1 00:00:00,030 --> 00:00:02,400 The following content is provided under a Creative 2 00:00:02,400 --> 00:00:03,780 Commons license. 3 00:00:03,780 --> 00:00:06,020 Your support will help MIT OpenCourseWare 4 00:00:06,020 --> 00:00:10,090 continue to offer high-quality, educational resources for free. 5 00:00:10,090 --> 00:00:12,660 To make a donation or to view additional materials 6 00:00:12,660 --> 00:00:16,580 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,580 --> 00:00:17,740 at ocw.mit.edu. 8 00:00:26,304 --> 00:00:29,580 CATHERINE DRENNAN: If you haven't clicked in yet, 9 00:00:29,580 --> 00:00:32,759 please pay attention to the clicker question, 10 00:00:32,759 --> 00:00:37,180 and I'll give you a little bit more time to click in. 11 00:00:37,180 --> 00:00:38,990 And I'll give you a 10-second warning. 12 00:00:48,260 --> 00:00:48,760 All right. 13 00:00:48,760 --> 00:00:51,562 Let's just go ahead and take 10 more seconds. 14 00:01:07,430 --> 00:01:09,800 All right. 15 00:01:09,800 --> 00:01:13,066 Does someone want to say how they got this one right? 16 00:01:17,830 --> 00:01:20,410 Anyone willing to say how they got it right? 17 00:01:20,410 --> 00:01:25,400 We have a American Chemical Society, 18 00:01:25,400 --> 00:01:28,010 whatever these are called that hang around your neck and clip 19 00:01:28,010 --> 00:01:29,120 things to them. 20 00:01:29,120 --> 00:01:29,800 Yes. 21 00:01:29,800 --> 00:01:31,900 There's the word. 22 00:01:31,900 --> 00:01:32,530 No? 23 00:01:32,530 --> 00:01:33,430 Oh, there we go. 24 00:01:45,680 --> 00:01:48,630 AUDIENCE: Thank you. 25 00:01:48,630 --> 00:01:54,610 So this molecule is the phosphorus 26 00:01:54,610 --> 00:01:57,630 has five valence electrons and then each hydrogen has three 27 00:01:57,630 --> 00:01:59,570 so it's per total of eight. 28 00:01:59,570 --> 00:02:03,110 So it has three bonding and then one lone pair, 29 00:02:03,110 --> 00:02:06,790 which makes it a tetrahedral, but then the lone pair 30 00:02:06,790 --> 00:02:10,775 pushed the other bond, so it's less than 109.5 degrees. 31 00:02:10,775 --> 00:02:13,450 CATHERINE DRENNAN: Excellent. 32 00:02:13,450 --> 00:02:14,860 Yeah. 33 00:02:14,860 --> 00:02:18,880 So I see that some people just decided that there 34 00:02:18,880 --> 00:02:21,370 were three things bound to it. 35 00:02:21,370 --> 00:02:26,730 And so then they decided either 120 or less than 120, 36 00:02:26,730 --> 00:02:29,010 but you really need to do the Lewis structure 37 00:02:29,010 --> 00:02:32,470 and see how many loan pairs there are first. 38 00:02:32,470 --> 00:02:34,320 So once you do the Lewis structure, 39 00:02:34,320 --> 00:02:36,680 then you figure out the parent geometry, 40 00:02:36,680 --> 00:02:40,440 Sn forces sum of tetrahedral system. 41 00:02:40,440 --> 00:02:40,940 All right. 42 00:02:40,940 --> 00:02:45,071 So more practice on these coming up. 43 00:02:45,071 --> 00:02:45,570 All right. 44 00:02:45,570 --> 00:02:50,940 So we're continuing on now with molecular orbital theory, 45 00:02:50,940 --> 00:02:55,080 and we started the course talking about atomic structure 46 00:02:55,080 --> 00:02:58,460 and then we talked about atomic orbitals or wave functions. 47 00:02:58,460 --> 00:03:02,440 And then we moved on to bonding, that atoms can come together 48 00:03:02,440 --> 00:03:06,150 and bond and talked about the structure of molecules, 49 00:03:06,150 --> 00:03:10,820 and now we're going to molecular orbitals. 50 00:03:10,820 --> 00:03:13,570 And then we'll also talk more about the structure 51 00:03:13,570 --> 00:03:16,870 of molecules based on those molecular orbitals 52 00:03:16,870 --> 00:03:18,240 on Wednesday. 53 00:03:18,240 --> 00:03:20,290 So we're really coming all the way around, 54 00:03:20,290 --> 00:03:23,170 we're using a lot of the ideas that you've seen before, 55 00:03:23,170 --> 00:03:25,580 but now we're applying them to molecules. 56 00:03:25,580 --> 00:03:28,020 And then, to me, this is really an exciting part. 57 00:03:28,020 --> 00:03:30,510 I love getting up to the molecules 58 00:03:30,510 --> 00:03:32,900 and talking about structures and molecules 59 00:03:32,900 --> 00:03:36,920 and how orbitals really play a role in those properties that 60 00:03:36,920 --> 00:03:38,260 molecules have. 61 00:03:38,260 --> 00:03:41,530 And then, to me, the really exciting-- I like reactions. 62 00:03:41,530 --> 00:03:43,800 So after we finish with the structures, 63 00:03:43,800 --> 00:03:46,312 we're going to talk more about how molecules react. 64 00:03:46,312 --> 00:03:47,770 And so on Friday, we're going to be 65 00:03:47,770 --> 00:03:49,960 starting that, reactions of molecules, 66 00:03:49,960 --> 00:03:51,540 and getting into thermodynamics. 67 00:03:51,540 --> 00:03:56,350 So we're sort of winding our way away from orbitals for a while. 68 00:03:56,350 --> 00:03:59,897 We will come back to d orbitals around Thanksgiving time, 69 00:03:59,897 --> 00:04:01,730 but we'll have a long time before that where 70 00:04:01,730 --> 00:04:03,500 we're talking about reactions. 71 00:04:03,500 --> 00:04:05,320 So we're about to do a transition 72 00:04:05,320 --> 00:04:07,800 in the type of material. 73 00:04:07,800 --> 00:04:12,610 But before we do that, more orbitals. 74 00:04:12,610 --> 00:04:17,790 But these are super cool because these are molecular orbitals. 75 00:04:17,790 --> 00:04:20,920 So we're going to talk today about MO theory, MO 76 00:04:20,920 --> 00:04:23,750 for molecular orbitals. 77 00:04:23,750 --> 00:04:27,690 So molecular orbital theory presents the idea 78 00:04:27,690 --> 00:04:30,210 that these valence electrons are really 79 00:04:30,210 --> 00:04:33,540 going to be delocalized around these molecules 80 00:04:33,540 --> 00:04:37,280 and not just sitting on individual atoms. 81 00:04:37,280 --> 00:04:40,470 So to think about this electron do localization, 82 00:04:40,470 --> 00:04:43,410 we need to think about molecular orbitals. 83 00:04:43,410 --> 00:04:46,380 Molecular orbitals, as we've learned, 84 00:04:46,380 --> 00:04:48,710 another word for orbital is also wave functions. 85 00:04:48,710 --> 00:04:49,960 Wave functions are orbitals. 86 00:04:49,960 --> 00:04:51,700 Orbitals are wave functions. 87 00:04:51,700 --> 00:04:54,570 You need to consider the wavelike properties 88 00:04:54,570 --> 00:04:57,320 of electrons to think about where the electrons are going 89 00:04:57,320 --> 00:04:59,830 to be, what is their probability density, 90 00:04:59,830 --> 00:05:01,540 how are they going to be arranged 91 00:05:01,540 --> 00:05:03,900 with respect to the nucleus. 92 00:05:03,900 --> 00:05:06,130 And so when we take atomic orbitals 93 00:05:06,130 --> 00:05:09,130 and we bring them together as atoms come together 94 00:05:09,130 --> 00:05:11,640 to form bonds, atomic orbitals come together 95 00:05:11,640 --> 00:05:13,510 to form molecular orbitals. 96 00:05:13,510 --> 00:05:17,430 So we're going to be adding superimposing, atomic orbitals 97 00:05:17,430 --> 00:05:21,400 to form these molecular orbitals. 98 00:05:21,400 --> 00:05:26,480 And this is called a linear combination of atomic orbitals, 99 00:05:26,480 --> 00:05:29,380 or LCAO. 100 00:05:29,380 --> 00:05:32,370 And so we're going to bring those atomic orbitals together 101 00:05:32,370 --> 00:05:34,240 and create molecular orbitals. 102 00:05:34,240 --> 00:05:36,770 And we're going to create two types of molecular orbitals. 103 00:05:36,770 --> 00:05:40,380 We're going to create bonding and antibonding. 104 00:05:40,380 --> 00:05:44,220 And some basic math principles apply here, 105 00:05:44,220 --> 00:05:51,480 and that is that you can create N molecular orbitals 106 00:05:51,480 --> 00:05:54,821 from N atomic orbitals. 107 00:05:54,821 --> 00:05:55,320 All right. 108 00:05:55,320 --> 00:05:58,810 So that's really the basis of molecular orbital theory, 109 00:05:58,810 --> 00:06:04,650 and now let's apply it to our friends, the s orbitals. 110 00:06:04,650 --> 00:06:05,150 All right. 111 00:06:05,150 --> 00:06:07,400 So we're going to think about really simple molecules, 112 00:06:07,400 --> 00:06:10,720 bringing together two atoms that are identical with each other 113 00:06:10,720 --> 00:06:14,790 and what happens to their s orbitals when this happens. 114 00:06:14,790 --> 00:06:19,410 So first we'll talk about bonding orbitals. 115 00:06:19,410 --> 00:06:21,700 So bonding orbitals, again, arise 116 00:06:21,700 --> 00:06:26,930 from this linear combination of atomic orbitals, the LCAO. 117 00:06:26,930 --> 00:06:28,750 And if it's a bonding orbital, it's 118 00:06:28,750 --> 00:06:31,970 going to arise from constructive interference. 119 00:06:31,970 --> 00:06:35,520 So we talked before about the properties of waves, and one 120 00:06:35,520 --> 00:06:37,720 of the great properties of waves is 121 00:06:37,720 --> 00:06:40,550 that they can constructively interfere, destructively 122 00:06:40,550 --> 00:06:41,710 interfere. 123 00:06:41,710 --> 00:06:45,120 And orbitals are wave functions so they can constructively 124 00:06:45,120 --> 00:06:48,000 interfere and destructively interfere. 125 00:06:48,000 --> 00:06:50,100 Bonding orbitals are generated by 126 00:06:50,100 --> 00:06:52,550 the constructive interference. 127 00:06:52,550 --> 00:06:55,510 So let's look at two atomic orbitals. 128 00:06:55,510 --> 00:06:56,850 And so here we have an orbital. 129 00:06:56,850 --> 00:06:58,360 The nucleus is in the middle. 130 00:06:58,360 --> 00:06:59,120 It's a little dot. 131 00:06:59,120 --> 00:07:00,310 It's a nucleus. 132 00:07:00,310 --> 00:07:03,070 And these two atomic orbitals are going to come together. 133 00:07:03,070 --> 00:07:05,060 There's going to be a bonding event. 134 00:07:05,060 --> 00:07:09,280 And so we have a 1s orbital from atom a 135 00:07:09,280 --> 00:07:12,440 and a 1s orbital from atom b, and they're 136 00:07:12,440 --> 00:07:14,280 going to come together, and they're 137 00:07:14,280 --> 00:07:16,380 going to form a molecular orbital, 138 00:07:16,380 --> 00:07:23,430 an ab molecular orbital, and this is called sigma 1s. 139 00:07:23,430 --> 00:07:30,110 So a sigma orbital is symmetric around the bond axis, 140 00:07:30,110 --> 00:07:34,800 so the bond axis here would be just a vertical, a line 141 00:07:34,800 --> 00:07:37,660 between these two nuclei here. 142 00:07:37,660 --> 00:07:42,620 And so this molecular orbital is symmetric around that bond 143 00:07:42,620 --> 00:07:43,600 axis. 144 00:07:43,600 --> 00:07:47,250 There are no nodal planes for something that is symmetric. 145 00:07:47,250 --> 00:07:51,870 There are no nodal planes for our s orbitals, 146 00:07:51,870 --> 00:07:55,500 and so there's none for the molecular orbital either. 147 00:07:55,500 --> 00:08:02,000 And we can also write this as 1sa plus 1sb. 148 00:08:02,000 --> 00:08:06,830 So the atomic orbital from 1sa, the atomic orbital 1sb coming 149 00:08:06,830 --> 00:08:10,150 together to form sigma orbital 1s. 150 00:08:10,150 --> 00:08:12,830 That is a bonding orbital because it's 151 00:08:12,830 --> 00:08:14,900 constructive interference. 152 00:08:14,900 --> 00:08:18,610 It's a bonding MO, or molecular orbital. 153 00:08:18,610 --> 00:08:21,830 So now let's consider the wavelike properties 154 00:08:21,830 --> 00:08:24,930 and think about these atomic orbitals coming together 155 00:08:24,930 --> 00:08:28,590 as waves in what is happening. 156 00:08:28,590 --> 00:08:32,090 So here we have the same equation up here. 157 00:08:32,090 --> 00:08:35,600 We're bringing together 1sa and 1sb, 158 00:08:35,600 --> 00:08:38,530 but now let's think about this as a wave function. 159 00:08:38,530 --> 00:08:40,830 So there is an amplitude associated 160 00:08:40,830 --> 00:08:45,370 with the wave function for 1sa, and there 161 00:08:45,370 --> 00:08:50,760 is an amplitude associated with the wave function for 1sb. 162 00:08:50,760 --> 00:08:52,630 These wave functions come together. 163 00:08:52,630 --> 00:08:56,130 Here is one nuclei, here's the other nuclei. 164 00:08:56,130 --> 00:08:58,700 And for a bonding orbital, it will 165 00:08:58,700 --> 00:09:03,270 be constructive interference, and so the amplitude 166 00:09:03,270 --> 00:09:07,630 where these atomic wave functions overlap 167 00:09:07,630 --> 00:09:11,120 will be increased when you have constructive interference. 168 00:09:11,120 --> 00:09:14,600 So our sigma 1s now has increased 169 00:09:14,600 --> 00:09:17,980 amplitude between these two nuclei 170 00:09:17,980 --> 00:09:22,180 due to that constructive interference. 171 00:09:22,180 --> 00:09:26,270 So an increased amplitude between these two nuclei, 172 00:09:26,270 --> 00:09:28,800 again, this is the bonding axis-- here is one nuclei, here 173 00:09:28,800 --> 00:09:33,060 is another-- so an increased amplitude here 174 00:09:33,060 --> 00:09:37,720 corresponds to an increased or enhanced probability density. 175 00:09:37,720 --> 00:09:41,360 Remember our wave function squared is probability density. 176 00:09:41,360 --> 00:09:43,270 It suggests the likelihood of finding 177 00:09:43,270 --> 00:09:47,660 an electron in a certain region of volume 178 00:09:47,660 --> 00:09:51,970 and if it's enhanced by this constructive interference. 179 00:09:51,970 --> 00:09:56,500 So if that probability density is enhanced, 180 00:09:56,500 --> 00:09:58,380 you have a greater chance of finding 181 00:09:58,380 --> 00:10:02,350 an electron between these two nuclei, which will 182 00:10:02,350 --> 00:10:05,000 be attracted by both nuclei. 183 00:10:05,000 --> 00:10:07,160 So now why don't you tell me what 184 00:10:07,160 --> 00:10:10,150 you think is going to happen to an electron that 185 00:10:10,150 --> 00:10:14,360 is in this region of constructive interference, 186 00:10:14,360 --> 00:10:17,568 this increased area of probability density. 187 00:10:31,860 --> 00:10:33,045 OK, 10 more seconds. 188 00:10:48,540 --> 00:10:49,440 Interesting. 189 00:10:52,210 --> 00:10:55,080 OK. 190 00:10:55,080 --> 00:11:02,240 So we should have probably not put up the answer there 191 00:11:02,240 --> 00:11:02,915 and re-pole. 192 00:11:05,401 --> 00:11:05,900 Yes. 193 00:11:05,900 --> 00:11:09,700 So here, if we have an electron that's 194 00:11:09,700 --> 00:11:12,480 attracted to both nuclei, then we 195 00:11:12,480 --> 00:11:14,560 want to think about whether that's 196 00:11:14,560 --> 00:11:16,950 going to be lower or higher in energy 197 00:11:16,950 --> 00:11:18,940 than something in an atomic orbital. 198 00:11:18,940 --> 00:11:20,940 So if it's attracted to both, it's 199 00:11:20,940 --> 00:11:23,580 going to be more stably bound to those, 200 00:11:23,580 --> 00:11:27,600 It will be harder to remove that electron, which means 201 00:11:27,600 --> 00:11:31,030 that it's lower down in energy. 202 00:11:31,030 --> 00:11:34,450 And so we should look at that, and we're going to. 203 00:11:34,450 --> 00:11:40,530 So the answer is it should be lower energy, more stable, 204 00:11:40,530 --> 00:11:42,960 harder to remove that electron. 205 00:11:42,960 --> 00:11:44,520 It's in a sweet spot. 206 00:11:44,520 --> 00:11:47,890 It has two positively-charged nuclei, 207 00:11:47,890 --> 00:11:50,140 and it's hanging out right in the middle. 208 00:11:50,140 --> 00:11:51,310 It's very happy. 209 00:11:51,310 --> 00:11:56,090 It's going to be more stable, and that means lower in energy. 210 00:11:56,090 --> 00:11:56,810 All right. 211 00:11:56,810 --> 00:11:59,040 So let's take a look at that. 212 00:11:59,040 --> 00:12:01,910 So the electron is lower in energy, 213 00:12:01,910 --> 00:12:04,480 and the bonding orbital energy is also 214 00:12:04,480 --> 00:12:08,660 going to be decreased compared to the atomic orbitals, 215 00:12:08,660 --> 00:12:12,790 and that has to be true if that's where the electron is. 216 00:12:12,790 --> 00:12:15,030 So let's look at the atomic orbital 217 00:12:15,030 --> 00:12:18,040 from a and the atomic orbital from b. 218 00:12:18,040 --> 00:12:23,310 And now, I'm going to put the bonding orbital at a lower 219 00:12:23,310 --> 00:12:24,850 energy level. 220 00:12:24,850 --> 00:12:26,920 First, I was going to put the electrons on, 221 00:12:26,920 --> 00:12:31,380 and now, I'm going to put the orbital at a lower energy. 222 00:12:31,380 --> 00:12:33,970 So remember, this is increasing energy here, 223 00:12:33,970 --> 00:12:37,000 so the atomic orbitals would be up here, 224 00:12:37,000 --> 00:12:39,845 whereas the molecular orbital is down here. 225 00:12:39,845 --> 00:12:44,220 The molecular bonding orbital will be lower in energy. 226 00:12:44,220 --> 00:12:47,150 And now we'll put our electrons there. 227 00:12:47,150 --> 00:12:50,800 So we have one electron up here and one here, 228 00:12:50,800 --> 00:12:52,720 and so when they come together, we're 229 00:12:52,720 --> 00:12:57,780 going to have two electrons in this molecular orbital. 230 00:12:57,780 --> 00:12:59,930 So when you have these two electrons 231 00:12:59,930 --> 00:13:02,370 and they both occupy the bonding orbital, 232 00:13:02,370 --> 00:13:05,730 and this is the case for H2, each H atom 233 00:13:05,730 --> 00:13:10,290 is bringing one electron, H2 has these two electrons, 234 00:13:10,290 --> 00:13:13,090 and that's going to make H2 more stable. 235 00:13:13,090 --> 00:13:18,090 And we saw that before that to associate the H2 bonds, 236 00:13:18,090 --> 00:13:20,450 you have to add energy into the system. 237 00:13:20,450 --> 00:13:26,070 H2 is more stable than free H plus H. 238 00:13:26,070 --> 00:13:29,340 So when you bring atomic orbitals together 239 00:13:29,340 --> 00:13:32,890 and you have constructive interference, an increased 240 00:13:32,890 --> 00:13:36,410 probability of electrons between those two nuclei, 241 00:13:36,410 --> 00:13:38,200 that's a sweet spot. 242 00:13:38,200 --> 00:13:40,970 Those electrons are going to be very happy there, 243 00:13:40,970 --> 00:13:45,200 and that will result in a more stable, lower energy structure. 244 00:13:47,780 --> 00:13:50,090 That's bonding. 245 00:13:50,090 --> 00:13:55,394 But whenever there is a positive event like this, 246 00:13:55,394 --> 00:13:57,310 there's always a negative event because that's 247 00:13:57,310 --> 00:13:58,890 just how life works. 248 00:13:58,890 --> 00:14:01,450 So we have bonding orbitals, but we also 249 00:14:01,450 --> 00:14:06,350 have antibonding orbitals. 250 00:14:06,350 --> 00:14:10,690 So antibonding arise from the linear combination 251 00:14:10,690 --> 00:14:14,740 of atomic orbitals, LCAO, through 252 00:14:14,740 --> 00:14:17,430 destructive interference. 253 00:14:17,430 --> 00:14:22,960 So here these are going to be destructively interfering, 254 00:14:22,960 --> 00:14:27,140 and that will generate a molecular orbital 255 00:14:27,140 --> 00:14:29,280 that is an antibonding orbital. 256 00:14:29,280 --> 00:14:31,820 So here are our little nuclei again, 257 00:14:31,820 --> 00:14:37,140 and this antibonding orbital is called sigma 1s star. 258 00:14:37,140 --> 00:14:40,080 So we can write an equation for this 259 00:14:40,080 --> 00:14:46,300 as 1sa minus 1sb equals sigma 1s star. 260 00:14:46,300 --> 00:14:50,440 That is an antibonding molecular orbital. 261 00:14:50,440 --> 00:14:53,900 And let's just think about how this kind of shape 262 00:14:53,900 --> 00:14:58,100 arises considering the wavelike properties 263 00:14:58,100 --> 00:15:00,850 of these atomic orbitals. 264 00:15:00,850 --> 00:15:04,440 So I'm going to now move this equation up to the top. 265 00:15:04,440 --> 00:15:10,360 And now, I have my 1sa here, my 1sb here, 266 00:15:10,360 --> 00:15:13,940 and now it's destructive interference. 267 00:15:13,940 --> 00:15:17,710 So we have opposite phase of the wave function. 268 00:15:17,710 --> 00:15:22,340 And we'll put up a wave function there. 269 00:15:22,340 --> 00:15:26,790 Now, the next one has the opposite phase, 270 00:15:26,790 --> 00:15:29,940 so they're going to destructively interfere. 271 00:15:29,940 --> 00:15:32,770 There is overlap over here, but when 272 00:15:32,770 --> 00:15:35,430 you have destructive interference, 273 00:15:35,430 --> 00:15:39,420 then the amplitude is going to decrease. 274 00:15:39,420 --> 00:15:43,600 So now, when we consider this destructive interference 275 00:15:43,600 --> 00:15:46,710 between these two orbitals, you see that you 276 00:15:46,710 --> 00:15:50,530 have what arises between them. 277 00:15:50,530 --> 00:15:54,480 Instead of enhanced probability of finding an electron, 278 00:15:54,480 --> 00:15:57,160 you actually get a node. 279 00:15:57,160 --> 00:16:01,220 So you have decreased amplitude translates 280 00:16:01,220 --> 00:16:06,240 to decreased probability density between these two nuclei-- one 281 00:16:06,240 --> 00:16:09,580 here, one here-- and that results in a node 282 00:16:09,580 --> 00:16:11,500 between the two nuclei. 283 00:16:11,500 --> 00:16:15,090 So in the antibonding orbital, there 284 00:16:15,090 --> 00:16:17,640 is a much lower probability that it 285 00:16:17,640 --> 00:16:23,520 will be in this sweet spot between the two nuclei 286 00:16:23,520 --> 00:16:25,860 that have this nice, positive charge for it's 287 00:16:25,860 --> 00:16:28,220 little negative charge, so there's 288 00:16:28,220 --> 00:16:32,380 pretty much no shot at being in that nice, sweet spot. 289 00:16:32,380 --> 00:16:34,790 And so what that ends up meaning is 290 00:16:34,790 --> 00:16:37,770 that an electron and an antibonding orbital 291 00:16:37,770 --> 00:16:42,410 is pretty much excluded from that internuclear 292 00:16:42,410 --> 00:16:46,180 region, that region between those two nuclei, 293 00:16:46,180 --> 00:16:49,110 and that results in a molecular orbital 294 00:16:49,110 --> 00:16:52,310 that has higher energy than the atomic orbital. 295 00:16:52,310 --> 00:16:55,650 There's just no chance of being in that wonderful spot. 296 00:16:55,650 --> 00:16:58,610 It's really very sad for the poor electron 297 00:16:58,610 --> 00:17:02,140 that has to occupy an antibonding orbital. 298 00:17:02,140 --> 00:17:06,970 So now, let's put this on our energy scale. 299 00:17:06,970 --> 00:17:09,780 So we'll go back to our energy scale. 300 00:17:09,780 --> 00:17:13,940 And we saw before that when we had 1sa and 1sb 301 00:17:13,940 --> 00:17:16,869 and you had a sigma 1s, a bonding orbital, 302 00:17:16,869 --> 00:17:19,020 that was lower in energy. 303 00:17:19,020 --> 00:17:22,500 Electrons that occupy it are more stable compared 304 00:17:22,500 --> 00:17:26,329 to their positions in the atomic orbital, but we also 305 00:17:26,329 --> 00:17:30,150 now have an antibonding orbital from destructive interference 306 00:17:30,150 --> 00:17:33,720 between the wave functions of the atomic orbitals, 307 00:17:33,720 --> 00:17:35,900 and that's higher in energy. 308 00:17:35,900 --> 00:17:38,470 And so that's up here. 309 00:17:38,470 --> 00:17:40,610 So this is what our diagram is going 310 00:17:40,610 --> 00:17:44,190 to look like that brings two atomic orbitals together 311 00:17:44,190 --> 00:17:48,430 to create two molecular orbitals. 312 00:17:48,430 --> 00:17:51,670 So the antibonding orbital up here 313 00:17:51,670 --> 00:17:54,860 is raised in energy by the same amount 314 00:17:54,860 --> 00:17:58,660 that the bonding energy is lowered. 315 00:17:58,660 --> 00:18:02,900 And so that gives rise to this diagram. 316 00:18:02,900 --> 00:18:06,370 And importantly, as I mentioned, we 317 00:18:06,370 --> 00:18:10,070 have N atomic orbitals forming N molecular orbitals. 318 00:18:10,070 --> 00:18:12,280 So if we have two atomic orbitals, 319 00:18:12,280 --> 00:18:15,290 we generate two molecular orbitals, 320 00:18:15,290 --> 00:18:20,250 one is bonding, lower in energy, and one is antibonding, higher 321 00:18:20,250 --> 00:18:22,151 in energy. 322 00:18:22,151 --> 00:18:22,650 All right. 323 00:18:22,650 --> 00:18:24,500 So let's take a look at some examples. 324 00:18:28,020 --> 00:18:33,390 So always start with hydrogen. So hydrogen has how many 325 00:18:33,390 --> 00:18:34,262 electrons? 326 00:18:37,280 --> 00:18:39,160 One hydrogen, hydrogen atom. 327 00:18:39,160 --> 00:18:39,966 AUDIENCE: One. 328 00:18:39,966 --> 00:18:41,140 CATHERINE DRENNAN: One. 329 00:18:41,140 --> 00:18:44,080 So we have two hydrogen atoms, and so we 330 00:18:44,080 --> 00:18:48,430 have two 1s orbitals, 1sa, 1sb. 331 00:18:48,430 --> 00:18:53,840 And now where do we want to put our electrons? 332 00:18:53,840 --> 00:18:56,160 In the highest energy possible, lower energy? 333 00:18:56,160 --> 00:18:57,370 Where do we want to put them? 334 00:18:57,370 --> 00:18:58,240 AUDIENCE: Lower. 335 00:18:58,240 --> 00:19:00,980 CATHERINE DRENNAN: Always start with lower energy. 336 00:19:00,980 --> 00:19:04,190 So we're going to put them down here. 337 00:19:04,190 --> 00:19:10,220 And so this is now the MO diagram for H2. 338 00:19:10,220 --> 00:19:13,180 And we can write the electron configuration 339 00:19:13,180 --> 00:19:16,870 for the MO diagram, which you'll note is a different electron 340 00:19:16,870 --> 00:19:19,260 configuration than you were writing when you were looking 341 00:19:19,260 --> 00:19:22,170 at the periodic table because now we're not writing it 342 00:19:22,170 --> 00:19:25,830 in terms of 1s 2, 2s 2, we're writing it 343 00:19:25,830 --> 00:19:28,750 in terms of molecular orbitals. 344 00:19:28,750 --> 00:19:30,990 And there are some of these on the problem set, 345 00:19:30,990 --> 00:19:33,440 and I tried to indicate example to make 346 00:19:33,440 --> 00:19:36,300 sure you know what kind of electron configurations 347 00:19:36,300 --> 00:19:37,420 we're talking about. 348 00:19:37,420 --> 00:19:40,860 So for MO diagrams, when it says electron configuration 349 00:19:40,860 --> 00:19:44,720 we're talking about where the electrons are with respect 350 00:19:44,720 --> 00:19:46,470 to the molecular orbitals. 351 00:19:46,470 --> 00:19:49,910 So the answer to this would be sigma 1s 2. 352 00:19:49,910 --> 00:19:54,120 There are two electrons in the molecular orbital, sigma 1s. 353 00:19:56,730 --> 00:19:58,630 Good. 354 00:19:58,630 --> 00:20:05,704 So that means that you can do the same thing for dihelium, 355 00:20:05,704 --> 00:20:06,953 and that's a clicker question. 356 00:20:27,650 --> 00:20:29,110 So let's just take 10 more seconds. 357 00:20:44,050 --> 00:20:46,050 OK, you can vote. 358 00:20:46,050 --> 00:20:46,555 All right. 359 00:20:49,640 --> 00:21:03,090 So does someone want to tell me-- that is correct-- 360 00:21:03,090 --> 00:21:07,034 what's number two for? 361 00:21:07,034 --> 00:21:13,702 For hydrogen. What about number three, what was wrong there? 362 00:21:13,702 --> 00:21:15,074 AUDIENCE: [INAUDIBLE]. 363 00:21:15,074 --> 00:21:17,240 CATHERINE DRENNAN: OK, everyone's doing really well. 364 00:21:17,240 --> 00:21:17,740 Yeah. 365 00:21:17,740 --> 00:21:24,650 So all of the electrons were parallel in there, 366 00:21:24,650 --> 00:21:26,730 and what does that violate? 367 00:21:26,730 --> 00:21:28,676 What would be true in that case? 368 00:21:28,676 --> 00:21:30,120 AUDIENCE: [INAUDIBLE]. 369 00:21:30,120 --> 00:21:31,120 CATHERINE DRENNAN: Yeah. 370 00:21:31,120 --> 00:21:36,650 And so they'd have the same four principle quantum numbers. 371 00:21:36,650 --> 00:21:38,120 This is not allowed. 372 00:21:38,120 --> 00:21:39,600 So that one's not good. 373 00:21:39,600 --> 00:21:41,212 And what's wrong with four? 374 00:21:41,212 --> 00:21:42,821 AUDIENCE: [INAUDIBLE]. 375 00:21:42,821 --> 00:21:44,820 CATHERINE DRENNAN: Yeah, star was on the bottom. 376 00:21:44,820 --> 00:21:46,100 So they were flipped around. 377 00:21:46,100 --> 00:21:48,770 Antibonding was lower in energy. 378 00:21:48,770 --> 00:21:50,810 Great. 379 00:21:50,810 --> 00:21:53,950 So we'll just put those in over here, 380 00:21:53,950 --> 00:21:57,450 and so we had two electrons. 381 00:21:57,450 --> 00:21:59,050 Helium brings two. 382 00:21:59,050 --> 00:22:02,300 So two went into the bonding, and two 383 00:22:02,300 --> 00:22:07,030 went into the antibonding with opposite spins. 384 00:22:07,030 --> 00:22:09,330 And we have the bonding, lower energy; 385 00:22:09,330 --> 00:22:11,191 antibonding, higher energy. 386 00:22:11,191 --> 00:22:11,690 All right. 387 00:22:11,690 --> 00:22:16,980 So then we can put in the electron configuration here, 388 00:22:16,980 --> 00:22:23,600 and we have sigma 1s 2, sigma 1s star 2, 389 00:22:23,600 --> 00:22:27,250 so that's the electron configuration. 390 00:22:27,250 --> 00:22:30,750 Now interestingly, you see, you have two 391 00:22:30,750 --> 00:22:33,790 at lower energy and two at higher energy, 392 00:22:33,790 --> 00:22:38,630 so there's no net loss or gain in energy of H2 393 00:22:38,630 --> 00:22:42,080 compared to just two helium atoms. 394 00:22:42,080 --> 00:22:48,190 And so that raises the question, does helium 2 exist? 395 00:22:48,190 --> 00:22:51,210 So what would molecular orbital theory 396 00:22:51,210 --> 00:22:54,900 tell you about whether it exists, and it would actually 397 00:22:54,900 --> 00:22:57,650 predict that it does not exist. 398 00:22:57,650 --> 00:23:00,710 And the way that molecular orbital theory gives you 399 00:23:00,710 --> 00:23:03,970 these predictions is through the calculation of something 400 00:23:03,970 --> 00:23:05,910 called bond order. 401 00:23:05,910 --> 00:23:09,300 So bond order is half of the number 402 00:23:09,300 --> 00:23:13,510 of bonding electrons minus the number of antibonding 403 00:23:13,510 --> 00:23:14,690 electrons. 404 00:23:14,690 --> 00:23:19,730 So let's just write out what the bond order for helium would be. 405 00:23:23,360 --> 00:23:28,800 So helium 2, our dihelium molecule. 406 00:23:28,800 --> 00:23:34,670 So we have a bond order equals 1/2. 407 00:23:34,670 --> 00:23:36,280 There's always 1/2. 408 00:23:36,280 --> 00:23:38,820 And now, the number of bonding electrons, so 409 00:23:38,820 --> 00:23:41,060 how many bonding electrons do we have for helium? 410 00:23:41,060 --> 00:23:42,066 AUDIENCE: Two. 411 00:23:42,066 --> 00:23:44,010 CATHERINE DRENNAN: Two. 412 00:23:44,010 --> 00:23:47,555 How many antibonding electrons do we have for dihelium? 413 00:23:47,555 --> 00:23:48,355 AUDIENCE: Two 414 00:23:48,355 --> 00:23:50,280 CATHERINE DRENNAN: Two. 415 00:23:50,280 --> 00:23:53,005 And can someone do this math for me? 416 00:23:53,005 --> 00:23:53,761 AUDIENCE: Zero. 417 00:23:53,761 --> 00:23:54,760 CATHERINE DRENNAN: Zero. 418 00:23:54,760 --> 00:23:55,550 Right. 419 00:23:55,550 --> 00:23:57,770 So that would suggest a bond order 420 00:23:57,770 --> 00:24:02,970 of 0, which means no bond. 421 00:24:02,970 --> 00:24:08,430 And let's just compare that to hydrogen, H2, 422 00:24:08,430 --> 00:24:13,080 which should have a bond order equal to 1/2. 423 00:24:13,080 --> 00:24:14,620 It's always a 1/2. 424 00:24:14,620 --> 00:24:18,634 In the hydrogen, how many bonding electrons did we have? 425 00:24:18,634 --> 00:24:19,238 AUDIENCE: Two. 426 00:24:19,238 --> 00:24:20,488 CATHERINE DRENNAN: We had two. 427 00:24:20,488 --> 00:24:23,030 How many antibonding electrons did we have? 428 00:24:23,030 --> 00:24:23,750 AUDIENCE: Zero. 429 00:24:23,750 --> 00:24:24,770 CATHERINE DRENNAN: Zero. 430 00:24:24,770 --> 00:24:26,120 And the math? 431 00:24:26,120 --> 00:24:26,995 Bond order is? 432 00:24:26,995 --> 00:24:27,505 AUDIENCE: 1. 433 00:24:27,505 --> 00:24:29,280 CATHERINE DRENNAN: 1. 434 00:24:29,280 --> 00:24:33,450 So that means 1 bond or a single bond. 435 00:24:37,740 --> 00:24:42,920 So MO theory would predict that dihelium, has no bond, i.e. 436 00:24:42,920 --> 00:24:45,690 it's not really a molecule without a bond, 437 00:24:45,690 --> 00:24:47,450 but H2 should exist. 438 00:24:52,200 --> 00:24:55,810 So let's take a look at what experiment tells us, 439 00:24:55,810 --> 00:25:02,340 and it does exist, but only really not that much. 440 00:25:02,340 --> 00:25:08,360 So it was not discovered until 1993, which for some of you 441 00:25:08,360 --> 00:25:10,570 might seem like quite a long time ago, 442 00:25:10,570 --> 00:25:12,200 but since we've been mostly talking 443 00:25:12,200 --> 00:25:16,120 about discoveries that were made in the 1800s, 444 00:25:16,120 --> 00:25:18,100 it took a long time before someone could 445 00:25:18,100 --> 00:25:21,030 prove that dihelium existed. 446 00:25:21,030 --> 00:25:25,460 And if we look at the bond association energy for H2, 447 00:25:25,460 --> 00:25:32,502 0.01, and compare that to H2, 432, 448 00:25:32,502 --> 00:25:34,840 dihelium really doesn't exist very much. 449 00:25:34,840 --> 00:25:40,670 0 is a much better approximation of its bond than 1 would be. 450 00:25:40,670 --> 00:25:43,390 It really is not a very good molecule. 451 00:25:43,390 --> 00:25:47,420 So I would call this a win for molecular orbital theory. 452 00:25:47,420 --> 00:25:53,326 It correctly predicts that our helium 2 is not 453 00:25:53,326 --> 00:25:54,700 going to be a very good molecule, 454 00:25:54,700 --> 00:26:00,220 but H2 will be a good molecule, and that works. 455 00:26:00,220 --> 00:26:01,015 All right. 456 00:26:03,560 --> 00:26:06,860 Now, let's consider 2s. 457 00:26:06,860 --> 00:26:10,740 So 2s orbitals are analogous to 1s 458 00:26:10,740 --> 00:26:15,090 except that you have to remember that they're bigger. 459 00:26:15,090 --> 00:26:19,200 So we have our 1s and our 2s, but for the purposes of this, 460 00:26:19,200 --> 00:26:22,070 it doesn't really matter. 461 00:26:22,070 --> 00:26:28,190 So let's look at a diagram now that has 1s and 2s. 462 00:26:28,190 --> 00:26:30,870 So we have lithium. 463 00:26:30,870 --> 00:26:34,640 So how many electrons does lithium have? 464 00:26:34,640 --> 00:26:35,500 AUDIENCE: Three. 465 00:26:35,500 --> 00:26:36,820 CATHERINE DRENNAN: Yep. 466 00:26:36,820 --> 00:26:39,410 So we'll put on lithium, dilithium. 467 00:26:39,410 --> 00:26:44,840 We'll put on lithiums has two in 1s and one in 2s, 468 00:26:44,840 --> 00:26:50,110 and so we have one lithium here and one lithium over here. 469 00:26:50,110 --> 00:26:53,600 And our 1s orbitals are going to be lower energy, 470 00:26:53,600 --> 00:26:54,930 so they're down here. 471 00:26:54,930 --> 00:26:57,770 Our 2s orbitals are higher in energy. 472 00:26:57,770 --> 00:27:01,830 So that goes for both the atomic and the molecular orbitals 473 00:27:01,830 --> 00:27:03,400 that are generated. 474 00:27:03,400 --> 00:27:09,280 So bringing together 1s with 1s, we get sigma 1s and also 475 00:27:09,280 --> 00:27:11,290 sigma star 1s. 476 00:27:11,290 --> 00:27:14,180 And so we can start putting our electrons in. 477 00:27:14,180 --> 00:27:17,210 We're going to start with the lowest energy and move on up. 478 00:27:17,210 --> 00:27:20,470 So we have four electrons that we need to put in, 479 00:27:20,470 --> 00:27:23,040 so we fill up everything here. 480 00:27:23,040 --> 00:27:25,720 And now we go up to our 2s. 481 00:27:25,720 --> 00:27:30,510 The 2s orbitals will generate signal 2s and sigma 2s star. 482 00:27:30,510 --> 00:27:36,020 We have two electrons, so they both can go down here. 483 00:27:36,020 --> 00:27:40,230 So here is what our MO diagram looks like. 484 00:27:40,230 --> 00:27:43,500 We can write out the electron configuration again, 485 00:27:43,500 --> 00:27:45,840 based on this diagram. 486 00:27:45,840 --> 00:27:50,970 So we have two electrons in sigma 1s, so we have a 2 there. 487 00:27:50,970 --> 00:27:54,460 We have two electrons in sigma 1s star, our antibonding 488 00:27:54,460 --> 00:27:59,540 orbital, and we have two electrons in sigma 2s. 489 00:27:59,540 --> 00:28:03,420 And now we can calculate the bond order, which 490 00:28:03,420 --> 00:28:04,847 is another clicker question. 491 00:28:22,050 --> 00:28:23,490 OK, just 10 more seconds. 492 00:28:38,820 --> 00:28:39,760 Excellent. 493 00:28:39,760 --> 00:28:41,780 84%. 494 00:28:41,780 --> 00:28:48,320 So if we do out the math here, we always have our 1/2. 495 00:28:48,320 --> 00:28:51,510 We have four bonding electrons. 496 00:28:51,510 --> 00:28:53,990 We have two down here and two up here. 497 00:28:53,990 --> 00:28:58,450 We have two antibonding electrons in our sigma 1s star, 498 00:28:58,450 --> 00:29:01,250 and so that gives us a bond order of 1. 499 00:29:01,250 --> 00:29:03,790 And in fact, the dissociation energy 500 00:29:03,790 --> 00:29:05,410 does suggest there is a bond. 501 00:29:05,410 --> 00:29:07,350 It's not a great bond. 502 00:29:07,350 --> 00:29:12,860 It's 105 kilojoules per mole, not necessarily enough to power 503 00:29:12,860 --> 00:29:18,290 a starship, but still this molecule does exist. 504 00:29:18,290 --> 00:29:21,040 All right. 505 00:29:21,040 --> 00:29:25,690 So let's look at beryllium now, do another example. 506 00:29:25,690 --> 00:29:31,180 So how many electrons is beryllium going to have? 507 00:29:31,180 --> 00:29:33,230 It will have four. 508 00:29:33,230 --> 00:29:35,300 So we'll put those up. 509 00:29:35,300 --> 00:29:39,670 Now, we're going to start with our lowest energy orbital, 510 00:29:39,670 --> 00:29:43,020 and we're going to put some in the antibonding as well. 511 00:29:43,020 --> 00:29:46,740 And then we'll do this, and then we'll do that. 512 00:29:46,740 --> 00:29:49,520 And we filled up everything. 513 00:29:49,520 --> 00:29:52,460 And so we can write out our configuration. 514 00:29:52,460 --> 00:29:57,050 We have two in our sigma 1s orbital. 515 00:29:57,050 --> 00:30:00,140 We have two in our sigma 1s star. 516 00:30:00,140 --> 00:30:05,430 We have two in our sigma 2s, and two in our sigma 2s star 517 00:30:05,430 --> 00:30:07,060 antibonding orbital there. 518 00:30:10,200 --> 00:30:12,130 And now there are two different ways 519 00:30:12,130 --> 00:30:14,850 that I can calculate the bond order here, 520 00:30:14,850 --> 00:30:17,470 and we'll do both of them and show you that they come out 521 00:30:17,470 --> 00:30:19,230 the same way. 522 00:30:19,230 --> 00:30:21,430 One way that we can calculate this 523 00:30:21,430 --> 00:30:25,580 is to consider all electrons. 524 00:30:25,580 --> 00:30:29,190 So if we consider all electrons, our bond order, 525 00:30:29,190 --> 00:30:36,380 and that's often just said B.O., is 1/2 of our bonding. 526 00:30:36,380 --> 00:30:40,690 And now we can count up both the 1s and the 2s. 527 00:30:40,690 --> 00:30:43,430 So how many bonding electrons do we have? 528 00:30:46,070 --> 00:30:53,920 We should have four, so we have two here, two here, so four. 529 00:30:53,920 --> 00:30:56,430 How many antibonding? 530 00:30:56,430 --> 00:31:03,370 Also four, so that suggest a bond order of 0. 531 00:31:03,370 --> 00:31:08,170 Or we could just consider our valence electrons, 532 00:31:08,170 --> 00:31:11,630 so that would be the electrons in 2s, 533 00:31:11,630 --> 00:31:15,550 and if we do that, bond order equals 1/2. 534 00:31:15,550 --> 00:31:18,930 It's always a 1/2, so how many valence electrons 535 00:31:18,930 --> 00:31:21,490 do we have in bonding orbitals? 536 00:31:21,490 --> 00:31:22,370 Two. 537 00:31:22,370 --> 00:31:24,980 How many in antibonding orbitals? 538 00:31:24,980 --> 00:31:26,620 Two. 539 00:31:26,620 --> 00:31:28,530 And that gives the answer of 0. 540 00:31:28,530 --> 00:31:32,860 So it should always work unless you do something very strange. 541 00:31:32,860 --> 00:31:37,250 You should be able to do it both ways and get the same answer. 542 00:31:37,250 --> 00:31:39,290 So if this is a complicated problem, 543 00:31:39,290 --> 00:31:42,200 you might want to only consider the valence electrons. 544 00:31:42,200 --> 00:31:44,230 In fact, on a test, you may only be 545 00:31:44,230 --> 00:31:47,090 asked to draw the molecular orbital diagrams 546 00:31:47,090 --> 00:31:49,020 for the valence electrons, and you don't 547 00:31:49,020 --> 00:31:53,740 have to do the other ones. 548 00:31:53,740 --> 00:31:56,010 So that should work both ways. 549 00:31:56,010 --> 00:31:59,940 And we get a bond order of 0, and in fact, 550 00:31:59,940 --> 00:32:03,980 the dissociation energy is only 9 kilojoules per mole. 551 00:32:03,980 --> 00:32:07,020 It's a little stronger than dihelium, 552 00:32:07,020 --> 00:32:09,970 but this is an exceedingly weak molecule. 553 00:32:09,970 --> 00:32:13,310 So when you have the same number of electrons and bonding 554 00:32:13,310 --> 00:32:18,186 as antibonding, it doesn't lead to a very strong molecule. 555 00:32:18,186 --> 00:32:20,400 All right. 556 00:32:20,400 --> 00:32:22,610 That's the orbitals. 557 00:32:22,610 --> 00:32:27,150 Now, it's time for molecules that have p orbitals as well. 558 00:32:30,160 --> 00:32:37,610 So in this case, now I have my p orbital and another p orbital. 559 00:32:37,610 --> 00:32:42,064 And we have our nuclei in the middle, 560 00:32:42,064 --> 00:32:43,730 and we're going to bring these together, 561 00:32:43,730 --> 00:32:47,370 and we will have constructive interference. 562 00:32:47,370 --> 00:32:50,940 And so here we're bringing together 563 00:32:50,940 --> 00:33:00,740 2p x of a and 2p xb or 2p ya and 2p yb. 564 00:33:00,740 --> 00:33:04,660 So just x and y we're considering right now. 565 00:33:04,660 --> 00:33:11,100 And if we bring those together with constructive interference, 566 00:33:11,100 --> 00:33:14,150 then we're going to form a bonding orbital that 567 00:33:14,150 --> 00:33:19,390 has enhanced probability density in both cases 568 00:33:19,390 --> 00:33:22,920 and nodal plane along the bond axis 569 00:33:22,920 --> 00:33:27,100 because we had nodal planes along there to begin with. 570 00:33:27,100 --> 00:33:31,540 So if we think about this and we have both of these, 571 00:33:31,540 --> 00:33:34,660 we're bringing them together and they're 572 00:33:34,660 --> 00:33:37,270 going to interfere constructively, enhance 573 00:33:37,270 --> 00:33:40,720 probability density here, enhance probability density 574 00:33:40,720 --> 00:33:44,750 down here, but we still have our nodal plane because we 575 00:33:44,750 --> 00:33:46,510 started out with one. 576 00:33:46,510 --> 00:33:52,440 And so if we have a nodal plane, this cannot be a sigma orbital. 577 00:33:52,440 --> 00:33:56,630 It has to be a pi orbital, because sigma orbitals are not 578 00:33:56,630 --> 00:34:01,340 going to have a nodal plane along the bonding access. 579 00:34:01,340 --> 00:34:01,840 All right. 580 00:34:01,840 --> 00:34:09,699 So we could generate pi 2px or pi 2py this way. 581 00:34:09,699 --> 00:34:12,429 So a pi orbital is a molecular orbital 582 00:34:12,429 --> 00:34:15,900 that has a nodal plane through the bond axis or maybe I 583 00:34:15,900 --> 00:34:19,429 should say along the bond axis, so here is our nodal plane 584 00:34:19,429 --> 00:34:21,263 right through the bond axis. 585 00:34:26,060 --> 00:34:30,909 We can also have antibonding, which 586 00:34:30,909 --> 00:34:33,690 means destructive interference. 587 00:34:33,690 --> 00:34:35,650 So now, I'm going to be subtracting 588 00:34:35,650 --> 00:34:38,760 one of these from one of these, and I'm 589 00:34:38,760 --> 00:34:42,130 going to get something that looks like this, 590 00:34:42,130 --> 00:34:51,780 and it will be pi 2px star or pi 2py star, 591 00:34:51,780 --> 00:34:56,179 and it will have two nodal planes. 592 00:34:56,179 --> 00:34:57,355 So let's look at this. 593 00:34:57,355 --> 00:34:59,430 So this is destructive interference. 594 00:34:59,430 --> 00:35:01,780 I'm subtracting one of these from one of these, 595 00:35:01,780 --> 00:35:03,910 so the phase has to change. 596 00:35:03,910 --> 00:35:06,230 So I'm going to change the phase on one of them 597 00:35:06,230 --> 00:35:08,060 and then bring them together. 598 00:35:08,060 --> 00:35:11,760 Now, we're not going to have that awesome, constructive 599 00:35:11,760 --> 00:35:15,760 interference increased probability density. 600 00:35:15,760 --> 00:35:18,820 These are negatively interacting with each other. 601 00:35:18,820 --> 00:35:23,510 And this generates a nodal plane between the molecules. 602 00:35:23,510 --> 00:35:25,990 They really look much more like this now, 603 00:35:25,990 --> 00:35:29,400 so we have still our nodal plane through the bond. 604 00:35:29,400 --> 00:35:30,390 We had that before. 605 00:35:30,390 --> 00:35:31,780 We're always going to have that. 606 00:35:31,780 --> 00:35:36,780 But now we have an additional nodal plane between the nuclei. 607 00:35:36,780 --> 00:35:40,950 So in one case, we have enhanced density, probability density 608 00:35:40,950 --> 00:35:41,450 again. 609 00:35:41,450 --> 00:35:43,950 And the other case, in antibonding, 610 00:35:43,950 --> 00:35:47,600 we have another nodal plane. 611 00:35:47,600 --> 00:35:48,160 All right. 612 00:35:48,160 --> 00:35:49,660 So now, let's look at what happens 613 00:35:49,660 --> 00:35:55,170 to the energies of these pi orbitals. 614 00:35:55,170 --> 00:35:58,360 And the diagrams that I'm about to show you, 615 00:35:58,360 --> 00:36:01,750 we're only talking about px and py now. 616 00:36:01,750 --> 00:36:05,320 We have for the moment forgotten 2pz. 617 00:36:05,320 --> 00:36:08,850 So these diagrams are rated I for incomplete. 618 00:36:08,850 --> 00:36:11,140 Warning to the viewer, people come to me 619 00:36:11,140 --> 00:36:13,790 and go where are the 2pz? 620 00:36:13,790 --> 00:36:16,740 Yes, they're not in these diagrams, 621 00:36:16,740 --> 00:36:19,450 but when you're asked for a complete diagram, 622 00:36:19,450 --> 00:36:22,085 you will always have to put those orbitals in. 623 00:36:22,085 --> 00:36:24,600 And in fact, completing these diagrams 624 00:36:24,600 --> 00:36:27,220 could be a question you get later. 625 00:36:27,220 --> 00:36:30,710 But for now, we're going to have 2pz here, 626 00:36:30,710 --> 00:36:34,880 but it's not forming a molecular orbital in this diagram. 627 00:36:34,880 --> 00:36:37,170 This diagram is, thus, incomplete, 628 00:36:37,170 --> 00:36:40,980 but we're going to start simple and build more complicated. 629 00:36:40,980 --> 00:36:45,280 So only 2p orbitals first, and then we'll add the third one. 630 00:36:45,280 --> 00:36:49,230 Because this compound doesn't actually need that orbital, 631 00:36:49,230 --> 00:36:51,450 so we're good for now. 632 00:36:51,450 --> 00:36:51,950 All right. 633 00:36:51,950 --> 00:36:55,680 So we have moved on to the first element that has 634 00:36:55,680 --> 00:36:59,000 a p electron in a p orbital. 635 00:36:59,000 --> 00:37:02,280 We have boron, and we have two of them. 636 00:37:02,280 --> 00:37:08,430 So now I dropped off 1s to simplify this. 637 00:37:08,430 --> 00:37:10,990 Now, we just have our valence electrons, 638 00:37:10,990 --> 00:37:13,900 so it's a good thing we can calculate bond order just using 639 00:37:13,900 --> 00:37:15,360 our valence electrons. 640 00:37:15,360 --> 00:37:15,860 All right. 641 00:37:15,860 --> 00:37:21,390 So we have two in 2s and one in 2px or 2py. 642 00:37:21,390 --> 00:37:24,210 I could have put it in either place. 643 00:37:24,210 --> 00:37:26,690 So let's put in where they would go. 644 00:37:26,690 --> 00:37:29,250 So we have 2s orbitals. 645 00:37:29,250 --> 00:37:34,120 They'll go into bonding sigma 2s first, then 646 00:37:34,120 --> 00:37:43,400 into antibonding, sigma 2s star, and now we have p electrons, 647 00:37:43,400 --> 00:37:47,490 and we're going to put them into our pi orbitals, 648 00:37:47,490 --> 00:37:48,960 our molecular orbitals. 649 00:37:48,960 --> 00:37:52,170 I'll put one in, and where am I going to put the other one? 650 00:37:52,170 --> 00:37:54,235 Am I going to put it next to it or over here? 651 00:37:54,235 --> 00:37:55,370 What do you think? 652 00:37:55,370 --> 00:37:56,600 AUDIENCE: [INAUDIBLE]. 653 00:37:56,600 --> 00:37:57,840 CATHERINE DRENNAN: Yeah. 654 00:37:57,840 --> 00:38:00,820 So we're going to do that because, again, when you're 655 00:38:00,820 --> 00:38:03,890 going to sit on a bus, you want to have if they're degenerate 656 00:38:03,890 --> 00:38:06,340 in energy levels as they are here, 657 00:38:06,340 --> 00:38:10,070 you're always going to put one electron in each orbital 658 00:38:10,070 --> 00:38:13,190 of the same energy first before you pair them up, 659 00:38:13,190 --> 00:38:15,970 and they'll have parallel spins. 660 00:38:15,970 --> 00:38:18,140 So we're reviewing things we learned before. 661 00:38:18,140 --> 00:38:20,720 I love doing that. 662 00:38:20,720 --> 00:38:25,210 So now, let's see what our electron configuration is, 663 00:38:25,210 --> 00:38:29,260 and this is just the valence electron configuration. 664 00:38:29,260 --> 00:38:30,130 We're simplifying. 665 00:38:30,130 --> 00:38:33,730 We're not going to consider the 1s orbital, 666 00:38:33,730 --> 00:38:35,000 and we can write this down. 667 00:38:35,000 --> 00:38:38,660 So we have two electrons in sigma 2s, 668 00:38:38,660 --> 00:38:42,880 and we have two electrons in sigma 2s star, our antibonding 669 00:38:42,880 --> 00:38:50,250 orbital, and we have one in pi 2px and one in pi 2py. 670 00:38:50,250 --> 00:38:52,940 And I can put a 1 or not put a 1. 671 00:38:52,940 --> 00:38:57,890 If I don't put anything, for a 1, 1 is assumed. 672 00:38:57,890 --> 00:39:02,080 And we can calculate our bond order as well. 673 00:39:02,080 --> 00:39:04,380 So we have 1/2, and again, we're just 674 00:39:04,380 --> 00:39:07,170 using our valence electrons, but that's OK. 675 00:39:07,170 --> 00:39:11,580 We have four now who are bonding, two down here, two 676 00:39:11,580 --> 00:39:13,960 up here, these are bonding orbitals, 677 00:39:13,960 --> 00:39:16,580 and we have two that are antibonding. 678 00:39:16,580 --> 00:39:18,960 And notice for our pi orbitals, this 679 00:39:18,960 --> 00:39:22,200 is what we saw before bonding are lower in energy, 680 00:39:22,200 --> 00:39:24,500 antibonding are higher in energy. 681 00:39:24,500 --> 00:39:27,810 With the bonding orbitals, we had constructive interference, 682 00:39:27,810 --> 00:39:31,590 enhanced probability of the electrons near the nuclei, 683 00:39:31,590 --> 00:39:33,650 and so that's lower in energy. 684 00:39:33,650 --> 00:39:36,710 But in our antibonding ones, we have a nodal plane 685 00:39:36,710 --> 00:39:38,230 in between our nuclei. 686 00:39:38,230 --> 00:39:40,860 So we don't have any probability that electrons 687 00:39:40,860 --> 00:39:43,740 are right in between there because there's a nodal plane, 688 00:39:43,740 --> 00:39:46,600 so those are higher in energy. 689 00:39:46,600 --> 00:39:50,670 So here is our B2 diagram. 690 00:39:50,670 --> 00:39:55,410 So now let's try the same thing for carbon, C2, 691 00:39:55,410 --> 00:39:57,000 and that is a clicker question. 692 00:40:22,540 --> 00:40:23,040 All right. 693 00:40:23,040 --> 00:40:25,756 Let's just take 10 more seconds. 694 00:40:42,080 --> 00:40:44,270 So let's take a look at that over here. 695 00:40:44,270 --> 00:40:47,490 The easiest thing to do to answer this question 696 00:40:47,490 --> 00:40:50,600 was to fill in the diagram in your handout. 697 00:40:50,600 --> 00:40:55,910 And so if you did that, you would have put two down here 698 00:40:55,910 --> 00:40:58,760 and you would have put two up here. 699 00:40:58,760 --> 00:41:04,070 Then you would have put one here, one there, 700 00:41:04,070 --> 00:41:06,880 another one there, and another one there. 701 00:41:09,460 --> 00:41:15,710 So now we have used these up, and so our configuration 702 00:41:15,710 --> 00:41:27,270 is sigma 2s 2, sigma star 2, pi 2px 2, pi 2py 2. 703 00:41:27,270 --> 00:41:30,270 And the bond order is 1/2. 704 00:41:30,270 --> 00:41:35,540 There are six bonding electrons-- 1, 2, 3, 4, 5, 6-- 705 00:41:35,540 --> 00:41:40,790 and two antibonding electrons, and so that adds up 706 00:41:40,790 --> 00:41:44,660 to a bond order of 2. 707 00:41:44,660 --> 00:41:46,750 And so sometimes on a test, they'll 708 00:41:46,750 --> 00:41:49,760 be a simple question what is the bond order, but to get there 709 00:41:49,760 --> 00:41:53,260 you have to draw your whole molecular orbital diagram 710 00:41:53,260 --> 00:41:56,430 and figure out how many bonding and how many antibonding, 711 00:41:56,430 --> 00:41:59,507 so these are not really that fast questions. 712 00:41:59,507 --> 00:42:00,090 And it's nice. 713 00:42:00,090 --> 00:42:01,839 Sometimes we give you like a little space, 714 00:42:01,839 --> 00:42:04,800 and you see this whole little molecular orbital diagram 715 00:42:04,800 --> 00:42:07,590 fit in there to answer the question. 716 00:42:07,590 --> 00:42:08,090 All right. 717 00:42:08,090 --> 00:42:11,450 So let's just compare these two diagrams for a minute. 718 00:42:11,450 --> 00:42:18,470 So in both cases, we had 2s orbitals, two atomic orbitals 719 00:42:18,470 --> 00:42:23,610 for 2s, and they both generated two molecular orbitals, 720 00:42:23,610 --> 00:42:26,050 a bonding and an antibonding. 721 00:42:26,050 --> 00:42:28,810 The bonding is lower in energy, and the antibonding 722 00:42:28,810 --> 00:42:30,520 is higher in energy. 723 00:42:30,520 --> 00:42:34,590 We also had two 2px atomic orbitals. 724 00:42:34,590 --> 00:42:41,320 They generated 2 pi 2 px orbitals, 725 00:42:41,320 --> 00:42:44,450 one bonding, one antibonding. 726 00:42:44,450 --> 00:42:49,130 And the same for our two atomic orbitals for 2 py. 727 00:42:49,130 --> 00:42:53,270 We had two of those, and they generated one lower energy 728 00:42:53,270 --> 00:42:58,500 bonding, pi, bonding and one pi star antibonding. 729 00:42:58,500 --> 00:43:02,220 So you always have N atomic orbitals generating 730 00:43:02,220 --> 00:43:06,390 N molecular orbitals. 731 00:43:06,390 --> 00:43:09,150 So the stability of the resulting molecules 732 00:43:09,150 --> 00:43:12,440 in these cases depend on how many of the electrons 733 00:43:12,440 --> 00:43:15,540 are bonding, how many are in energy lower 734 00:43:15,540 --> 00:43:18,070 as a result of formation of the molecule, 735 00:43:18,070 --> 00:43:22,370 and how many are at higher energy as a result of formation 736 00:43:22,370 --> 00:43:23,570 of the molecule. 737 00:43:23,570 --> 00:43:27,410 And if the net result are more electrons in lower energy, more 738 00:43:27,410 --> 00:43:30,620 electrons in bonding orbitals, then that molecule 739 00:43:30,620 --> 00:43:31,820 is more stable. 740 00:43:31,820 --> 00:43:34,920 If there's a very slight or no difference, 741 00:43:34,920 --> 00:43:37,600 then that's not a very stable molecule. 742 00:43:37,600 --> 00:43:39,820 So now let's just compare these two 743 00:43:39,820 --> 00:43:44,640 and think about which of these is going to be more stable. 744 00:43:44,640 --> 00:43:48,000 So we have our configurations again. 745 00:43:48,000 --> 00:43:52,020 So in the case of B2, how many electrons 746 00:43:52,020 --> 00:43:54,470 are in lower energy or bonding orbitals? 747 00:43:54,470 --> 00:43:55,745 AUDIENCE: [INAUDIBLE]. 748 00:43:55,745 --> 00:43:58,590 CATHERINE DRENNAN: Yeah, we have four-- 1, 2, 3, 4. 749 00:43:58,590 --> 00:44:00,010 How many in higher? 750 00:44:00,010 --> 00:44:00,892 AUDIENCE: Two. 751 00:44:00,892 --> 00:44:01,850 CATHERINE DRENNAN: Two. 752 00:44:01,850 --> 00:44:03,370 Up here. 753 00:44:03,370 --> 00:44:10,720 For carbon, we had six-- 1, 2, 3, 4, 5, 6-- two in higher. 754 00:44:10,720 --> 00:44:16,080 And so the bond order here was 1, the bond order here was 2. 755 00:44:16,080 --> 00:44:19,000 Which is more stable? 756 00:44:19,000 --> 00:44:22,496 Higher dissociation energy, which one do you think? 757 00:44:22,496 --> 00:44:23,412 AUDIENCE: [INAUDIBLE]. 758 00:44:23,412 --> 00:44:24,680 CATHERINE DRENNAN: Carbon. 759 00:44:24,680 --> 00:44:25,310 Right. 760 00:44:25,310 --> 00:44:27,100 Has a bond order of two. 761 00:44:27,100 --> 00:44:31,150 It has more electrons in lower energy orbitals. 762 00:44:31,150 --> 00:44:35,000 So it cannot really well out of this bonding deal, 763 00:44:35,000 --> 00:44:43,350 and the dissociation energy for B2, 289, whereas, for C2, 599. 764 00:44:43,350 --> 00:44:49,000 So when molecules come together such that more of the electrons 765 00:44:49,000 --> 00:44:52,270 are in lower energy or bonding orbitals, 766 00:44:52,270 --> 00:44:54,630 you form a nice, stable molecule. 767 00:44:54,630 --> 00:44:57,950 When molecules come together such that more 768 00:44:57,950 --> 00:45:01,750 of their electrons are an antibonding or higher energy, 769 00:45:01,750 --> 00:45:03,660 that's not a happy molecule. 770 00:45:03,660 --> 00:45:06,840 So I'll just and with one way to think about this. 771 00:45:06,840 --> 00:45:09,990 In this cartoon molecular, break up lines, 772 00:45:09,990 --> 00:45:14,950 sometimes two atoms just have an incompatible number 773 00:45:14,950 --> 00:45:16,880 of valence electrons. 774 00:45:16,880 --> 00:45:19,960 And there are just too many-- just here this molecule saying, 775 00:45:19,960 --> 00:45:20,830 I'm sorry. 776 00:45:20,830 --> 00:45:24,560 Too many of your electrons are in my antibonding regions. 777 00:45:24,560 --> 00:45:27,050 I don't know how many times we've all heard that, 778 00:45:27,050 --> 00:45:32,610 but it's time to dissociate, but our atomic orbitals, well, they 779 00:45:32,610 --> 00:45:34,360 can still be friends. 780 00:45:34,360 --> 00:45:34,870 OK. 781 00:45:34,870 --> 00:45:36,960 See you on Wednesday. 782 00:45:36,960 --> 00:45:38,550 Take a look at the clicker question. 783 00:45:59,350 --> 00:45:59,850 All right. 784 00:45:59,850 --> 00:46:02,130 Let's just take 10 more seconds. 785 00:46:23,420 --> 00:46:23,920 All right. 786 00:46:23,920 --> 00:46:25,410 Let's just go through this one. 787 00:46:25,410 --> 00:46:27,683 So this is a review of where we were last time. 788 00:46:31,990 --> 00:46:35,600 So the correct answer is 1. 789 00:46:35,600 --> 00:46:43,250 So sigma orbitals are cylindrically symmetrical. 790 00:46:43,250 --> 00:46:45,190 Let's quiet down a minute. 791 00:46:45,190 --> 00:46:47,610 You can hear the answer. 792 00:46:47,610 --> 00:46:50,240 So this one is true. 793 00:46:50,240 --> 00:46:52,300 The second one is not true. 794 00:46:52,300 --> 00:46:55,140 A bond order of zero doesn't mean that you just 795 00:46:55,140 --> 00:46:56,810 have antibonding orbitals. 796 00:46:56,810 --> 00:46:59,640 Whenever you bring together two atomic orbitals, 797 00:46:59,640 --> 00:47:02,190 you have to make two molecular orbitals. 798 00:47:02,190 --> 00:47:04,990 So it isn't that sometimes you make bonding orbitals 799 00:47:04,990 --> 00:47:07,360 and sometimes you make antibonding orbitals. 800 00:47:07,360 --> 00:47:10,140 Every time you bring together two atomic orbitals, 801 00:47:10,140 --> 00:47:14,346 you make two molecular orbitals, one that's lower in energy, 802 00:47:14,346 --> 00:47:15,970 and that's the bonding orbital, and one 803 00:47:15,970 --> 00:47:20,300 that's higher in energy, and that's the antibonding orbital. 804 00:47:20,300 --> 00:47:21,790 So that is not what that means. 805 00:47:21,790 --> 00:47:23,590 A bond order of zero means that you 806 00:47:23,590 --> 00:47:27,260 have equal numbers of electrons in your bonding and antibonding 807 00:47:27,260 --> 00:47:28,360 orbitals. 808 00:47:28,360 --> 00:47:32,400 So there's no net stabilization due to the formation 809 00:47:32,400 --> 00:47:35,210 of these bonds. 810 00:47:35,210 --> 00:47:38,340 So here bonding occurs when you bring together 811 00:47:38,340 --> 00:47:41,690 two atomic orbitals to make two molecular orbitals that 812 00:47:41,690 --> 00:47:43,120 are both of lower energy. 813 00:47:43,120 --> 00:47:43,720 No. 814 00:47:43,720 --> 00:47:47,630 Every time you make the two orbitals, one is lower energy, 815 00:47:47,630 --> 00:47:48,790 one is higher that energy. 816 00:47:48,790 --> 00:47:51,370 You can't make two that are both lower in energy. 817 00:47:51,370 --> 00:47:54,000 And bond order of 1 means constructive interference 818 00:47:54,000 --> 00:47:58,370 is generated at one bonding orbital. 819 00:47:58,370 --> 00:48:00,460 That's not what a bond order of 1 is. 820 00:48:00,460 --> 00:48:02,740 And again, every time you generate a bonding orbital, 821 00:48:02,740 --> 00:48:04,780 you generate an antibonding orbital. 822 00:48:04,780 --> 00:48:10,360 And 1 means that you have twice as many electrons 823 00:48:10,360 --> 00:48:12,790 in your bonding orbitals as antibonding orbitals 824 00:48:12,790 --> 00:48:15,700 because the formula is 1/2 the number of bonding 825 00:48:15,700 --> 00:48:17,620 minus antibonding. 826 00:48:17,620 --> 00:48:20,360 But that's good, and it's important to remember 827 00:48:20,360 --> 00:48:25,640 that sigma orbitals are symmetric around the bond axis. 828 00:48:25,640 --> 00:48:26,140 All right. 829 00:48:26,140 --> 00:48:29,830 So we had these diagrams for boron and carbon, 830 00:48:29,830 --> 00:48:37,400 just talking about the interactions of the px and py, 831 00:48:37,400 --> 00:48:40,350 and so we had forgotten about our pz. 832 00:48:40,350 --> 00:48:41,810 And you can't do that on a test. 833 00:48:41,810 --> 00:48:44,350 You get into trouble, so I'm always 834 00:48:44,350 --> 00:48:47,240 telling people for these two handouts, 835 00:48:47,240 --> 00:48:49,360 you must include the molecular orbitals that 836 00:48:49,360 --> 00:48:51,640 are derived from p to z. 837 00:48:51,640 --> 00:48:54,120 So on a test, you need to put them even if they're empty. 838 00:48:54,120 --> 00:48:56,160 Even if they don't have anything in them, 839 00:48:56,160 --> 00:48:58,659 they need to be part of your molecular orbital diagram. 840 00:48:58,659 --> 00:49:00,075 We didn't have them in the diagram 841 00:49:00,075 --> 00:49:01,900 because we hadn't talked about them yet, 842 00:49:01,900 --> 00:49:04,100 so now we're going to talk about them. 843 00:49:04,100 --> 00:49:09,690 So two pz orbitals, again, this is on Monday's handout. 844 00:49:09,690 --> 00:49:14,270 You have this linear combination of atomic orbitals. 845 00:49:14,270 --> 00:49:15,850 And all are p orbitals. 846 00:49:15,850 --> 00:49:17,760 They all look the same as each other, 847 00:49:17,760 --> 00:49:19,470 they're just different in orientation. 848 00:49:19,470 --> 00:49:22,860 You have one along x, one along y, one along z, 849 00:49:22,860 --> 00:49:24,200 but they're the same. 850 00:49:24,200 --> 00:49:30,150 So now we're going to bring our two pz orbitals together, 851 00:49:30,150 --> 00:49:32,320 and we're going to do it along the bonding axis. 852 00:49:32,320 --> 00:49:35,790 So we've defined this as the bonding axis in the class, 853 00:49:35,790 --> 00:49:38,620 so we'll bring them together, and they'll 854 00:49:38,620 --> 00:49:42,675 be constructive interference with our bonding orbitals. 855 00:49:42,675 --> 00:49:44,550 There's always constructive interference that 856 00:49:44,550 --> 00:49:46,650 generates bonding orbitals. 857 00:49:46,650 --> 00:49:53,730 And so we're going to create a enhanced amplitude as the wave 858 00:49:53,730 --> 00:49:55,730 functions come together, and it's 859 00:49:55,730 --> 00:49:59,120 going to be cylindrically symmetric. 860 00:49:59,120 --> 00:50:02,190 So what type of orbital do you think this is going to be, 861 00:50:02,190 --> 00:50:03,175 sigma or pi? 862 00:50:03,175 --> 00:50:04,030 AUDIENCE: Sigma. 863 00:50:04,030 --> 00:50:06,530 CATHERINE DRENNAN: It'll be sigma 864 00:50:06,530 --> 00:50:09,380 because it's cylindrically symmetric. 865 00:50:09,380 --> 00:50:14,440 So we do not have any bonding plane along the bond axis, 866 00:50:14,440 --> 00:50:16,730 and it's symmetric around. 867 00:50:16,730 --> 00:50:20,530 And we have enhanced probability density, 868 00:50:20,530 --> 00:50:23,590 and we have the wave function squared 869 00:50:23,590 --> 00:50:26,590 enhanced probability of having an electron between the two 870 00:50:26,590 --> 00:50:27,700 nuclei. 871 00:50:27,700 --> 00:50:31,730 And so this is a sigma 2pz. 872 00:50:31,730 --> 00:50:37,100 So p orbitals can form sigma molecular orbitals. 873 00:50:37,100 --> 00:50:41,120 So we do have nodes passing through our nuclei. 874 00:50:41,120 --> 00:50:42,680 Here are our nuclei again. 875 00:50:42,680 --> 00:50:43,520 We do have them. 876 00:50:43,520 --> 00:50:45,900 They were here before in our p orbitals. 877 00:50:45,900 --> 00:50:51,240 There's the nodal plane in our p orbitals, but we do not have, 878 00:50:51,240 --> 00:50:56,220 in this case, a node along the bond axis. 879 00:50:56,220 --> 00:50:58,910 So that is our bonding. 880 00:50:58,910 --> 00:51:02,720 So whenever you generate a bonding orbital, which 881 00:51:02,720 --> 00:51:06,520 is going to be lower energy, we're 882 00:51:06,520 --> 00:51:09,780 going to have our increased amplitude between the nuclei, 883 00:51:09,780 --> 00:51:13,430 again, our increased probability density and therefore, 884 00:51:13,430 --> 00:51:15,100 lower energy. 885 00:51:15,100 --> 00:51:17,310 So whenever you have constructive interference 886 00:51:17,310 --> 00:51:21,180 generating a molecular orbital of lower energy, 887 00:51:21,180 --> 00:51:23,260 you got to create something of higher energy. 888 00:51:23,260 --> 00:51:25,140 That's just how life works. 889 00:51:25,140 --> 00:51:28,520 So we also are going to have antibonding 890 00:51:28,520 --> 00:51:31,814 orbitals, which are generated by destructive interference. 891 00:51:31,814 --> 00:51:33,480 And again, these orbitals can be thought 892 00:51:33,480 --> 00:51:35,890 about as wave functions, and a property of waves 893 00:51:35,890 --> 00:51:39,370 is that they constructively interfere and destructively 894 00:51:39,370 --> 00:51:40,330 interfere. 895 00:51:40,330 --> 00:51:45,040 So now we can subtract our two orbitals, 896 00:51:45,040 --> 00:51:48,010 which we're going to switch the sign 897 00:51:48,010 --> 00:51:50,410 and they're going to be out of phase. 898 00:51:50,410 --> 00:51:53,780 So they'll destructively interfere, 899 00:51:53,780 --> 00:51:56,560 and that's going to look like this. 900 00:51:56,560 --> 00:52:00,460 So now, you're going to generate a nodal plane between the two 901 00:52:00,460 --> 00:52:04,890 nuclei, but it's still symmetric around the bond axis. 902 00:52:04,890 --> 00:52:12,270 So this is a sigma 2pz star, so it's an antibonding orbital. 903 00:52:12,270 --> 00:52:14,960 So again, it's sigma, so it's still 904 00:52:14,960 --> 00:52:19,750 cylindrically symmetrical with no nodal plane along that bond 905 00:52:19,750 --> 00:52:25,210 axis, but you do have a new nodal plane that's generated. 906 00:52:25,210 --> 00:52:28,400 So nodes pass, again, through the nuclei, 907 00:52:28,400 --> 00:52:31,970 but also now between these two orbitals. 908 00:52:31,970 --> 00:52:33,600 So we have a new nodal plane that's 909 00:52:33,600 --> 00:52:37,490 generated that's between these nuclei, 910 00:52:37,490 --> 00:52:41,160 and that's a result of destructive interference. 911 00:52:41,160 --> 00:52:42,980 Generates that nodal plane. 912 00:52:42,980 --> 00:52:46,310 You have decreased probability density 913 00:52:46,310 --> 00:52:50,040 for an electron being found there. 914 00:52:50,040 --> 00:52:53,880 And so that poor electron is shut out of that sweet spot. 915 00:52:53,880 --> 00:52:56,800 The electrons like to be between those two nuclei 916 00:52:56,800 --> 00:53:00,800 where they have the two positive charges of the nuclei and then 917 00:53:00,800 --> 00:53:03,600 their little negative charge, and they can sit right there 918 00:53:03,600 --> 00:53:06,530 and be very happy in a low-energy state. 919 00:53:06,530 --> 00:53:09,940 But here there's really lower probability density, 920 00:53:09,940 --> 00:53:12,840 lower likelihood the electron will be found here, 921 00:53:12,840 --> 00:53:14,730 and that generates a molecular orbital 922 00:53:14,730 --> 00:53:18,370 that's antibonding or higher in energy. 923 00:53:18,370 --> 00:53:18,870 All right. 924 00:53:18,870 --> 00:53:21,400 So now, we have to go back to our MO diagrams 925 00:53:21,400 --> 00:53:25,050 and figure out where to put these new molecular orbitals 926 00:53:25,050 --> 00:53:27,550 onto our nice diagrams. 927 00:53:27,550 --> 00:53:32,440 And it's not as simple as it was before because where 928 00:53:32,440 --> 00:53:37,630 we put these new sigma 2pz molecular orbitals depends 929 00:53:37,630 --> 00:53:40,100 on what z is. 930 00:53:40,100 --> 00:53:44,800 So it depends on the value of z. 931 00:53:44,800 --> 00:53:49,840 So if z is less than the magic number of 8, 932 00:53:49,840 --> 00:53:57,570 then we have our pi 2px and 2py orbitals are lower in energy 933 00:53:57,570 --> 00:54:02,980 than our sigma 2pz molecular orbital. 934 00:54:02,980 --> 00:54:09,250 But if we are equal to or greater than 8, 935 00:54:09,250 --> 00:54:14,810 then the sigma 2pz orbital is lower energy 936 00:54:14,810 --> 00:54:19,080 than the pi 2px and 2py. 937 00:54:19,080 --> 00:54:22,780 So less than 8, pi is first. 938 00:54:22,780 --> 00:54:27,560 It's lower in energy as you go up your energy scale. 939 00:54:27,560 --> 00:54:32,710 And if z is equal to or greater than 8, pi is second 940 00:54:32,710 --> 00:54:35,530 and sigma is first. 941 00:54:35,530 --> 00:54:37,390 So how are you going to remember this? 942 00:54:37,390 --> 00:54:39,730 There could be many different ways one can remember it, 943 00:54:39,730 --> 00:54:41,770 but I'll tell you how I remember it. 944 00:54:41,770 --> 00:54:47,780 And my life revolves around my daughter and my dog. 945 00:54:47,780 --> 00:54:51,260 And so at Thanksgiving, we always have the question, 946 00:54:51,260 --> 00:54:53,980 can I eat pie first? 947 00:54:53,980 --> 00:54:58,430 So if you are under the age of 8, 948 00:54:58,430 --> 00:55:02,530 you always want your pie first. 949 00:55:02,530 --> 00:55:08,120 So if z is less than 8, pi comes first. 950 00:55:08,120 --> 00:55:11,920 Pi is lower in energy and sigma is higher. 951 00:55:11,920 --> 00:55:15,670 However, when you mature to the grand age of 9, 952 00:55:15,670 --> 00:55:19,280 say, or 10, if you were a kid, 10 953 00:55:19,280 --> 00:55:21,090 is like the oldest you can possibly 954 00:55:21,090 --> 00:55:23,480 imagine being, very mature. 955 00:55:23,480 --> 00:55:25,230 And you can eat your Thanksgiving dinner 956 00:55:25,230 --> 00:55:26,700 and wait for pie. 957 00:55:26,700 --> 00:55:29,920 So that is how I would remember it, 958 00:55:29,920 --> 00:55:34,230 under 8 pi is first, equal to 8 or greater, 959 00:55:34,230 --> 00:55:36,650 you can wait till after dinner to have your pie, 960 00:55:36,650 --> 00:55:38,710 pi comes second. 961 00:55:38,710 --> 00:55:42,010 Note that the ordering of the antibonding orbitals 962 00:55:42,010 --> 00:55:45,440 is the same, so all you have to remember 963 00:55:45,440 --> 00:55:53,420 is down here depends on z, is pi first or is pi second? 964 00:55:53,420 --> 00:55:56,020 So let's take a look at an example. 965 00:55:56,020 --> 00:55:59,090 Let's look at our friend molecular oxygen that has a z 966 00:55:59,090 --> 00:56:00,650 equal to 8. 967 00:56:00,650 --> 00:56:05,310 So oxygen is at the old, mature age of 8, 968 00:56:05,310 --> 00:56:08,710 and so it's going to have its sigma 2pz first. 969 00:56:08,710 --> 00:56:12,520 It can wait for its pi orbitals until later. 970 00:56:12,520 --> 00:56:15,130 So let's start putting in our electrons. 971 00:56:15,130 --> 00:56:20,830 So we have each oxygen making up molecular oxygen, or O2. 972 00:56:20,830 --> 00:56:26,570 Brings two 2s orbitals to the Thanksgiving dinner table, 973 00:56:26,570 --> 00:56:29,350 and two of them go down in energy 974 00:56:29,350 --> 00:56:33,280 into the bonding sigma 2s orbital and two 975 00:56:33,280 --> 00:56:38,750 go into our antibonding, sigma star 2s orbital. 976 00:56:38,750 --> 00:56:44,940 Now, we have four electrons in our atomic pz 977 00:56:44,940 --> 00:56:47,450 orbitals, four from each molecule, 978 00:56:47,450 --> 00:56:50,010 so we need to put all of those in. 979 00:56:50,010 --> 00:56:53,080 So we always start with the lowest energy orbital. 980 00:56:53,080 --> 00:56:55,980 So we'll put two in there, then we'll go up. 981 00:56:55,980 --> 00:56:58,590 We have two more here, two more here. 982 00:56:58,590 --> 00:57:02,050 We'll put them in singly with their spins parallel, 983 00:57:02,050 --> 00:57:05,240 and then we'll pair them up in the lowest energy orbitals. 984 00:57:05,240 --> 00:57:08,080 And then we have two more left, so we're 985 00:57:08,080 --> 00:57:11,200 going to have to put those up in our antibonding orbitals. 986 00:57:11,200 --> 00:57:18,570 So they go into pi 2px and pi 2py star orbitals up here. 987 00:57:18,570 --> 00:57:19,090 All right. 988 00:57:19,090 --> 00:57:23,260 So now we can calculate the bond order for oxygen, 989 00:57:23,260 --> 00:57:24,530 and that's a clicker question. 990 00:57:52,920 --> 00:57:53,420 All right. 991 00:57:53,420 --> 00:57:55,070 Let's just take 10 more seconds. 992 00:58:10,940 --> 00:58:12,360 All right. 993 00:58:12,360 --> 00:58:15,000 So let's take a look over here. 994 00:58:15,000 --> 00:58:19,120 So bond order, again, is 1/2 the number 995 00:58:19,120 --> 00:58:23,480 of bonding electrons minus the number of antibonding 996 00:58:23,480 --> 00:58:25,250 electrons. 997 00:58:25,250 --> 00:58:30,280 And we have eight bonding-- 1, 2, 3, 4, 5, 6, 7, 8. 998 00:58:30,280 --> 00:58:33,870 And we have four antibonding-- 1, 2, 3, 4. 999 00:58:33,870 --> 00:58:36,830 So that gives us a bond order of 2. 1000 00:58:36,830 --> 00:58:38,452 And the bond order equation is one 1001 00:58:38,452 --> 00:58:39,660 that you do have to memorize. 1002 00:58:39,660 --> 00:58:42,890 That will not be given to you on an exam. 1003 00:58:42,890 --> 00:58:47,670 And with a bond order of 2, we have a pretty big number 1004 00:58:47,670 --> 00:58:49,390 for dissociation energy. 1005 00:58:49,390 --> 00:58:52,350 Again, that's energy you have to put into a bond to break it, 1006 00:58:52,350 --> 00:58:56,160 to dissociate it, and that means it's a pretty strong bond 1007 00:58:56,160 --> 00:58:57,290 if it's a big number. 1008 00:58:57,290 --> 00:59:00,580 If you need a lot of energy, that's a strong bond. 1009 00:59:00,580 --> 00:59:03,880 Another thing that you can see from this diagram 1010 00:59:03,880 --> 00:59:07,080 is that O2 is a biradical. 1011 00:59:07,080 --> 00:59:15,390 It has two lone pair electrons, so two unpaired electrons, 1012 00:59:15,390 --> 00:59:18,770 which also makes it paramagnetic, 1013 00:59:18,770 --> 00:59:21,240 or attracted to a magnetic field. 1014 00:59:21,240 --> 00:59:23,640 So whenever you have unpaired electrons, 1015 00:59:23,640 --> 00:59:26,050 you will have a paramagnetic species, 1016 00:59:26,050 --> 00:59:28,230 and diamagnetic means they're all paired. 1017 00:59:28,230 --> 00:59:31,200 And so there are some questions on problem sets and on exams, 1018 00:59:31,200 --> 00:59:33,490 so you need to know the definitions of those. 1019 00:59:33,490 --> 00:59:34,270 All right. 1020 00:59:34,270 --> 00:59:37,050 So we talked about this when we were doing Lewis structures, 1021 00:59:37,050 --> 00:59:38,630 if you recall. 1022 00:59:38,630 --> 00:59:42,700 And we drew a beautiful Lewis structure of molecular oxygen 1023 00:59:42,700 --> 00:59:46,950 that had two lone pairs on each oxygen and a double bond. 1024 00:59:46,950 --> 00:59:49,330 But I told you that that was not really 1025 00:59:49,330 --> 00:59:53,410 a complete description of molecular oxygen, 1026 00:59:53,410 --> 00:59:56,810 that molecular oxygen was actually a biradical, 1027 00:59:56,810 --> 01:00:00,360 but you would not get a hint of that from the Lewis structure. 1028 01:00:00,360 --> 01:00:05,030 So if you draw the Lewis structure as a biradical, 1029 01:00:05,030 --> 01:00:07,940 then you have a single electron here 1030 01:00:07,940 --> 01:00:10,830 and a single electron there and a single bond. 1031 01:00:10,830 --> 01:00:13,300 But we also see the bond orders 2, 1032 01:00:13,300 --> 01:00:16,930 so this one describes the biradical nature, 1033 01:00:16,930 --> 01:00:19,300 but doesn't really describe that double bond 1034 01:00:19,300 --> 01:00:20,860 character that it has. 1035 01:00:20,860 --> 01:00:24,100 So neither of these Lewis structures really completely 1036 01:00:24,100 --> 01:00:28,460 describe molecular oxygen. And we 1037 01:00:28,460 --> 01:00:32,020 need our molecular orbital diagram to really help 1038 01:00:32,020 --> 01:00:36,080 us understand the properties of molecular oxygen, 1039 01:00:36,080 --> 01:00:38,330 that it's pretty strong bond between it, 1040 01:00:38,330 --> 01:00:42,920 it has double bond character, but it also is very reactive. 1041 01:00:42,920 --> 01:00:44,270 It's a biradical. 1042 01:00:44,270 --> 01:00:46,710 So this is just a bizarre molecule. 1043 01:00:46,710 --> 01:00:51,000 And really that is why this diagram right here really tells 1044 01:00:51,000 --> 01:00:55,120 us why our life, our planet is what it is, 1045 01:00:55,120 --> 01:00:57,720 right here, that describes it. 1046 01:00:57,720 --> 01:01:00,230 It's because of oxygen that we have 1047 01:01:00,230 --> 01:01:01,920 the life forms that we did. 1048 01:01:01,920 --> 01:01:03,960 Life was very different on this planet 1049 01:01:03,960 --> 01:01:07,300 before molecular oxygen came about. 1050 01:01:07,300 --> 01:01:12,010 You did have microbes that lived anaerobically without oxygen. 1051 01:01:12,010 --> 01:01:15,040 But when oxygen came, everything changed. 1052 01:01:15,040 --> 01:01:19,900 And so if I say, can you explain life to me? 1053 01:01:19,900 --> 01:01:22,670 You can draw this, and there it is. 1054 01:01:22,670 --> 01:01:25,680 This explains life as we know it because life 1055 01:01:25,680 --> 01:01:30,980 as we know it exists because of this crazy molecule that is O2, 1056 01:01:30,980 --> 01:01:32,680 nothing else really like it. 1057 01:01:32,680 --> 01:01:36,760 It is an amazing molecule that allows us to live. 1058 01:01:36,760 --> 01:01:37,805 So there you go. 1059 01:01:37,805 --> 01:01:40,180 I was going to say you don't learn anything in chemistry. 1060 01:01:40,180 --> 01:01:42,510 This diagram I just explains life 1061 01:01:42,510 --> 01:01:45,160 as we know it to you, right there. 1062 01:01:45,160 --> 01:01:47,450 All right. 1063 01:01:47,450 --> 01:01:50,060 It's not just oxygen, there's a few other elements that, yeah, 1064 01:01:50,060 --> 01:01:51,601 are pretty important, and one of them 1065 01:01:51,601 --> 01:01:54,400 is nitrogen. We wouldn't really be much anywhere 1066 01:01:54,400 --> 01:01:55,960 without nitrogen either. 1067 01:01:55,960 --> 01:01:59,920 Oxygen is, no, nitrogen is pretty special too. 1068 01:01:59,920 --> 01:02:01,120 This also helps. 1069 01:02:01,120 --> 01:02:02,870 Maybe these two molecular orbital 1070 01:02:02,870 --> 01:02:05,450 diagrams really sum up life as we know it. 1071 01:02:05,450 --> 01:02:05,950 All right. 1072 01:02:05,950 --> 01:02:10,280 So let's look at molecular nitrogen, N2. 1073 01:02:10,280 --> 01:02:14,750 So we have two electrons in our 2s orbitals, 1074 01:02:14,750 --> 01:02:16,610 so we're going to bring them together. 1075 01:02:16,610 --> 01:02:20,050 We're going to put two in the lower energy orbital, our sigma 1076 01:02:20,050 --> 01:02:23,820 2s, and two in our antibonding orbital. 1077 01:02:23,820 --> 01:02:26,580 And then we have three in our p orbitals 1078 01:02:26,580 --> 01:02:30,660 from this nitrogen, three electrons from this nitrogen, 1079 01:02:30,660 --> 01:02:32,890 and so we'll put them down here. 1080 01:02:32,890 --> 01:02:36,510 We'll put in 2, 3, 4, 5, 6. 1081 01:02:36,510 --> 01:02:40,040 So we didn't need to use any of these antibonding orbitals, 1082 01:02:40,040 --> 01:02:43,190 and this is a z less than 8 case. 1083 01:02:43,190 --> 01:02:45,900 So here we have our pi orbitals first 1084 01:02:45,900 --> 01:02:50,520 because it is z less than 8. 1085 01:02:50,520 --> 01:02:53,760 So let's look at the bond order here. 1086 01:02:53,760 --> 01:02:59,735 And the bond order is 1/2 of 8-- 1, 2, 3, 4, 5, 6, 7, 1087 01:02:59,735 --> 01:03:03,720 8-- eight bonding electrons and just 1088 01:03:03,720 --> 01:03:09,930 these two antibonding electrons, so 1/2 of 8 minus 2 is 3. 1089 01:03:09,930 --> 01:03:13,740 And you have a really big number for your dissociation energy, 1090 01:03:13,740 --> 01:03:15,680 941. 1091 01:03:15,680 --> 01:03:18,300 This is a very stable molecule, and you 1092 01:03:18,300 --> 01:03:22,900 can draw the Lewis structure of this without much difficulty. 1093 01:03:22,900 --> 01:03:26,330 This one works quite well, and you get a triple bond 1094 01:03:26,330 --> 01:03:28,530 and two lone pairs. 1095 01:03:28,530 --> 01:03:30,780 So this would be a diamagnetic molecule, 1096 01:03:30,780 --> 01:03:35,300 no unpaired electrons, no radicals here. 1097 01:03:35,300 --> 01:03:38,740 But this is a crazy, strong bond. 1098 01:03:38,740 --> 01:03:42,530 It's really hard to split nitrogen 1099 01:03:42,530 --> 01:03:44,500 because of this triple bond. 1100 01:03:44,500 --> 01:03:47,190 And molecular orbital theory tells you 1101 01:03:47,190 --> 01:03:48,770 it should be its triple bond. 1102 01:03:48,770 --> 01:03:52,440 It should be really, really strong interactions 1103 01:03:52,440 --> 01:03:53,816 between these nitrogens. 1104 01:03:53,816 --> 01:03:55,190 And so this is a very hard thing. 1105 01:03:55,190 --> 01:03:56,856 We want to do is industrially, and we'll 1106 01:03:56,856 --> 01:03:59,480 talk more about this when we get a chemical equilibrium. 1107 01:03:59,480 --> 01:04:02,110 How do you split the nitrogen bond. 1108 01:04:02,110 --> 01:04:06,060 This is actually, currently, a big area of research, 1109 01:04:06,060 --> 01:04:09,036 how you break that bond because we need nitrogen for life. 1110 01:04:09,036 --> 01:04:10,160 And so how do you split it? 1111 01:04:10,160 --> 01:04:12,840 There's lots of nitrogen N2 in the atmosphere, 1112 01:04:12,840 --> 01:04:16,010 but we need it here, and we need it usable, 1113 01:04:16,010 --> 01:04:18,580 so we need to break that bond to use it. 1114 01:04:18,580 --> 01:04:20,670 So we'll come back to this in chemical equilibrium 1115 01:04:20,670 --> 01:04:23,920 and how people are able to split the nitrogen bond. 1116 01:04:23,920 --> 01:04:25,420 So forget man of steel. 1117 01:04:25,420 --> 01:04:28,020 We should have man of nitrogen. That's strong. 1118 01:04:28,020 --> 01:04:29,170 Nitrogen is strong. 1119 01:04:29,170 --> 01:04:30,560 Forget steel. 1120 01:04:30,560 --> 01:04:35,450 Man of nitrogen. 1121 01:04:35,450 --> 01:04:39,600 One more thing to do before we move on to today's handout 1122 01:04:39,600 --> 01:04:42,350 and this is really fast, you can also 1123 01:04:42,350 --> 01:04:45,380 be asked to draw molecular orbital diagrams where 1124 01:04:45,380 --> 01:04:48,650 both atoms are not the same. 1125 01:04:48,650 --> 01:04:51,600 So if you were asked to do that, you 1126 01:04:51,600 --> 01:04:54,450 can use the following rules. 1127 01:04:54,450 --> 01:05:01,230 If z is less than 8 for both atoms, pi is first. 1128 01:05:01,230 --> 01:05:07,840 If z is not less than 8 for both atoms, 1129 01:05:07,840 --> 01:05:09,770 it's hard to know what to do, so you 1130 01:05:09,770 --> 01:05:12,000 don't need to know what to do. 1131 01:05:12,000 --> 01:05:15,230 And that's it. 1132 01:05:15,230 --> 01:05:17,240 So we might tell you something about it 1133 01:05:17,240 --> 01:05:20,340 and then you can do it, but otherwise, just 1134 01:05:20,340 --> 01:05:23,240 worry about things when z is less than 8. 1135 01:05:23,240 --> 01:05:26,150 So that's molecular orbital theory.