. 470 00:21:12,121 --> 00:21:14,657 These are both He atoms still, but one of them 471 00:21:14,657 --> 00:21:18,194 is plus in this picture. 472 00:21:18,194 --> 00:21:19,028 But see now, OK. 473 00:21:19,028 --> 00:21:20,596 I've got three electrons. 474 00:21:20,596 --> 00:21:21,998 They're going to go here. 475 00:21:21,998 --> 00:21:25,434 And I've got to put one up here. 476 00:21:25,434 --> 00:21:26,802 I have to. 477 00:21:26,802 --> 00:21:27,536 Cause I had three. 478 00:21:27,536 --> 00:21:30,840 I got to keep on filling, just like in an atom. 479 00:21:30,840 --> 00:21:34,410 But now I'm filling bonding and antibonding orbitals. 480 00:21:34,410 --> 00:21:34,910 All right. 481 00:21:34,910 --> 00:21:40,683 And here I've got this and two up there. 482 00:21:40,683 --> 00:21:42,785 So if you look at the bond order, 483 00:21:42,785 --> 00:21:46,622 here the bond order is still positive. 484 00:21:46,622 --> 00:21:49,692 Here the bond order is zero. 485 00:21:49,692 --> 00:21:54,263 And, in fact, that's why He2 is not a stable molecule. 486 00:21:54,263 --> 00:21:57,099 Because you're putting just as much charge on this thing that 487 00:21:57,099 --> 00:21:58,968 wants to bond it as you are on this thing 488 00:21:58,968 --> 00:22:01,737 that doesn't want to bond it. 489 00:22:01,737 --> 00:22:05,141 And at the end of the day, it leads to a molecule 490 00:22:05,141 --> 00:22:07,143 that is not stable. 491 00:22:07,143 --> 00:22:08,244 So that would be He2. 492 00:22:08,244 --> 00:22:10,813 But He2 plus has a bond order that's similar. 493 00:22:14,150 --> 00:22:15,918 Did I get something wrong? 494 00:22:15,918 --> 00:22:17,553 He2 plus 1/2. 495 00:22:20,856 --> 00:22:21,824 OK. 496 00:22:21,824 --> 00:22:26,696 Now, because this weakened it. 497 00:22:26,696 --> 00:22:27,196 Right. 498 00:22:27,196 --> 00:22:29,398 This weakened the molecule, compared 499 00:22:29,398 --> 00:22:31,934 to this, because now I added charge 500 00:22:31,934 --> 00:22:33,336 to an antibonding orbital. 501 00:22:33,336 --> 00:22:35,504 So you would expect from the bond order 502 00:22:35,504 --> 00:22:37,907 that this one is more stable than this. 503 00:22:37,907 --> 00:22:39,975 And, in fact, that's what you find. 504 00:22:39,975 --> 00:22:40,476 Right. 505 00:22:40,476 --> 00:22:44,647 The H2 molecule has a stronger bonding energy. 506 00:22:44,647 --> 00:22:49,652 Now, we can write the molecular orbital configurations 507 00:22:49,652 --> 00:22:52,955 just like we did with the atomic orbital configurations. 508 00:22:52,955 --> 00:22:53,923 OK. 509 00:22:53,923 --> 00:23:00,029 And so like for here, so for this case-- 510 00:23:00,029 --> 00:23:01,931 I'm going to write it up top if I can fit it. 511 00:23:01,931 --> 00:23:06,202 So here we would have sigma 1s. 512 00:23:06,202 --> 00:23:09,338 And we're populating it with-- 513 00:23:09,338 --> 00:23:10,406 Ah. 514 00:23:10,406 --> 00:23:11,307 That's not my example. 515 00:23:11,307 --> 00:23:14,143 [GRUNTING] 516 00:23:14,143 --> 00:23:14,910 This is my example. 517 00:23:17,913 --> 00:23:19,749 Sigma 1s is the orbital. 518 00:23:19,749 --> 00:23:22,685 And we're populating it with one electron. 519 00:23:22,685 --> 00:23:23,486 Right. 520 00:23:23,486 --> 00:23:25,321 So that's how we would write that. 521 00:23:25,321 --> 00:23:28,157 Now, if we go to the next examples, 522 00:23:28,157 --> 00:23:33,496 we would have this one is this molecule you 523 00:23:33,496 --> 00:23:36,966 would write as sigma 1s 2. 524 00:23:36,966 --> 00:23:40,770 So this would be sigma 1s 2. 525 00:23:40,770 --> 00:23:47,076 And oh, now I've got sigma 1s 2. 526 00:23:47,076 --> 00:23:48,844 Oh, this is getting interesting. 527 00:23:48,844 --> 00:23:52,615 Because now it's sigma star 1s 1. 528 00:23:52,615 --> 00:23:55,551 So everybody see that? 529 00:23:55,551 --> 00:23:56,519 I populate. 530 00:23:56,519 --> 00:23:59,088 This is just like SPD. 531 00:23:59,088 --> 00:24:01,824 But now I'm just filling those MOs up. 532 00:24:01,824 --> 00:24:04,560 And I'm showing you what the molecular configuration 533 00:24:04,560 --> 00:24:08,697 is with those molecular orbital names. 534 00:24:08,697 --> 00:24:09,198 Sigma 1s. 535 00:24:09,198 --> 00:24:10,299 Sigma 1s star. 536 00:24:10,299 --> 00:24:10,766 OK. 537 00:24:10,766 --> 00:24:11,901 Good. 538 00:24:11,901 --> 00:24:15,571 Now, we can keep going. 539 00:24:15,571 --> 00:24:19,008 We could do this all day. 540 00:24:19,008 --> 00:24:20,109 Actually, we kind of will. 541 00:24:20,109 --> 00:24:23,779 But we're going to move on-- don't worry-- from sigma. 542 00:24:23,779 --> 00:24:24,280 Let's see. 543 00:24:24,280 --> 00:24:26,882 Let me go over here. 544 00:24:26,882 --> 00:24:28,551 There's another concept that I want 545 00:24:28,551 --> 00:24:29,952 you to know about MO theory. 546 00:24:34,457 --> 00:24:39,595 So if I kept going, I could have, for example, let's 547 00:24:39,595 --> 00:24:40,930 do lithium. 548 00:24:40,930 --> 00:24:41,430 OK. 549 00:24:41,430 --> 00:24:44,099 So now, lithium 1s. 550 00:24:44,099 --> 00:24:44,867 Oh-ho. 551 00:24:44,867 --> 00:24:47,002 2s. 552 00:24:47,002 --> 00:24:49,472 Lithium brings this. 553 00:24:49,472 --> 00:24:50,239 What does it bring? 554 00:24:50,239 --> 00:24:52,441 It brings three electrons. 555 00:24:52,441 --> 00:25:02,551 And over here, 1s and 2s, three electrons. 556 00:25:02,551 --> 00:25:05,721 So this would be the lithium dimer. 557 00:25:05,721 --> 00:25:07,289 But I want to make an important point. 558 00:25:07,289 --> 00:25:12,728 When you would draw this one, here's how I would draw it. 559 00:25:12,728 --> 00:25:17,399 Whereas when I would draw this one, I would draw it like this. 560 00:25:17,399 --> 00:25:18,133 OK. 561 00:25:18,133 --> 00:25:20,169 Now, those are supposed to be the same spacing. 562 00:25:20,169 --> 00:25:21,637 I'll tell you in a second. 563 00:25:24,240 --> 00:25:26,542 Notice that the distance here between the bonding 564 00:25:26,542 --> 00:25:31,046 and antibonding orbital is larger than it is here. 565 00:25:31,046 --> 00:25:35,618 The reason is because it's related to the overlap. 566 00:25:35,618 --> 00:25:42,725 So there's another point, which is that the overlap of AOs 567 00:25:42,725 --> 00:25:46,495 is related. 568 00:25:46,495 --> 00:25:52,535 So the greater the overlap of AOs, 569 00:25:52,535 --> 00:26:01,977 the greater the change in energy between bonding and antibonding 570 00:26:01,977 --> 00:26:02,478 orbitals. 571 00:26:14,623 --> 00:26:15,391 And let's be clear. 572 00:26:15,391 --> 00:26:17,693 Those are molecular. 573 00:26:17,693 --> 00:26:20,596 But see, you could see like, if I'm lithium, 574 00:26:20,596 --> 00:26:23,999 those 1ses aren't going to overlap too much. 575 00:26:23,999 --> 00:26:24,500 Right. 576 00:26:24,500 --> 00:26:26,502 They're kind of close to the core. 577 00:26:26,502 --> 00:26:27,903 So you do get MOs there. 578 00:26:27,903 --> 00:26:30,606 But the difference that you get depends 579 00:26:30,606 --> 00:26:35,411 on how much these electrons are near in energy and overlapping. 580 00:26:35,411 --> 00:26:36,145 All right. 581 00:26:36,145 --> 00:26:40,249 So the 2s can overlap a lot more. 582 00:26:40,249 --> 00:26:40,950 OK. 583 00:26:40,950 --> 00:26:42,518 Now, if I were to fill this up, we 584 00:26:42,518 --> 00:26:43,786 would get something like this. 585 00:26:46,589 --> 00:26:53,062 These sigma 1ses-- oh, sigma 1s. 586 00:26:53,062 --> 00:26:56,098 What do you think these are called? 587 00:26:56,098 --> 00:26:56,599 2s. 588 00:26:56,599 --> 00:26:58,734 Sigma 2s. 589 00:26:58,734 --> 00:26:59,702 Sigma 2s. 590 00:26:59,702 --> 00:27:01,370 Sigma 2s. 591 00:27:01,370 --> 00:27:01,870 OK. 592 00:27:01,870 --> 00:27:03,305 This is getting a little bit-- 593 00:27:03,305 --> 00:27:04,740 I'm going to draw this out here. 594 00:27:04,740 --> 00:27:07,276 That's the sigma 1s star. 595 00:27:07,276 --> 00:27:07,776 Right. 596 00:27:07,776 --> 00:27:10,245 And this would be the sigma 2s star. 597 00:27:10,245 --> 00:27:11,580 Well, what am I going to occupy? 598 00:27:11,580 --> 00:27:13,882 Well, how many electrons do I have to pour 599 00:27:13,882 --> 00:27:15,250 into the molecular orbitals? 600 00:27:15,250 --> 00:27:17,519 [GRUNTING] 601 00:27:21,857 --> 00:27:27,730 Lithium 2 is stable, because its bond order is-- you see. 602 00:27:27,730 --> 00:27:28,497 Bond order. 603 00:27:28,497 --> 00:27:30,599 Number of electrons in bonding orbitals, 604 00:27:30,599 --> 00:27:33,235 one, two, three, four, minus the number 605 00:27:33,235 --> 00:27:36,872 of electrons in antibonding, minus 1, 2, divided by 2. 606 00:27:36,872 --> 00:27:40,976 So the lithium dimer bonding order is 1. 607 00:27:40,976 --> 00:27:41,710 All right. 608 00:27:41,710 --> 00:27:43,812 And then you can go on, and you could say, 609 00:27:43,812 --> 00:27:46,782 well, if I had beryllium, I'd have another electron here 610 00:27:46,782 --> 00:27:47,449 and here. 611 00:27:47,449 --> 00:27:50,152 And I'd fill those antibonding orbitals up again, 612 00:27:50,152 --> 00:27:52,321 like in the He2 dimer. 613 00:27:52,321 --> 00:27:54,356 And I would have, again, an unstable molecule, 614 00:27:54,356 --> 00:27:56,191 which is, in fact, true. 615 00:27:56,191 --> 00:27:57,226 OK. 616 00:27:57,226 --> 00:28:00,629 This is sort of the simplest way you 617 00:28:00,629 --> 00:28:02,297 can think about molecular orbital theory 618 00:28:02,297 --> 00:28:03,832 because it's the simplest orbital. 619 00:28:03,832 --> 00:28:07,469 But you could spend the whole night. 620 00:28:07,469 --> 00:28:10,339 And it is a Friday. 621 00:28:10,339 --> 00:28:11,540 What else do you have-- 622 00:28:11,540 --> 00:28:14,076 this is what you do on a Friday. 623 00:28:14,076 --> 00:28:17,780 After I watch Dr. Quantum I'm going 624 00:28:17,780 --> 00:28:20,816 to just add every single one of these with every single one. 625 00:28:20,816 --> 00:28:22,284 It's finite. 626 00:28:22,284 --> 00:28:24,920 It's not going to take forever. 627 00:28:24,920 --> 00:28:26,989 Let's just do p. 628 00:28:26,989 --> 00:28:27,589 OK. 629 00:28:27,589 --> 00:28:29,858 Now, with p orbitals there's something interesting that 630 00:28:29,858 --> 00:28:32,261 happens, because now that sign-- 631 00:28:32,261 --> 00:28:34,163 you see how the p has a plus and a minus? 632 00:28:34,163 --> 00:28:34,663 Right. 633 00:28:34,663 --> 00:28:37,132 And so you've got to kind of think about that a little bit. 634 00:28:40,502 --> 00:28:41,804 OK. 635 00:28:41,804 --> 00:28:48,444 If I take a p orbital, and I'm going to do it like this. 636 00:28:48,444 --> 00:28:49,812 Minus, plus. 637 00:28:49,812 --> 00:28:53,949 And I'm going to add it to a p orbital that looks like this. 638 00:28:53,949 --> 00:28:56,051 And notice, I'm taking these and I'm 639 00:28:56,051 --> 00:28:59,755 adding them along an axis where they're 640 00:28:59,755 --> 00:29:02,725 kind of both along the axis. 641 00:29:02,725 --> 00:29:03,692 Right. 642 00:29:03,692 --> 00:29:05,160 They're both along the axis. 643 00:29:05,160 --> 00:29:11,700 And by convention, we'll do the pz as the one along the axis. 644 00:29:11,700 --> 00:29:16,105 Remember, there's px, py, and pz. 645 00:29:16,105 --> 00:29:18,307 When we solve for the p orbitals, 646 00:29:18,307 --> 00:29:21,410 those are the Ms. Those are the Ms. Right. 647 00:29:21,410 --> 00:29:21,910 One. 648 00:29:21,910 --> 00:29:22,411 Zero. 649 00:29:22,411 --> 00:29:23,345 And minus 1. 650 00:29:23,345 --> 00:29:28,150 Now, by convention we put the pz along the bonding axis. 651 00:29:28,150 --> 00:29:31,120 And you can see right away, so if I do this, 652 00:29:31,120 --> 00:29:32,855 well, I'm going to start adding these wave 653 00:29:32,855 --> 00:29:34,757 functions constructively. 654 00:29:34,757 --> 00:29:36,892 And what you're going to get is-- 655 00:29:36,892 --> 00:29:39,495 let's see if I can draw this-- 656 00:29:39,495 --> 00:29:41,964 something that looks like that. 657 00:29:41,964 --> 00:29:46,502 And where this is actually going to be plus. 658 00:29:46,502 --> 00:29:47,903 And this is minus. 659 00:29:47,903 --> 00:29:50,472 And notice that I'm going to have nodes in there. 660 00:29:50,472 --> 00:29:50,973 Right. 661 00:29:50,973 --> 00:29:52,775 I had nodes in the original orbitals. 662 00:29:52,775 --> 00:29:55,477 But I got a lot of bonding in between. 663 00:29:55,477 --> 00:29:58,480 I got a lot of bonding density in between. 664 00:29:58,480 --> 00:29:59,681 That is a bonding orbital. 665 00:30:02,484 --> 00:30:04,086 And the other thing we see about this 666 00:30:04,086 --> 00:30:07,422 is that it is symmetric around that bonding axis. 667 00:30:07,422 --> 00:30:11,126 So it's actually a sigma pz orbital. 668 00:30:11,126 --> 00:30:12,161 It's a sigma. 669 00:30:12,161 --> 00:30:14,696 We call it a sigma, because it's symmetric around the bonding 670 00:30:14,696 --> 00:30:15,197 axis. 671 00:30:15,197 --> 00:30:17,833 Now, if I were to take a px-- 672 00:30:17,833 --> 00:30:20,736 oh, well, let's actually subtract these. 673 00:30:20,736 --> 00:30:21,503 OK. 674 00:30:21,503 --> 00:30:23,172 So minus, plus, minus. 675 00:30:26,341 --> 00:30:29,778 Now, what you see is something very different, right. 676 00:30:29,778 --> 00:30:32,147 So now, oh, boy. 677 00:30:32,147 --> 00:30:33,749 Can I draw this? 678 00:30:33,749 --> 00:30:35,851 Maybe. 679 00:30:35,851 --> 00:30:36,885 I don't know. 680 00:30:36,885 --> 00:30:37,820 OK. 681 00:30:37,820 --> 00:30:39,454 I'll take that. 682 00:30:39,454 --> 00:30:40,289 Right. 683 00:30:40,289 --> 00:30:41,690 And so now what you see-- 684 00:30:41,690 --> 00:30:43,025 so I'm subtracting these. 685 00:30:43,025 --> 00:30:44,793 And so the density goes down. 686 00:30:44,793 --> 00:30:47,129 And now, you're going to get minus, minus. 687 00:30:47,129 --> 00:30:47,696 Right. 688 00:30:47,696 --> 00:30:48,730 Plus, plus. 689 00:30:48,730 --> 00:30:50,799 But I've reduced the electron density. 690 00:30:50,799 --> 00:30:53,268 And even worse, I'm back to that situation 691 00:30:53,268 --> 00:30:56,638 where right in between where I want to share the most, 692 00:30:56,638 --> 00:30:58,040 I'm saying no. 693 00:30:58,040 --> 00:31:00,275 No probability density there. 694 00:31:00,275 --> 00:31:03,612 And that's an antibonding sigma p orbital. 695 00:31:03,612 --> 00:31:07,149 So this would be sigma star pz. 696 00:31:07,149 --> 00:31:07,950 OK. 697 00:31:07,950 --> 00:31:10,786 Sigma star pz. 698 00:31:10,786 --> 00:31:12,621 Now, the other thing that you can do 699 00:31:12,621 --> 00:31:15,190 is look at the other directions. 700 00:31:15,190 --> 00:31:15,691 Right. 701 00:31:15,691 --> 00:31:18,060 And so I'll just take one of those really quick. 702 00:31:18,060 --> 00:31:20,462 And if you do that, you see something different. 703 00:31:20,462 --> 00:31:20,963 All right. 704 00:31:20,963 --> 00:31:23,932 So now, let's combine these like this. 705 00:31:23,932 --> 00:31:27,703 By the way, some textbooks. 706 00:31:27,703 --> 00:31:30,138 We're adding and subtracting. 707 00:31:30,138 --> 00:31:34,343 We're constructively interfering and destructively interfering. 708 00:31:34,343 --> 00:31:37,579 So sometimes you'll see a textbook add like this, 709 00:31:37,579 --> 00:31:41,783 or add the other way, which is subtracting like this. 710 00:31:41,783 --> 00:31:42,885 But it's the same thing. 711 00:31:42,885 --> 00:31:43,352 Right? 712 00:31:43,352 --> 00:31:45,254 You can decide how you want to orient it. 713 00:31:45,254 --> 00:31:47,923 But we're adding and subtracting constructively 714 00:31:47,923 --> 00:31:48,690 and destructively. 715 00:31:48,690 --> 00:31:49,758 That's what we're doing. 716 00:31:49,758 --> 00:31:51,560 So I'm going to choose to add it like this. 717 00:31:51,560 --> 00:31:53,962 Because then you just see, if I do this, 718 00:31:53,962 --> 00:31:57,599 then those are going to have some kind of overlap. 719 00:31:57,599 --> 00:31:58,634 Right. 720 00:31:58,634 --> 00:32:01,003 Those are going to have some overlap of plus 721 00:32:01,003 --> 00:32:04,439 appear and some overlap of minus down there. 722 00:32:04,439 --> 00:32:08,677 And that is called, oh, a pi orbital. 723 00:32:08,677 --> 00:32:09,912 Yeah. 724 00:32:09,912 --> 00:32:10,412 Yeah. 725 00:32:10,412 --> 00:32:12,848 But if I subtracted them, then what you would see 726 00:32:12,848 --> 00:32:15,384 is something that looks more like this, where you 727 00:32:15,384 --> 00:32:17,686 got that node in between again. 728 00:32:17,686 --> 00:32:18,253 Right. 729 00:32:18,253 --> 00:32:22,457 And this would be a pi star orbital. 730 00:32:22,457 --> 00:32:24,927 This would be for like px orbitals. 731 00:32:24,927 --> 00:32:28,897 Now, notice, these cannot be sigmas, 732 00:32:28,897 --> 00:32:32,501 because the pi orbital is not symmetric around the bonding 733 00:32:32,501 --> 00:32:33,335 axis. 734 00:32:33,335 --> 00:32:34,569 OK. 735 00:32:34,569 --> 00:32:37,306 These cannot be sigmas. 736 00:32:37,306 --> 00:32:39,274 But that's why we have another symbol for them. 737 00:32:39,274 --> 00:32:40,776 Luckily, we've got a lot of symbols, 738 00:32:40,776 --> 00:32:43,111 and the chemists are geniuses at naming things. 739 00:32:43,111 --> 00:32:44,780 And so these are called pi orbitals. 740 00:32:44,780 --> 00:32:47,282 And as you can see, OK. 741 00:32:47,282 --> 00:32:49,184 I have three orbitals. 742 00:32:49,184 --> 00:32:51,086 One, I put it along the axis. 743 00:32:51,086 --> 00:32:53,155 And then I've got two going perpendicular 744 00:32:53,155 --> 00:32:54,923 in the other plane. 745 00:32:54,923 --> 00:32:55,924 And this is one of them. 746 00:32:55,924 --> 00:33:00,162 And then the other one would be the other one, py. 747 00:33:00,162 --> 00:33:05,767 So as you can see, I'm going to have a sigma star, two pi 748 00:33:05,767 --> 00:33:08,737 orbitals, and two pi star orbitals. 749 00:33:08,737 --> 00:33:10,005 Right. 750 00:33:10,005 --> 00:33:12,007 And then what we got to do is we got to put them 751 00:33:12,007 --> 00:33:13,942 on our energy scale. 752 00:33:13,942 --> 00:33:15,777 And instead of going through drawing it all, 753 00:33:15,777 --> 00:33:17,446 I'll save myself a few minutes here. 754 00:33:17,446 --> 00:33:18,780 I'll show it to you. 755 00:33:18,780 --> 00:33:19,281 All right. 756 00:33:19,281 --> 00:33:21,817 So there is that energy scale. 757 00:33:21,817 --> 00:33:23,552 And oh, they're pointing out the nodes. 758 00:33:23,552 --> 00:33:24,586 Isn't that beautiful? 759 00:33:24,586 --> 00:33:25,620 You can see right here. 760 00:33:25,620 --> 00:33:27,489 They're not saying what molecule this is yet. 761 00:33:27,489 --> 00:33:30,292 This is a 2p orbital. 762 00:33:30,292 --> 00:33:35,197 And it's pointing along the same bond axis as the other one. 763 00:33:35,197 --> 00:33:38,734 So this is going to be a sigma p orbital. 764 00:33:38,734 --> 00:33:40,268 This is a sigma p orbital. 765 00:33:40,268 --> 00:33:41,203 And you can see that. 766 00:33:41,203 --> 00:33:43,271 And there's a sigma star. 767 00:33:43,271 --> 00:33:43,872 Right. 768 00:33:43,872 --> 00:33:44,673 Good. 769 00:33:44,673 --> 00:33:47,209 Now, if we go to that, there's the next one. 770 00:33:47,209 --> 00:33:49,077 There's a pi orbital. 771 00:33:49,077 --> 00:33:50,612 And you get the same exact effect. 772 00:33:50,612 --> 00:33:52,447 You've got a lowering of the energy, 773 00:33:52,447 --> 00:33:54,683 cause you're putting electrons on the bond, 774 00:33:54,683 --> 00:33:58,353 and a raising of the energy cause you're taking them away. 775 00:33:58,353 --> 00:33:59,588 Right. 776 00:33:59,588 --> 00:34:02,190 And that's what it looks like for the pi orbital. 777 00:34:02,190 --> 00:34:04,960 And we can put it all together. 778 00:34:04,960 --> 00:34:07,763 And if you put it all together, what I want to do 779 00:34:07,763 --> 00:34:10,899 is put it together for O2 and then show you a video, 780 00:34:10,899 --> 00:34:12,234 and then do my why this matters. 781 00:34:14,770 --> 00:34:17,406 Now, if you put this together, I'm 782 00:34:17,406 --> 00:34:23,378 going to show you the system for oxygen and nitrogen. OK. 783 00:34:23,378 --> 00:34:26,114 And then we'll do a couple other cases too. 784 00:34:26,114 --> 00:34:28,050 But we're going to do oxygen first. 785 00:34:28,050 --> 00:34:33,989 So if I take oxygen, then I'm not even 786 00:34:33,989 --> 00:34:36,058 going to write 1s anymore. 787 00:34:36,058 --> 00:34:37,926 That's way down in energy. 788 00:34:37,926 --> 00:34:39,661 It's not really involved in the bonding. 789 00:34:39,661 --> 00:34:41,362 I'm going to leave it out. 790 00:34:41,362 --> 00:34:46,534 But I've got my oxygen 1s, oxygen 1s. 791 00:34:46,534 --> 00:34:47,569 OK. 792 00:34:47,569 --> 00:34:48,070 Good. 793 00:34:48,070 --> 00:34:52,507 So those are going to come in and form molecular orbitals 794 00:34:52,507 --> 00:34:53,742 like that. 795 00:34:53,742 --> 00:34:56,178 And we know that they are all filled. 796 00:34:56,178 --> 00:34:56,678 OK. 797 00:34:56,678 --> 00:35:01,850 Now, up here I've got my oxygen. Sorry. 798 00:35:01,850 --> 00:35:04,152 I just said I wasn't going to do 1s. 799 00:35:04,152 --> 00:35:05,053 And I'm not. 800 00:35:05,053 --> 00:35:06,788 Those are 2s. 801 00:35:06,788 --> 00:35:08,490 Those are 2s. 802 00:35:08,490 --> 00:35:10,425 Sigma 2s. 803 00:35:10,425 --> 00:35:12,794 Sigma star 2s. 804 00:35:12,794 --> 00:35:13,295 OK. 805 00:35:13,295 --> 00:35:13,829 Good. 806 00:35:13,829 --> 00:35:14,996 All right. 807 00:35:14,996 --> 00:35:16,264 Oh. 808 00:35:16,264 --> 00:35:16,765 Let's see. 809 00:35:16,765 --> 00:35:19,634 Now, over here, I start with my ps. 810 00:35:19,634 --> 00:35:23,872 And I start with px, py, pz. 811 00:35:23,872 --> 00:35:26,675 And in oxygen, how many electrons do I have in here? 812 00:35:26,675 --> 00:35:27,442 So it's like this. 813 00:35:30,345 --> 00:35:31,313 [INAUDIBLE] 814 00:35:31,313 --> 00:35:33,548 Everybody should be shouting. 815 00:35:36,585 --> 00:35:37,486 [SIGHS] 816 00:35:37,486 --> 00:35:39,087 That's so much better. 817 00:35:39,087 --> 00:35:40,989 That was close. 818 00:35:40,989 --> 00:35:43,825 And then I've got to-- well, I'm not going to have enough room. 819 00:35:43,825 --> 00:35:46,728 I've got these over here. 820 00:35:46,728 --> 00:35:50,198 px, py, pz. 821 00:35:50,198 --> 00:35:52,434 Ha, ha, ha, ha. 822 00:35:52,434 --> 00:35:55,003 And there is oxygen. 823 00:35:55,003 --> 00:35:57,439 But you see, now, they come together. 824 00:35:57,439 --> 00:35:58,740 And they form these MOs. 825 00:35:58,740 --> 00:36:00,675 And we just went over what types they are. 826 00:36:00,675 --> 00:36:01,176 Right. 827 00:36:01,176 --> 00:36:02,644 There's a sigma pz orbital. 828 00:36:02,644 --> 00:36:05,680 And there's a sigma M. But the ordering 829 00:36:05,680 --> 00:36:09,918 is about the same thing that we learned, 830 00:36:09,918 --> 00:36:11,686 which is that it has to do-- 831 00:36:11,686 --> 00:36:13,755 this delta is up there. 832 00:36:13,755 --> 00:36:16,091 This delta is up there. 833 00:36:16,091 --> 00:36:20,762 And so in that pz for oxygen, you can overlap more. 834 00:36:20,762 --> 00:36:23,398 It pushes those apart more. 835 00:36:23,398 --> 00:36:27,903 And so what you get is that the pis are inside like that. 836 00:36:27,903 --> 00:36:31,673 The pis are inside. 837 00:36:31,673 --> 00:36:32,174 Right. 838 00:36:32,174 --> 00:36:37,546 So if I write in here, it's going to get too small. 839 00:36:37,546 --> 00:36:39,080 So I'm going to do this. 840 00:36:39,080 --> 00:36:41,983 This would be a sigma 2pz. 841 00:36:44,486 --> 00:36:48,590 This would be a sigma 2pz star. 842 00:36:48,590 --> 00:36:55,830 And over here, these would be pi orbitals. 843 00:36:55,830 --> 00:37:01,603 Pi px, pi py. 844 00:37:01,603 --> 00:37:10,612 And these almost can fit pi star px and pi star py. 845 00:37:10,612 --> 00:37:13,481 All looking like the shapes that we've been drawing. 846 00:37:13,481 --> 00:37:14,182 Right. 847 00:37:14,182 --> 00:37:17,452 And then the filling part comes from the filling of the AOs. 848 00:37:17,452 --> 00:37:17,953 Right. 849 00:37:17,953 --> 00:37:20,689 I've got my filling of the AOs here. 850 00:37:20,689 --> 00:37:22,490 I've got the valence filling for oxygen. 851 00:37:22,490 --> 00:37:23,825 There is a 1s down there. 852 00:37:23,825 --> 00:37:24,359 Right. 853 00:37:24,359 --> 00:37:26,595 And so I've got to put four electrons from there 854 00:37:26,595 --> 00:37:28,597 and four electrons from here into the middle. 855 00:37:28,597 --> 00:37:29,297 So let's do that. 856 00:37:29,297 --> 00:37:36,705 One, two, three, four, five, six, seven, eight. 857 00:37:36,705 --> 00:37:38,873 Pauli. 858 00:37:38,873 --> 00:37:39,808 Pauli. 859 00:37:39,808 --> 00:37:40,308 Right. 860 00:37:43,745 --> 00:37:49,484 So for oxygen, the bond order, if you add it up, 861 00:37:49,484 --> 00:37:52,187 the BO is two. 862 00:37:52,187 --> 00:37:53,488 It's a double bond. 863 00:37:53,488 --> 00:37:54,322 We know that. 864 00:37:54,322 --> 00:37:56,124 Oh, but now we know so much more. 865 00:37:56,124 --> 00:37:59,394 And this is what I want to make a point. 866 00:37:59,394 --> 00:38:02,163 Lewis could have gotten us this. 867 00:38:02,163 --> 00:38:05,567 But Lewis can't get us magnetism. 868 00:38:05,567 --> 00:38:07,969 Lewis can't get us magnetism. 869 00:38:07,969 --> 00:38:10,438 Molecular orbital theory can. 870 00:38:10,438 --> 00:38:11,373 OK. 871 00:38:11,373 --> 00:38:14,242 And let me show you magnetism right up close. 872 00:38:14,242 --> 00:38:17,345 Because if I take liquid nitrogen. That's not me though. 873 00:38:17,345 --> 00:38:20,582 And I pour it through a huge magnet. 874 00:38:20,582 --> 00:38:22,484 I want that magnet so badly. 875 00:38:22,484 --> 00:38:24,152 But if I did that, look at that. 876 00:38:24,152 --> 00:38:27,656 Liquid nitrogen just goes right on through. 877 00:38:27,656 --> 00:38:30,358 And it's really fun to do actually. 878 00:38:30,358 --> 00:38:31,493 But there you go. 879 00:38:31,493 --> 00:38:33,428 That's liquid nitrogen. 880 00:38:33,428 --> 00:38:37,999 But look at liquid oxygen. Liquid oxygen. Now 881 00:38:37,999 --> 00:38:42,637 you pour it through, and the magnet holds it in place. 882 00:38:42,637 --> 00:38:43,138 All right. 883 00:38:43,138 --> 00:38:44,039 Whoa is right. 884 00:38:48,343 --> 00:38:50,979 There's four more things we've got to cover. 885 00:38:50,979 --> 00:38:52,380 One is paramagnetism. 886 00:38:58,053 --> 00:39:02,190 Another is something called mixing. 887 00:39:02,190 --> 00:39:05,694 Another is what happens when you go hetero nuclear. 888 00:39:05,694 --> 00:39:06,995 Oh, yeah. 889 00:39:06,995 --> 00:39:09,531 You'll see what that means in a second. 890 00:39:09,531 --> 00:39:12,767 And finally, what I said I would get to, 891 00:39:12,767 --> 00:39:16,338 which is non-bonding, which are not the same as antibonding. 892 00:39:19,074 --> 00:39:24,312 What I'm covering right now, there, is paramagnetism. 893 00:39:24,312 --> 00:39:27,182 Because as you saw on the exam in one of the questions, 894 00:39:27,182 --> 00:39:27,849 we explained it. 895 00:39:27,849 --> 00:39:34,856 We said if you got unpaired electrons, then you are-- 896 00:39:34,856 --> 00:39:36,057 what does paramagnetism mean? 897 00:39:36,057 --> 00:39:39,627 It means that if you put a huge magnet on it, you'll respond. 898 00:39:39,627 --> 00:39:43,665 You will feel a force from that magnetic field. 899 00:39:43,665 --> 00:39:44,933 And so we did that in the exam. 900 00:39:44,933 --> 00:39:47,268 We had a silicon atom, because we hadn't done molecules. 901 00:39:47,268 --> 00:39:48,703 But now we got molecules. 902 00:39:48,703 --> 00:39:51,039 So I can tell you why that experiment happened. 903 00:39:51,039 --> 00:39:52,340 What's happening? 904 00:39:52,340 --> 00:39:55,310 I can tell you why that experiment happens. 905 00:39:55,310 --> 00:39:55,810 Really? 906 00:39:55,810 --> 00:39:57,212 I didn't even know there was more. 907 00:39:57,212 --> 00:39:59,481 [LAUGHTER] 908 00:39:59,481 --> 00:40:03,518 It happens because of Hund's rule, molecular orbitals, 909 00:40:03,518 --> 00:40:06,121 and the fact that I've got these two unpaired electrons 910 00:40:06,121 --> 00:40:08,590 in the O2 molecule. 911 00:40:08,590 --> 00:40:11,993 And you know that in nitrogen those two electrons are gone, 912 00:40:11,993 --> 00:40:14,596 cause nitrogen is missing one more here and here. 913 00:40:14,596 --> 00:40:15,730 So you've got two less. 914 00:40:15,730 --> 00:40:18,433 Everything's filled. 915 00:40:18,433 --> 00:40:19,667 Everything's filled. 916 00:40:19,667 --> 00:40:22,404 Paramagnetism. 917 00:40:22,404 --> 00:40:23,872 Now, OK. 918 00:40:23,872 --> 00:40:26,408 Speaking of magnetism, I couldn't help but show 919 00:40:26,408 --> 00:40:28,076 you this. 920 00:40:28,076 --> 00:40:29,077 This is diamagnetism. 921 00:40:29,077 --> 00:40:31,212 Now, diamagnetism, everything is filled. 922 00:40:31,212 --> 00:40:34,082 But you still feel a little repulsion to a magnetic field. 923 00:40:34,082 --> 00:40:36,484 And some of you may know there is this thing called the Ig 924 00:40:36,484 --> 00:40:37,385 Noble Prize. 925 00:40:37,385 --> 00:40:39,387 Only one person in history has won 926 00:40:39,387 --> 00:40:42,223 both the Ig Noble and the Nobel Prize, 927 00:40:42,223 --> 00:40:45,493 Andre Geim who discovered graphene with scotch tape. 928 00:40:45,493 --> 00:40:47,262 But before that he won the Ig Noble Prize 929 00:40:47,262 --> 00:40:50,031 because he did this to frogs. 930 00:40:50,031 --> 00:40:53,835 Because water is diamagnetic. 931 00:40:53,835 --> 00:40:55,336 And so it repels a magnetic field. 932 00:40:55,336 --> 00:40:58,907 It's just got to be really, really, really high. 933 00:40:58,907 --> 00:41:00,909 I hope that frog was OK. 934 00:41:00,909 --> 00:41:02,110 It looked sort of OK. 935 00:41:02,110 --> 00:41:03,645 So the frog was floating. 936 00:41:03,645 --> 00:41:06,815 And it was like a study about levitation using magnetism. 937 00:41:06,815 --> 00:41:08,049 Why am I showing that to you? 938 00:41:08,049 --> 00:41:09,117 No particular reason. 939 00:41:09,117 --> 00:41:11,019 [LAUGHTER] 940 00:41:11,019 --> 00:41:12,921 But this does get me to the why this matters, 941 00:41:12,921 --> 00:41:14,889 which has to do with how you cook pasta. 942 00:41:14,889 --> 00:41:22,831 And, of course, since we're talking about O2, 943 00:41:22,831 --> 00:41:27,068 when I have finished cooking pasta, what do I do? 944 00:41:27,068 --> 00:41:28,136 I pour it. 945 00:41:28,136 --> 00:41:28,803 There it is. 946 00:41:28,803 --> 00:41:30,638 It's like it's sophisticated. 947 00:41:30,638 --> 00:41:32,707 I pour it through a colander. 948 00:41:32,707 --> 00:41:34,943 That's a membrane. 949 00:41:34,943 --> 00:41:35,710 That's a membrane. 950 00:41:35,710 --> 00:41:36,845 You did use a membrane. 951 00:41:36,845 --> 00:41:38,012 You did a filter. 952 00:41:38,012 --> 00:41:40,982 Now, but I could also have done that separation, 953 00:41:40,982 --> 00:41:44,619 that same separation, I could have left it on the stove. 954 00:41:44,619 --> 00:41:46,221 I could have. 955 00:41:46,221 --> 00:41:48,356 And it would have boiled out all the water 956 00:41:48,356 --> 00:41:51,960 and left me still with the pasta separated from the water. 957 00:41:51,960 --> 00:41:54,195 I've accomplished the same exact thing. 958 00:41:54,195 --> 00:41:56,164 I have separated the pasta from the water. 959 00:41:56,164 --> 00:41:58,132 Test done. 960 00:41:58,132 --> 00:42:00,034 Pasta may not taste as good. 961 00:42:00,034 --> 00:42:01,302 [LAUGHTER] 962 00:42:01,302 --> 00:42:02,103 But you've done it. 963 00:42:02,103 --> 00:42:04,973 But see, the thing is that if you separate things this way 964 00:42:04,973 --> 00:42:08,142 versus that way, you can just feel how much less energy 965 00:42:08,142 --> 00:42:08,943 it's going to take. 966 00:42:08,943 --> 00:42:11,513 In fact, you can save over 80% of the energy 967 00:42:11,513 --> 00:42:13,748 if you do a membrane based separation 968 00:42:13,748 --> 00:42:16,050 as opposed to a thermal one. 969 00:42:16,050 --> 00:42:17,185 Gazuntite. 970 00:42:17,185 --> 00:42:18,853 So those are two ways to separate pasta. 971 00:42:18,853 --> 00:42:21,756 But see, there's two ways to separate lots of things. 972 00:42:21,756 --> 00:42:24,392 Like how about 1 to 10 nanometer particles? 973 00:42:24,392 --> 00:42:25,493 How about chemistry? 974 00:42:25,493 --> 00:42:27,228 How about molecules? 975 00:42:27,228 --> 00:42:29,697 How do you separate those? 976 00:42:29,697 --> 00:42:31,332 Well, you got the same two ways. 977 00:42:31,332 --> 00:42:35,136 And if you count up all the things we separate this way, 978 00:42:35,136 --> 00:42:36,004 it's a lot. 979 00:42:36,004 --> 00:42:37,071 It goes on and on. 980 00:42:37,071 --> 00:42:39,474 And it will go all the way down the Infinite Corridor. 981 00:42:39,474 --> 00:42:41,442 And this is how we do chemistry. 982 00:42:41,442 --> 00:42:46,281 In fact, has anyone seen this on the side of the road? 983 00:42:46,281 --> 00:42:47,615 That's a distillation column. 984 00:42:47,615 --> 00:42:50,018 It's a big pasta cooker. 985 00:42:50,018 --> 00:42:53,621 That's all you're doing is boiling one molecule off 986 00:42:53,621 --> 00:42:59,694 of another over a long time with a whole lot of fossil fuel. 987 00:42:59,694 --> 00:43:01,996 In fact, if you look at the US energy consumption, 988 00:43:01,996 --> 00:43:04,299 roughly a third of it goes into industry. 989 00:43:04,299 --> 00:43:06,868 40% of that is for this one thing. 990 00:43:06,868 --> 00:43:08,002 It's boiling pasta. 991 00:43:08,002 --> 00:43:12,206 But the pasta is 1 nanometer to 10 nanometer particles. 992 00:43:12,206 --> 00:43:15,543 40% goes into boiling one chemical species off 993 00:43:15,543 --> 00:43:16,144 of another. 994 00:43:16,144 --> 00:43:18,179 Separation. 995 00:43:18,179 --> 00:43:20,415 Separation. 996 00:43:20,415 --> 00:43:23,384 That's 12% of all the energy. 997 00:43:23,384 --> 00:43:25,853 That's the same as every single drop 998 00:43:25,853 --> 00:43:29,257 of gasoline in every single car truck and bus. 999 00:43:29,257 --> 00:43:31,426 Just to give you a sense of how much energy that is. 1000 00:43:31,426 --> 00:43:34,495 You'll say, well, why aren't we using a colander? 1001 00:43:34,495 --> 00:43:36,331 Why don't we just pour it through a colander 1002 00:43:36,331 --> 00:43:38,032 like we do our boiling pasta? 1003 00:43:38,032 --> 00:43:39,834 Well, we do that for one field. 1004 00:43:39,834 --> 00:43:40,835 Desalination. 1005 00:43:40,835 --> 00:43:43,171 I got a [INAUDIBLE] on that another time. 1006 00:43:43,171 --> 00:43:45,273 But we don't do it for all those other things. 1007 00:43:45,273 --> 00:43:46,741 And there's a really simple reason. 1008 00:43:46,741 --> 00:43:50,511 We don't have the right pasta colander. 1009 00:43:50,511 --> 00:43:51,913 We don't. 1010 00:43:51,913 --> 00:43:55,283 There's no option for that size scale 1011 00:43:55,283 --> 00:43:59,420 that can withstand the conditions that are in all 1012 00:43:59,420 --> 00:44:01,356 of those chemical separations. 1013 00:44:01,356 --> 00:44:04,258 But if we did-- 1014 00:44:04,258 --> 00:44:08,429 we take so much O2 out of the air. 1015 00:44:08,429 --> 00:44:09,497 We need O2. 1016 00:44:09,497 --> 00:44:11,065 But we don't want the N2. 1017 00:44:11,065 --> 00:44:12,734 So we have to separate it. 1018 00:44:12,734 --> 00:44:13,735 How do we do it? 1019 00:44:13,735 --> 00:44:14,969 We go cryogenic. 1020 00:44:14,969 --> 00:44:16,537 We go to very, very cold temperatures, 1021 00:44:16,537 --> 00:44:18,640 which is the same as boiling. 1022 00:44:18,640 --> 00:44:19,574 Right. 1023 00:44:19,574 --> 00:44:21,509 But you're still spending all this fossil fuel 1024 00:44:21,509 --> 00:44:23,244 to lower the temperature. 1025 00:44:23,244 --> 00:44:26,514 That's how much O2 we generate each year. 1026 00:44:26,514 --> 00:44:28,082 And this is how much energy it takes. 1027 00:44:28,082 --> 00:44:31,285 It's like 1/2 a percent of all US energy, just to get-- 1028 00:44:31,285 --> 00:44:34,455 But what if you could use something 1029 00:44:34,455 --> 00:44:36,524 like O2's paramagnetism? 1030 00:44:36,524 --> 00:44:39,927 What if you could use something about the chemistry or O2 1031 00:44:39,927 --> 00:44:43,431 to do this separation more efficiently, 1032 00:44:43,431 --> 00:44:47,635 lower energy, or maybe make a new colander that does that? 1033 00:44:47,635 --> 00:44:50,672 And if any of you have ideas, come talk to me. 1034 00:44:50,672 --> 00:44:54,042 This is a problem I care a lot about. 1035 00:44:54,042 --> 00:44:55,243 OK. 1036 00:44:55,243 --> 00:44:55,743 Ah. 1037 00:44:55,743 --> 00:44:57,345 But I had some other-- paramagnetism. 1038 00:44:57,345 --> 00:44:58,279 Unpaired electrons. 1039 00:44:58,279 --> 00:44:59,514 We got that one. 1040 00:44:59,514 --> 00:45:01,983 Ha. 1041 00:45:01,983 --> 00:45:02,950 [SIGHS] 1042 00:45:02,950 --> 00:45:04,952 Why is chemistry not-- 1043 00:45:04,952 --> 00:45:07,555 why can't they follow the rules? 1044 00:45:07,555 --> 00:45:08,322 Why? 1045 00:45:08,322 --> 00:45:10,992 But they always got to break them. 1046 00:45:10,992 --> 00:45:14,962 And what we see, this was oxygen. Sigma. 1047 00:45:14,962 --> 00:45:16,964 Sigma S. Sigma. 1048 00:45:16,964 --> 00:45:17,832 Sigma star. 1049 00:45:17,832 --> 00:45:18,332 Pi. 1050 00:45:18,332 --> 00:45:19,133 Pi star. 1051 00:45:19,133 --> 00:45:23,071 But look at what happens for nitrogen. Why? 1052 00:45:23,071 --> 00:45:26,641 Because of something some people like to call mixing. 1053 00:45:26,641 --> 00:45:29,777 Remember, I said that-- 1054 00:45:29,777 --> 00:45:35,850 where did it-- somewhere I said that the closer in energy, 1055 00:45:35,850 --> 00:45:38,720 or the closer in symmetry orbitals are, 1056 00:45:38,720 --> 00:45:40,755 the more overlap they can have, and the more they 1057 00:45:40,755 --> 00:45:43,391 interact and can mix together in the ways 1058 00:45:43,391 --> 00:45:44,759 that I've been talking about. 1059 00:45:44,759 --> 00:45:45,460 Yeah. 1060 00:45:45,460 --> 00:45:48,863 Well, it turns out that if you go below oxygen, in what 1061 00:45:48,863 --> 00:45:51,332 are called homonuclear dimers, which is where the atoms are 1062 00:45:51,332 --> 00:45:54,368 the same, then you can get mixing even 1063 00:45:54,368 --> 00:45:58,673 between this sigma and that sigma. 1064 00:45:58,673 --> 00:46:00,308 And so what happens is, instead of them 1065 00:46:00,308 --> 00:46:02,643 being kind of separate like this for N2, 1066 00:46:02,643 --> 00:46:04,812 there is an interaction. 1067 00:46:04,812 --> 00:46:05,580 You see. 1068 00:46:05,580 --> 00:46:07,081 You can think about it the same way. 1069 00:46:07,081 --> 00:46:09,317 I'm throwing more orbitals into the mix. 1070 00:46:09,317 --> 00:46:12,820 And so because they can contribute to overlapping, 1071 00:46:12,820 --> 00:46:15,123 you're changing that delta E even more. 1072 00:46:15,123 --> 00:46:17,892 That's effectively what's happening. 1073 00:46:17,892 --> 00:46:21,062 And so you can see this one for nitrogen goes down, 1074 00:46:21,062 --> 00:46:22,830 but that one goes up. 1075 00:46:22,830 --> 00:46:26,134 Because that's the delta E. Because it's able to mix in. 1076 00:46:26,134 --> 00:46:28,469 It's able to mix in because they have the same symmetry. 1077 00:46:28,469 --> 00:46:29,637 And they're closer. 1078 00:46:29,637 --> 00:46:33,775 For those smaller atoms, they're a lot closer in energy. 1079 00:46:33,775 --> 00:46:38,112 And so if you look at this, what happens is those switch. 1080 00:46:38,112 --> 00:46:38,646 They switch. 1081 00:46:38,646 --> 00:46:39,881 It's real. 1082 00:46:39,881 --> 00:46:40,381 They switch. 1083 00:46:40,381 --> 00:46:42,583 Now, it doesn't change the thing I just talked about, 1084 00:46:42,583 --> 00:46:44,218 which is the magnetic properties of N2, 1085 00:46:44,218 --> 00:46:47,054 because they are still all filled. 1086 00:46:47,054 --> 00:46:48,389 But it is important. 1087 00:46:48,389 --> 00:46:51,659 Because if I were to pull an electron out of N2, 1088 00:46:51,659 --> 00:46:55,563 it would come from a sigma orbital, not a pi orbital, 1089 00:46:55,563 --> 00:46:56,831 because of those interactions. 1090 00:46:56,831 --> 00:46:58,800 And those happen below O2. 1091 00:46:58,800 --> 00:47:00,468 So this is from your textbook. 1092 00:47:00,468 --> 00:47:03,638 And you see, it says 2s 2pz interaction. 1093 00:47:03,638 --> 00:47:04,572 Remember, 2pz is sigma. 1094 00:47:04,572 --> 00:47:05,239 Sigma. 1095 00:47:05,239 --> 00:47:06,908 Same symmetry. 1096 00:47:06,908 --> 00:47:08,276 Able to mix. 1097 00:47:08,276 --> 00:47:09,944 Don't mix very well here. 1098 00:47:09,944 --> 00:47:12,747 But here they're strong enough to change 1099 00:47:12,747 --> 00:47:16,517 the ordering of that orbital and that orbital. 1100 00:47:16,517 --> 00:47:17,018 Right. 1101 00:47:17,018 --> 00:47:18,920 You see that? 1102 00:47:18,920 --> 00:47:20,888 That's an important effect. 1103 00:47:20,888 --> 00:47:22,056 OK. 1104 00:47:22,056 --> 00:47:22,557 All right. 1105 00:47:25,092 --> 00:47:27,094 But it only happens below O2. 1106 00:47:27,094 --> 00:47:29,063 It happens below O2, because that's 1107 00:47:29,063 --> 00:47:31,999 where those energies and orbitals can line up 1108 00:47:31,999 --> 00:47:34,669 in that way. 1109 00:47:34,669 --> 00:47:35,169 OK. 1110 00:47:35,169 --> 00:47:36,370 So we just covered that. 1111 00:47:36,370 --> 00:47:37,605 Now, there's two more things. 1112 00:47:40,975 --> 00:47:43,477 And then that's all of MO theory. 1113 00:47:43,477 --> 00:47:46,647 One is I've been giving you the same atoms. 1114 00:47:46,647 --> 00:47:49,750 But what if we go from a homonuclear dimer 1115 00:47:49,750 --> 00:47:52,286 to a heteronuclear dimer, which just means one is one and one 1116 00:47:52,286 --> 00:47:54,589 is another type of atom. 1117 00:47:54,589 --> 00:47:58,860 How do we draw an MO diagram for that? 1118 00:47:58,860 --> 00:48:02,597 And the second thing is what happens? 1119 00:48:02,597 --> 00:48:05,733 The second thing is what happens in this case? 1120 00:48:05,733 --> 00:48:11,505 In HCl, H is bringing only one S electron to the party. 1121 00:48:11,505 --> 00:48:13,374 But Cl is bringing all of the-- it's 1122 00:48:13,374 --> 00:48:17,211 bringing S. It's bringing P. What does it do? 1123 00:48:17,211 --> 00:48:17,812 Right. 1124 00:48:17,812 --> 00:48:20,348 How does the MO diagram look in that case, where 1125 00:48:20,348 --> 00:48:22,183 I've got all these extra electrons coming 1126 00:48:22,183 --> 00:48:24,518 in from one of the atoms. 1127 00:48:24,518 --> 00:48:26,988 Now, I will not do this in 30 seconds. 1128 00:48:26,988 --> 00:48:30,858 But I will, next week, give you a nice sort 1129 00:48:30,858 --> 00:48:35,229 of thorough explanation for each of these two last MO cases. 1130 00:48:35,229 --> 00:48:37,331 In the meantime, have a very good weekend.