WEBVTT 00:02.290 --> 00:04.310 Prof: Okay, let's get started. 00:04.310 --> 00:08.640 The stuff we're doing these few days are really the focus of the 00:08.637 --> 00:10.627 first half of the semester. 00:10.630 --> 00:14.360 So pay attention and think about it. 00:14.360 --> 00:20.580 Okay, so the topics today are Overlap and Energy-Match, 00:20.581 --> 00:25.421 as determinants of how strong bonds are. 00:25.420 --> 00:28.100 So we'll start with overlap. 00:28.100 --> 00:32.860 We saw last time that overlap is what creates the difference 00:32.862 --> 00:35.942 density, what focuses some small amount 00:35.937 --> 00:40.237 of the electron density between the atoms and serves to hold 00:40.240 --> 00:41.480 them together. 00:41.480 --> 00:46.980 The overlap integral is the total amount of that product of 00:46.981 --> 00:47.931 A and B. 00:47.930 --> 00:52.630 Remember, you square (A+B) and you get A^2 00:52.630 --> 00:54.290 + B^2 + 2AB. 00:54.290 --> 00:56.470 That 2AB term is the overlap. 00:56.470 --> 01:00.820 It's called overlap because it has values when both functions 01:00.820 --> 01:04.740 have appreciable magnitude, at the same point in space; 01:04.736 --> 01:05.966 they overlap. 01:05.968 --> 01:08.988 And summing that over all space, or integrating it, 01:08.986 --> 01:11.576 gives what's called the overlap integral. 01:11.579 --> 01:13.829 It'll depend on the distance. 01:13.828 --> 01:15.788 Obviously if they're very far apart, 01:15.790 --> 01:18.930 they don't give simultaneous values to the same point in 01:18.926 --> 01:20.986 space, because it's far from either 01:20.994 --> 01:23.614 one or the other, or from both. 01:23.610 --> 01:24.980 So it depends on distance. 01:24.980 --> 01:27.390 It also depends on hybridization, 01:27.391 --> 01:31.161 and that's what we're going to talk about first. 01:31.159 --> 01:34.079 Okay, first let's just look for scale. 01:34.080 --> 01:38.040 Here are the 2s orbitals of carbon atom, 01:38.037 --> 01:41.477 and you can work out, with your formulas, 01:41.479 --> 01:46.299 that the diameter of the spherical node is 0.7 angstroms. 01:46.297 --> 01:47.327 Right? 01:47.330 --> 01:51.080 That means we have a distance scale here. 01:51.080 --> 01:56.330 Now, the distance between two carbons is roughly 1.4,1.5, 01:56.333 --> 02:01.773 when they're forming a bond from one another -- between one 02:01.774 --> 02:02.904 another. 02:02.900 --> 02:03.690 Okay. 02:03.688 --> 02:07.268 So that means we can use that 0.7 angstrom scale to see how 02:07.271 --> 02:10.731 far we have to slide these together, in order to get them 02:10.729 --> 02:12.149 to bonded distance. 02:12.150 --> 02:15.180 If we superimposed the X's -- remember those diameters are 02:15.179 --> 02:18.109 each 0.7 -- so if we slide them together 02:18.110 --> 02:23.960 until we superimpose the X's, then they're 1.4 angstroms 02:23.961 --> 02:24.871 apart. 02:24.870 --> 02:28.160 So that's about the distance that these two orbitals are, 02:28.157 --> 02:31.147 in the proper scale, when they're in a carbon-carbon 02:31.151 --> 02:31.681 bond. 02:31.680 --> 02:39.200 Now, how big is the overlap integral, the sum of the product 02:39.199 --> 02:43.149 of A times B, over all space? 02:43.150 --> 02:46.910 Now I want you to guess, guess how big that integral is. 02:46.910 --> 02:48.540 And we have a hint. 02:48.538 --> 02:53.828 What would the overlap integral be if we moved them until they 02:53.825 --> 02:57.115 superimposed on one another exactly? 02:57.120 --> 03:00.440 That's the maximum we could get, if the distance were zero. 03:00.438 --> 03:04.268 So if pulled them all together, then A and B would be measured 03:04.266 --> 03:05.706 from the same center. 03:05.710 --> 03:07.600 So it would be the same thing as A^2. 03:07.599 --> 03:09.039 Okay? 03:09.038 --> 03:14.048 So what would the integral of A^2^( )be, over all space? 03:14.050 --> 03:15.130 Student: One. 03:15.128 --> 03:17.798 Prof: One; that's normalization. 03:17.800 --> 03:21.370 Okay, so the maximum value you can get when they're right on 03:21.366 --> 03:24.746 top of one another -- negatives multiply negatives to get 03:24.752 --> 03:26.472 positive; positive areas, 03:26.468 --> 03:29.008 multiply positive areas to get positive. 03:29.008 --> 03:31.518 Everything is optimum, is going to be one. 03:31.520 --> 03:34.230 Now I want somebody to give me an idea, a guess, 03:34.228 --> 03:37.048 of how big it's going to be here, or at least some 03:37.051 --> 03:39.531 considerations that would go into that. 03:39.530 --> 03:41.940 The maximum value you can get is one. 03:41.940 --> 03:44.520 How big do you think it would be here? 03:44.520 --> 03:49.850 What's something that would hurt it; 03:49.848 --> 03:51.588 that is, make it less than one? 03:51.592 --> 03:52.102 Russell? 03:52.098 --> 03:53.868 Student: When there's very little overlap on the 03:53.872 --> 03:54.422 opposite sides. 03:54.419 --> 03:57.089 Prof: Yeah, out beyond the red areas, 03:57.092 --> 03:59.642 there's very little overlap altogether. 03:59.639 --> 04:02.859 So you lose whatever overlap you'd get from there, 04:02.855 --> 04:04.755 in doing the normalization. 04:04.758 --> 04:07.058 Now, in the middle, right in the middle, 04:07.061 --> 04:08.891 you have blue on top of blue. 04:08.889 --> 04:10.419 That's good. 04:10.419 --> 04:13.909 But notice there's also a node that's going to interfere with 04:13.914 --> 04:16.424 some of the wave functions' overlapping, 04:16.420 --> 04:19.850 and there's going to be a little bit of blue on top of 04:19.851 --> 04:20.241 red. 04:20.240 --> 04:22.180 Everybody got that? 04:22.180 --> 04:24.760 So I just want people to guess. 04:24.759 --> 04:25.969 Okay, I know what I'll do. 04:25.970 --> 04:27.350 We'll do a poll. 04:27.350 --> 04:30.260 This is a democracy after all; we're about to get into 04:30.257 --> 04:30.807 November. 04:30.810 --> 04:34.670 So I'm going to start with 0.1, as what you think it would be. 04:34.673 --> 04:35.183 Right? 04:35.180 --> 04:36.730 The maximum, if you put them right on top of 04:36.733 --> 04:37.533 one another, is one. 04:37.529 --> 04:41.009 So I'm going to start with 0.1, and move up and see hands. 04:41.009 --> 04:43.499 Okay, how many people think it's 0.1? 04:43.500 --> 04:46.070 0.2? 04:46.069 --> 04:48.109 0.3? 04:48.110 --> 04:50.320 0.4? 04:50.319 --> 04:53.269 0.5? 04:53.269 --> 04:54.929 0.6? 04:54.930 --> 04:58.350 7,8, 9, one? 04:58.350 --> 04:59.180 Obviously not one. 04:59.180 --> 05:03.640 Now, I think, my sense of this is it peaked 05:03.644 --> 05:07.694 between 0.3 and 0.4, but there were some votes for 05:07.690 --> 05:09.680 0.2, and I would've voted for 0.2, 05:09.680 --> 05:12.140 because it looks like you've lost an awful lot here. 05:12.139 --> 05:15.829 But in fact I personally am surprised that it's pretty big. 05:15.829 --> 05:17.689 It's 0.41. 05:17.689 --> 05:20.629 It's almost half as big as it would be if they were right on 05:20.625 --> 05:23.535 top of one another, despite the fact that you're 05:23.541 --> 05:26.871 losing great parts of it, that they don't overlap at all, 05:26.867 --> 05:29.747 and there's negative overlap where red's on top of blue. 05:29.750 --> 05:33.020 Still the fact is it's 0.41; so pretty big. 05:33.019 --> 05:35.949 Now that's going to depend on distance obviously. 05:35.951 --> 05:36.441 Right? 05:36.440 --> 05:38.210 So here's how it depends on distance. 05:38.209 --> 05:43.329 There's that point; at 1.4 angstroms it's 0.41. 05:43.329 --> 05:46.179 And I've put on here for reference the distance of a 05:46.178 --> 05:49.308 carbon-carbon single bond, the distance of a carbon-carbon 05:49.307 --> 05:52.027 double bond, and a carbon-carbon triple bond. 05:52.029 --> 05:54.649 And zero, notice, would be way down, 05:54.646 --> 05:56.816 out in the hallway someplace. 05:56.815 --> 05:57.485 Right? 05:57.490 --> 06:01.110 We're only looking at the region that's carbon-carbon 06:01.108 --> 06:04.378 bonds -- or maybe just about to the far wall. 06:04.379 --> 06:05.249 Okay? 06:05.250 --> 06:09.070 Here's half an angstrom; we got to go two more halves. 06:09.072 --> 06:09.672 Right? 06:09.670 --> 06:13.640 Okay, so here's how -- how do you think -- what should the 06:13.644 --> 06:14.834 line look like? 06:14.829 --> 06:16.919 Should it be sine wave? 06:16.920 --> 06:19.680 Should it be increasing as we go to the left? 06:19.680 --> 06:21.390 Should it be decreasing as we go to the left? 06:21.389 --> 06:27.209 What do you think? 06:27.209 --> 06:28.299 Some guess. 06:28.300 --> 06:29.540 <> 06:29.540 --> 06:30.510 Prof: Should probably decrease. 06:30.509 --> 06:33.479 Because we know it's going to approach one. 06:33.475 --> 06:34.035 Right? 06:34.040 --> 06:34.960 And there it is. 06:34.959 --> 06:38.079 Yes, it decreases -- pardon me, it increases as you go to the 06:38.079 --> 06:41.359 left, and ultimately it'll go up to one, when you get out to the 06:41.355 --> 06:41.975 hallway. 06:41.980 --> 06:44.030 Okay? 06:44.029 --> 06:45.229 So that's s with s. 06:45.230 --> 06:48.060 Now let's look at some other orbitals that might overlap, 06:48.060 --> 06:50.640 and see how big their overlap integrals would be. 06:50.639 --> 06:55.029 Okay, suppose you have s on one, overlapping with 06:55.033 --> 06:56.953 p on the other. 06:56.949 --> 06:59.549 Now that p is called, for this purpose, 06:59.550 --> 07:00.360 π. 07:00.360 --> 07:06.020 p is the Greek version of p; 07:06.019 --> 07:09.809 in fact, in Greek you pronounce it 'pee,' not 'pie'. 07:09.814 --> 07:10.414 Right? 07:10.410 --> 07:12.710 So that's the Greek letter p. 07:12.709 --> 07:14.709 Am I right about that? 07:14.709 --> 07:16.919 Student: It depends on classical or modern Greek. 07:16.920 --> 07:19.190 Prof: Okay, which way is it? 07:19.189 --> 07:21.689 Student: It'd be 'pee' in modern Greek; 07:21.689 --> 07:23.239 it'd be 'pie' in classical. 07:23.240 --> 07:24.530 Prof: Uh-huh, okay, good. 07:24.529 --> 07:26.559 So anyhow, ‘pie'. 07:26.560 --> 07:27.400 > 07:27.399 --> 07:31.499 Prof: Now, so that symbol is used to talk 07:31.495 --> 07:36.635 about molecular orbitals, or parts of molecular orbitals; 07:36.639 --> 07:39.309 where p is used to talk about atomic orbitals. 07:39.310 --> 07:41.030 They correspond to one another. 07:41.029 --> 07:44.919 Now what is it that characterizes a p atomic 07:44.920 --> 07:45.700 orbital? 07:45.699 --> 07:47.309 Has a nodal plane. 07:47.310 --> 07:51.430 And in the same way a π orbital has a nodal 07:51.428 --> 07:55.468 plane that contains the nuclei that are in question. 07:55.466 --> 07:56.256 Right? 07:56.259 --> 07:59.209 So you see, if those two came together there'd be a nodal 07:59.208 --> 08:02.048 plane in the orbital on the right that contains the two 08:02.050 --> 08:02.630 nuclei. 08:02.629 --> 08:03.209 Okay? 08:03.209 --> 08:05.429 So that's called a π orbital. 08:05.430 --> 08:06.180 Okay? 08:06.180 --> 08:09.560 Now, but notice the contributions to the overlap. 08:09.560 --> 08:13.080 Below that plane, you're going to have blue 08:13.079 --> 08:15.089 overlapping with blue. 08:15.088 --> 08:17.458 So that's going to be a positive contribution. 08:17.459 --> 08:20.339 But above, you're going to have blue overlapping with red; 08:20.339 --> 08:22.669 that's going to be a negative contribution, 08:22.665 --> 08:23.935 and it's symmetrical. 08:23.939 --> 08:27.809 So what will the total be? 08:27.810 --> 08:30.020 What will the total overlap integral be; 08:30.019 --> 08:32.229 the sum of all the overlaps? 08:32.230 --> 08:33.620 Student: One. 08:33.620 --> 08:35.380 Prof: One? 08:35.379 --> 08:37.219 Prof: It'll be zero, because for every contribution 08:37.220 --> 08:39.580 on the bottom that's positive, there'll be one on the top 08:39.582 --> 08:41.452 that's the same value and is negative. 08:41.450 --> 08:43.310 So it's going to be zero. 08:43.308 --> 08:47.268 So the one on the left is called σ. 08:47.269 --> 08:50.559 Now σ is the Greek equivalence of 's.' 08:50.562 --> 08:51.092 Right? 08:51.090 --> 08:53.100 So it means, for a molecular orbital, 08:53.096 --> 08:55.546 what s meant for an atomic orbital; 08:55.548 --> 08:58.638 there are no nodes that contain the nucleus. 08:58.639 --> 09:02.259 Okay? 09:02.259 --> 09:05.079 Okay, so if you have σ overlapping with 09:05.077 --> 09:07.177 a π, there's going to be this 09:07.178 --> 09:09.388 symmetry that causes a cancellation. 09:09.389 --> 09:12.439 So you can never get any overlap, by overlapping a 09:12.441 --> 09:15.681 σ orbital with a π orbital. 09:15.678 --> 09:18.728 Does that make sense to everyone? 09:18.730 --> 09:21.770 It does make sense, doesn't make sense? 09:21.769 --> 09:24.499 If you have one that doesn't have a horizontal node, 09:24.500 --> 09:28.490 that's the same top and bottom, and one that does have a node 09:28.490 --> 09:31.300 that's plus on the top, minus on the bottom, 09:31.302 --> 09:34.172 then you're going to get this cancellation everywhere, 09:34.169 --> 09:34.819 and zero. 09:34.820 --> 09:37.140 And that's called ‘orthogonal'. 09:37.139 --> 09:41.779 Okay, so you won't get any net interaction there. 09:41.779 --> 09:44.899 Okay, but if you turn the p orbital so that it is 09:44.898 --> 09:48.318 also σ -- notice it has a plane, 09:48.315 --> 09:51.635 a nodal plane, that contains that nucleus, 09:51.635 --> 09:55.485 but it doesn't contain the other nucleus you're interested 09:55.494 --> 09:55.904 in. 09:55.899 --> 09:59.659 So to call σ and π, we need a plane 09:59.659 --> 10:01.969 that contains both nuclei. 10:01.970 --> 10:05.360 That'll create this symmetry that cancels things out. 10:05.360 --> 10:08.340 Okay, so this one will give overlap. 10:08.340 --> 10:11.260 Now what would you expect for the trend of this one, 10:11.263 --> 10:14.133 as you go from great distance to small distance? 10:14.129 --> 10:15.899 If they're very, very far apart, 10:15.897 --> 10:18.117 how big will the overlap integral be; 10:18.120 --> 10:19.990 like ten meters apart? 10:19.990 --> 10:20.390 Student: Zero. 10:20.389 --> 10:22.229 Prof: Zero. Okay? 10:22.230 --> 10:26.420 Now, as you bring it together, as they start coming together, 10:26.418 --> 10:29.488 will you get positive or negative overlap? 10:29.490 --> 10:30.190 Students: Positive. 10:30.190 --> 10:32.270 Prof: Positive; right, the blue will overlap 10:32.273 --> 10:32.943 with the blue. 10:32.940 --> 10:36.060 And you keep coming, it'll get bigger and bigger. 10:36.059 --> 10:38.699 And then what will happen? 10:38.700 --> 10:40.910 Prof: Then the red is going to start coming in and -- 10:40.908 --> 10:44.448 well the blue is going to start, the blue on the right, 10:44.450 --> 10:45.670 from the p orbital, will start -- 10:45.668 --> 10:50.088 and going to overlap that red part on the left. 10:50.090 --> 10:53.450 And then, as it slides on over, till they get exactly on top of 10:53.451 --> 10:56.601 one another -- when they get exactly on top of one another, 10:56.595 --> 10:57.675 what will it be? 10:57.679 --> 10:58.529 Students: Zero. 10:58.529 --> 11:00.529 Prof: Zero, because it'll be canceling 11:00.532 --> 11:01.262 right to left. 11:01.259 --> 11:04.339 Okay, so here's a plot of that, for s-p 11:04.341 --> 11:06.331 σ_ overlap. 11:06.331 --> 11:06.911 Right? 11:06.908 --> 11:09.468 It's almost the same as s with s. 11:09.470 --> 11:12.290 In fact, it's a little bigger at great distance, 11:12.288 --> 11:14.508 a little smaller at small distance; 11:14.509 --> 11:18.589 except, at very small distance what will happen? 11:18.590 --> 11:19.860 <> 11:19.860 --> 11:23.910 Prof: When you approach zero? 11:23.909 --> 11:25.299 It'll go to zero. 11:25.298 --> 11:27.218 Whereas the other one went to one. 11:27.215 --> 11:27.675 Right? 11:27.678 --> 11:29.438 The s with s went to one. 11:29.440 --> 11:31.750 So, but in the region we're interested in, 11:31.751 --> 11:34.911 the carbon-carbon bond distances, it's about the same. 11:34.908 --> 11:39.448 Okay, now how about p_σ with 11:39.452 --> 11:41.612 p_σ? 11:41.610 --> 11:44.720 Well we won't go through an elaborate guessing game. 11:44.720 --> 11:47.090 If they're very far apart it'll be zero. 11:47.090 --> 11:51.880 How about if they were on top of one another? 11:51.879 --> 11:55.019 It's obviously going to grow as blue gets on top of blue, 11:55.019 --> 11:57.149 and then as they get really close, the blue up from the 11:57.154 --> 12:00.634 right will be on top of the red, and the red on top of the blue. 12:00.628 --> 12:01.098 Right? 12:01.100 --> 12:03.200 So what will it approach? 12:03.200 --> 12:04.170 Zack, what do you say? 12:04.169 --> 12:05.209 Student: Zero. 12:05.210 --> 12:06.430 Prof: Approach zero? 12:06.428 --> 12:12.438 What will it be when they're right on top of one another? 12:12.440 --> 12:16.910 So red on blue here; blue on red here. 12:16.909 --> 12:18.609 Will the overlap be zero? 12:18.610 --> 12:20.320 Student: Negative one. 12:20.320 --> 12:21.490 Prof: Pardon me? 12:21.490 --> 12:22.550 Student: Negative one. 12:22.548 --> 12:24.738 Prof: It'll be minus one, 12:24.740 --> 12:27.400 because it would be like the orbital on top of itself -- 12:27.399 --> 12:31.069 that would be one -- except you've changed the sign, 12:31.070 --> 12:33.250 of one of them. Right? 12:33.250 --> 12:35.260 So every contribution will be negative. 12:35.259 --> 12:38.219 So that one starts there, and it's heading toward minus 12:38.221 --> 12:38.551 one. 12:38.549 --> 12:42.509 So it's going down. 12:42.509 --> 12:43.039 Okay? 12:43.038 --> 12:44.878 So that's p_σ with p_σ. 12:44.879 --> 12:46.999 Can you think of any other way we should talk about it? 12:47.000 --> 12:48.690 We've talked about s with s. 12:48.690 --> 12:51.610 We saw that s with p_π_ was 12:51.613 --> 12:53.533 orthogonal; s with 12:53.525 --> 12:57.665 p_σ_ we've got there; 12:57.668 --> 12:59.028 p_σ with p_σ. 12:59.029 --> 13:01.379 Any others we need to think about? 13:01.379 --> 13:02.689 Student: p_σ with 13:02.692 --> 13:03.262 p_π? 13:03.259 --> 13:07.019 Prof: How about p_σ_ with 13:07.024 --> 13:08.144 p_π? 13:08.139 --> 13:13.969 Can anybody guess that one? 13:13.970 --> 13:16.520 P_σ_ is the same sign, 13:16.515 --> 13:19.415 top and bottom; p_π_ is 13:19.417 --> 13:21.687 opposite signs, top and bottom. 13:21.690 --> 13:22.350 Student: So it's zero. 13:22.350 --> 13:23.300 Prof: That's going to be zero. 13:23.299 --> 13:24.669 There'll be orthogonal. 13:24.668 --> 13:26.598 So have we done it now, or is there anything else to 13:26.600 --> 13:27.130 think about? 13:27.129 --> 13:28.119 Student: π, π. 13:28.120 --> 13:29.910 Prof: We could do p_π with 13:29.908 --> 13:30.588 p_π. 13:30.590 --> 13:33.350 Okay, so there's p_π with p_π. 13:33.350 --> 13:35.380 Okay? 13:35.379 --> 13:37.699 Now at great distance they'll be nothing. 13:37.700 --> 13:39.620 We'll bring them together, they'll begin to overlap. 13:39.620 --> 13:41.760 What will it approach as we go to zero? 13:41.759 --> 13:42.589 Student: Zero. 13:42.590 --> 13:43.860 Prof: Zero? 13:43.860 --> 13:45.950 If they're on top of one another, the product will be 13:45.947 --> 13:46.227 zero? 13:46.230 --> 13:47.400 <> 13:47.399 --> 13:48.289 Prof: It'll be one, right? 13:48.288 --> 13:51.568 It'll be the orbital with itself, normalized. 13:51.570 --> 13:54.150 So that'll be one. Right? 13:54.149 --> 13:56.599 But now which do you think is going to be bigger, 13:56.600 --> 13:58.070 p_σ_ with 13:58.070 --> 14:00.390 p_σ,_ or p_π with 14:00.394 --> 14:01.254 p_π? 14:01.250 --> 14:02.860 Any guesses? 14:02.860 --> 14:05.400 Well, I'll give you the answer. 14:05.397 --> 14:05.967 Right? 14:05.970 --> 14:08.500 p_π with p_π is approaching 14:08.500 --> 14:08.830 one. 14:08.830 --> 14:10.860 At big distance, it's smaller than 14:10.861 --> 14:11.781 σ. 14:11.784 --> 14:12.344 Right? 14:12.340 --> 14:15.140 But at small distance, it must get much bigger, 14:15.144 --> 14:17.284 and in this region it's crossing; 14:17.279 --> 14:18.589 so it's bigger. 14:18.590 --> 14:25.490 Okay, so there are the kinds of overlaps of simple 2p 14:25.493 --> 14:26.783 orbitals. 14:26.779 --> 14:28.889 Now, there's a curiosity here. 14:28.889 --> 14:32.319 Over most of this range, more than half of the range, 14:32.320 --> 14:34.910 2s overlaps with 2p_σ_ 14:34.914 --> 14:38.264 better than either 2s with 2s or 14:38.259 --> 14:41.489 2p_σ_ with 2p_σ. 14:41.490 --> 14:43.140 That just seems curious to me. 14:43.139 --> 14:46.369 You'd think that one of them would have a shape that gives 14:46.370 --> 14:47.220 better overlap. 14:47.220 --> 14:47.730 Right? 14:47.730 --> 14:50.700 So two of those together would do the best job. 14:50.700 --> 14:52.380 But it's not that way. 14:52.379 --> 14:56.079 It's that an s with a p is the best, 14:56.083 --> 14:58.053 over most of this range. 14:58.048 --> 15:00.918 I just think that's curious, and it has an important 15:00.918 --> 15:03.278 implication, which you'll see right now. 15:03.278 --> 15:06.938 What if we use hybrid orbitals, that are partly s and 15:06.942 --> 15:08.062 partly p? 15:08.058 --> 15:11.238 Now, since this one is partly s, it's s plus a 15:11.236 --> 15:12.796 certain amount of p. 15:12.798 --> 15:14.828 This one's s with a certain amount of p. 15:14.830 --> 15:17.780 The overlap will be s here with s here; 15:17.778 --> 15:20.728 s here with p here; 15:20.730 --> 15:22.890 s here with p here; 15:22.889 --> 15:24.429 and p here with p here. 15:24.427 --> 15:24.767 Right? 15:24.769 --> 15:28.439 There'll be four contributions: s with s; 15:28.440 --> 15:30.620 p with p; s with p; 15:30.621 --> 15:31.711 p with s. 15:31.712 --> 15:32.142 Right? 15:32.139 --> 15:36.399 So if we took sp^3, for example -- and we can make, 15:36.395 --> 15:40.275 remember, four such orbitals -- then you get that. 15:40.279 --> 15:44.169 It's better than any of the pure hybrids. 15:44.171 --> 15:44.951 Right? 15:44.950 --> 15:48.830 And the reason is that it has s with s, 15:48.832 --> 15:52.982 and p with p; and also s with 15:52.982 --> 15:56.862 p, that comes in as a bonus, twice. 15:56.860 --> 16:00.630 Okay, now how about if we use, instead of sp^3, 16:00.629 --> 16:03.049 how about if we use sp^2? 16:03.048 --> 16:06.618 Remember what happens as we approach sp? 16:06.620 --> 16:09.640 The orbitals extend more. 16:09.639 --> 16:10.919 So what do you expect? 16:10.919 --> 16:12.339 Student: More overlap. 16:12.340 --> 16:15.530 Prof: More overlap. 16:15.528 --> 16:19.188 So there's sp^2 with sp^2, a little better. 16:19.190 --> 16:21.050 How about sp with sp? 16:21.049 --> 16:25.069 Better still. 16:25.070 --> 16:26.800 Could we get any better? 16:26.798 --> 16:30.578 How about s^2p with s^2p, or 16:34.447 --> 16:35.367 Right? 16:35.370 --> 16:39.740 It's a little better at short distance, and a little not so 16:39.740 --> 16:41.550 good at long distance. 16:41.548 --> 16:45.138 So it optimizes around sp hybridization. 16:45.139 --> 16:46.379 That gives the best overlap. 16:46.379 --> 16:50.469 Why do we think now you want good overlap? 16:50.470 --> 16:52.770 Why would it be good to have good overlap? 16:52.769 --> 16:53.659 Student: Keep the bonds strong. 16:53.658 --> 16:55.828 Prof: Because that's what's building up the 16:55.830 --> 16:57.560 difference density, as we saw last time. 16:57.557 --> 16:57.997 Right? 16:58.000 --> 17:01.540 That's putting the glue in the orbital. 17:01.538 --> 17:05.708 Okay, so there's an interesting observation here, 17:05.712 --> 17:10.672 that hybrids overlap about twice as well as pure orbitals. 17:10.670 --> 17:11.540 Right? 17:11.538 --> 17:17.108 All the hybrids are roughly twice as good as the pure ones. 17:17.109 --> 17:18.059 Okay? 17:18.058 --> 17:20.718 And they're not very, very different from one 17:20.715 --> 17:21.315 another. 17:21.318 --> 17:25.278 But sp is about the best, over much of this range. 17:25.278 --> 17:28.628 The trouble with sp is you can only make two of them, 17:28.630 --> 17:31.980 because each involves 50% of s, and you only have one 17:31.980 --> 17:34.800 s to go in it; you have one s and three 17:34.798 --> 17:35.338 p's. 17:35.338 --> 17:38.608 So if you want to make just one orbital, fine, 17:38.606 --> 17:41.866 use sp, because you'll get good -- only 17:41.874 --> 17:45.924 one bond from the carbon; fine use sp and get the 17:45.915 --> 17:46.815 best overlap. 17:46.818 --> 17:50.588 Or maybe even s^2p, depending on the distance. 17:50.588 --> 17:51.168 Right? 17:51.170 --> 17:54.340 But if you want to make more bonds, more than two bonds, 17:54.336 --> 17:57.786 then you're going to have to cut back on the s in each 17:57.790 --> 17:58.310 bond. 17:58.308 --> 18:02.908 Because you only have 100% to use, you can't use more than 50% 18:02.914 --> 18:05.864 in more than two bonds you're making. 18:05.859 --> 18:06.359 Okay. 18:06.358 --> 18:09.428 And what you see here is that sp^3^( )isn't much worse 18:09.428 --> 18:10.398 than sp^2. 18:10.400 --> 18:12.910 So why not make four -- right? 18:12.906 --> 18:14.576 -- because you can. 18:14.578 --> 18:18.508 Okay, anyhow, that's the hybridization of 18:18.506 --> 18:19.386 carbon. 18:19.390 --> 18:22.300 So, and the reason they do this, as I already said, 18:22.298 --> 18:25.618 is because they allow nearly full measure of s with 18:25.623 --> 18:28.383 p overlap, plus s with s, 18:28.375 --> 18:31.875 and p with p, when you have mixtures. 18:31.880 --> 18:35.850 So that all depends on the fact that s-p_σ 18:35.853 --> 18:38.223 is so good in its overlap. 18:38.220 --> 18:41.410 Now, so sp gives the best overlap, 18:41.414 --> 18:45.334 but only allows two orbitals, with 50% in each; 18:45.328 --> 18:48.618 sp^3 gives four, and nearly as much overlap. 18:48.619 --> 18:49.869 Okay? 18:49.868 --> 18:52.988 Now we're going to look at the influence of overlap on 18:52.990 --> 18:54.580 molecular orbital energy. 18:54.578 --> 18:56.888 But we're going to use Erwin Meets Goldilocks, 18:56.894 --> 18:57.924 just for familiarity. 18:57.920 --> 19:00.350 So we're working here in just one-dimension, 19:00.352 --> 19:01.712 to get the idea of it. 19:01.710 --> 19:07.310 And we'll also then think in more general terms. 19:07.308 --> 19:11.338 And we've already done this, so it's partly review. 19:11.338 --> 19:13.928 So we'll assume that there's perfect energy match; 19:13.930 --> 19:16.240 that is, the two atoms we're talking about. 19:16.240 --> 19:18.990 Of course, atoms would be Coulombic potentials, 19:18.986 --> 19:21.786 not harmonic oscillator, Hooke's Law potentials. 19:21.791 --> 19:22.391 Right? 19:22.390 --> 19:24.880 But the idea of a double-minimum is the same. 19:24.880 --> 19:27.760 So we'll suppose that the atoms are equivalent. 19:27.759 --> 19:31.579 So the bottom of the well is the same on both sides. 19:31.579 --> 19:33.009 And guess an energy. 19:33.009 --> 19:36.679 And lo and behold we were right; we got the solution, 19:36.681 --> 19:38.491 and you've seen that one. 19:38.490 --> 19:38.950 Okay? 19:38.950 --> 19:42.090 But you can also get that one, one with one node. 19:42.086 --> 19:42.606 Right? 19:42.608 --> 19:45.358 And on the far left you can see that they have the same 19:45.363 --> 19:46.743 curvature-over-amplitude. 19:46.740 --> 19:48.930 So they have essentially the same energy. 19:48.930 --> 19:52.640 If the green energy is right, the red energy is the same 19:52.635 --> 19:52.965 deal. 19:52.972 --> 19:53.582 Right? 19:53.578 --> 19:57.838 They're ‘degenerate' orbitals, because they're far 19:57.839 --> 19:58.459 apart. 19:58.460 --> 19:58.970 Okay? 19:58.970 --> 20:01.230 No significant energy difference. 20:01.230 --> 20:04.350 Now, suppose we increase the overlap. 20:04.348 --> 20:06.968 What will happen if we shorten the distance? 20:06.970 --> 20:09.370 You did this on a problem set with Erwin. 20:09.371 --> 20:09.781 Right? 20:09.778 --> 20:13.078 So you bring them closer together, and you have the one 20:13.080 --> 20:15.710 with no nodes, and the one with one node. 20:15.710 --> 20:19.280 And now there's a little -- right halfway between there's 20:19.278 --> 20:22.778 more electron density in one than there is in the other. 20:22.781 --> 20:23.421 Right? 20:23.420 --> 20:27.360 The antibonding one has zero and the bonding one has some 20:27.363 --> 20:30.253 buildup of electron density in between. 20:30.250 --> 20:35.000 But the energy hasn't changed visibly on this scale that we're 20:34.997 --> 20:35.617 using. 20:35.619 --> 20:37.679 It looks just the same. 20:37.680 --> 20:38.790 Okay? 20:38.788 --> 20:41.688 Now we increase it more and now there's a big difference in the 20:41.691 --> 20:42.021 middle. 20:42.018 --> 20:42.438 Right? 20:42.440 --> 20:45.430 And now the energies are beginning to change. 20:45.430 --> 20:49.080 The unfavorable orbital is going up and the favorable 20:49.075 --> 20:52.015 bonding orbital is going down in energy. 20:52.019 --> 20:56.199 And if we get it still closer together, we can see that 20:56.202 --> 20:59.612 there's now a big difference between them. 20:59.609 --> 21:01.349 Okay? 21:01.348 --> 21:06.068 So that increasing overlap creates the splitting that we 21:06.065 --> 21:07.175 talk about. 21:07.180 --> 21:09.260 This is just review, as you know, 21:09.258 --> 21:12.628 but it's worth -- it's so important that it's good to 21:12.634 --> 21:14.004 mention it again. 21:14.000 --> 21:16.810 Now that overlap holds the atoms together. 21:16.808 --> 21:20.498 And this again is a picture we saw before, except we're going 21:20.499 --> 21:23.019 to do it with writing-in the equations. 21:23.019 --> 21:28.059 Remember, a good guess of the form of the molecular orbital is 21:28.058 --> 21:32.518 1/√2 (A+B), or 1/√2 (A-B). 21:32.519 --> 21:36.509 And that will give two new orbitals, one better and one 21:36.509 --> 21:37.099 worse. 21:37.098 --> 21:39.748 And, in fact, if you think about 21:39.753 --> 21:42.823 normalization, it should be a little less than 21:42.819 --> 21:45.739 1/√2, in the one that's going to have 21:45.738 --> 21:48.028 +2AB in it, when you square it, 21:48.029 --> 21:50.819 and a little less than 1/√2 when it's 21:50.817 --> 21:53.887 going to have a minus sign for the 2AB term. 21:53.890 --> 21:55.000 Okay? 21:55.000 --> 21:58.280 Now, because of that ‘a little bit greater' and ‘a 21:58.275 --> 22:00.995 little bit less', the energies aren't quite, 22:00.998 --> 22:05.038 as we saw them before, equally split, up and down. 22:05.038 --> 22:07.358 The one that goes down doesn't go down quite as much, 22:07.358 --> 22:10.358 because this is less than, and the one that goes up, 22:10.358 --> 22:12.868 goes up a little more because it's greater than. 22:12.868 --> 22:18.478 The mathematical requirement for that isn't immediately 22:18.482 --> 22:21.812 obvious to you, but it's true. 22:21.808 --> 22:24.778 Okay, so there are the new orbitals you get when you bring 22:24.776 --> 22:25.866 the atoms together. 22:25.869 --> 22:27.149 Okay? 22:27.150 --> 22:30.480 And if you had more overlap, there'd be a bigger difference. 22:30.480 --> 22:32.410 So that's why overlap is important. 22:32.410 --> 22:34.090 The more overlap, the more splitting. 22:34.088 --> 22:36.978 We just saw that in one-dimension with Erwin 22:36.976 --> 22:38.416 Meets Goldilocks. 22:38.420 --> 22:42.350 Now, how many electrons do we have to put in these orbitals? 22:42.348 --> 22:44.248 That's going to make a big difference. 22:44.250 --> 22:47.190 So suppose we have just one electron for these two orbitals. 22:47.190 --> 22:50.910 When we bring the two wells together, when we bring the two 22:50.909 --> 22:53.729 atoms together, that electron will go down in 22:53.730 --> 22:56.360 energy, to the new molecular orbital. 22:56.359 --> 22:57.849 So that's going to be good. 22:57.848 --> 22:59.218 And if we tried to pull them apart, 22:59.220 --> 23:01.200 the electron would have to go back up in energy, 23:01.200 --> 23:05.360 and that would require energy, and that would oppose the 23:05.357 --> 23:06.187 breaking. 23:06.190 --> 23:07.760 So that's the bond strength. 23:07.758 --> 23:08.148 Right? 23:08.150 --> 23:10.170 You have to put an electron up that much. 23:10.170 --> 23:12.860 Now suppose there were two electrons. 23:12.858 --> 23:14.898 Now a second one goes down the same way. 23:14.900 --> 23:17.210 So it's even stronger. 23:17.210 --> 23:21.340 It won't, in truth, be quite twice as strong. 23:21.339 --> 23:24.429 Do you see why? 23:24.430 --> 23:25.070 Yes? 23:25.068 --> 23:25.948 Student: Electron repulsion. 23:25.950 --> 23:27.420 Prof: Because the electrons will repel one 23:27.423 --> 23:27.733 another. 23:27.730 --> 23:30.950 We haven't taken that into account when we think about the 23:30.945 --> 23:31.845 energies here. 23:31.848 --> 23:35.378 But it'll be certainly stronger, considerably stronger. 23:35.380 --> 23:36.380 Okay. 23:36.380 --> 23:39.530 Now suppose we had three electrons. 23:39.529 --> 23:43.559 What's going to happen? 23:43.558 --> 23:46.538 Prof: One of them is going to have to go up instead 23:46.537 --> 23:47.057 of down. 23:47.058 --> 23:50.218 And, in fact, it will go up further than 23:50.222 --> 23:54.682 either of the others went down, even neglecting electron 23:54.683 --> 23:56.553 repulsion -- right? 23:56.548 --> 23:58.978 -- because of that ‘greater than/less than' 23:58.984 --> 24:01.324 thing that shifted the pair up a little bit. 24:01.319 --> 24:01.979 Okay? 24:01.980 --> 24:05.480 So that's going to be even weaker than having one electron 24:05.478 --> 24:08.238 to hold them together, when you have three. 24:08.240 --> 24:10.230 How about if you have four? 24:10.230 --> 24:13.110 Student: No more bonds. 24:13.109 --> 24:13.769 Prof: Wilson? 24:13.769 --> 24:15.079 Student: They'll be antibonding, so -- 24:15.078 --> 24:17.718 Prof: Yeah, you're now definitely losing, 24:17.723 --> 24:20.993 because the two that go up, go up more than the two that go 24:20.987 --> 24:21.997 down, go down. 24:22.000 --> 24:22.950 So that's bad. 24:22.950 --> 24:25.480 So we can summarize that here, the effect on the bond. 24:25.480 --> 24:27.590 If you have one electron, it's bonding; 24:27.588 --> 24:29.438 two electrons is strongly bonding; 24:29.440 --> 24:32.830 three electrons is weakly bonding, probably; 24:32.828 --> 24:35.748 and four electrons will definitely be antibonding. 24:35.750 --> 24:38.810 So that's why helium bounces off helium, 24:38.808 --> 24:41.618 until it gets fifty-two angstroms apart, 24:41.618 --> 24:45.408 and then there's this very, very, very weak bond, 24:45.410 --> 24:48.380 that we talked about, due to the correlation of the 24:48.381 --> 24:48.971 electrons. 24:48.974 --> 24:49.514 Right? 24:49.509 --> 24:53.449 But as soon as you get overlap with helium, it's repulsive, 24:53.450 --> 24:56.100 when you start to split these levels. 24:56.098 --> 25:00.098 Okay, now let's look at the other end. 25:00.098 --> 25:03.918 Why doesn't increasing overlap, as you bring things closer 25:03.919 --> 25:08.139 together, why doesn't that make these plum-puddings collapse? 25:08.140 --> 25:11.910 The electrons are getting more and more stable as you increase 25:11.910 --> 25:14.940 the overlap by bringing things closer together. 25:14.940 --> 25:22.670 So why doesn't it just collapse? 25:22.670 --> 25:28.060 In fact, the electron -- if a hydrogen molecule collapsed to 25:28.055 --> 25:30.315 helium -- it would be a funny helium 25:30.317 --> 25:32.107 because it would have no neutrons -- 25:32.108 --> 25:34.038 but if it collapsed, the electrons, 25:34.038 --> 25:37.878 indeed, would become 55% more stable. 25:37.880 --> 25:42.120 The electrons in helium are lower in energy than the 25:42.117 --> 25:43.527 electrons in H_2. 25:43.530 --> 25:44.280 Right? 25:44.279 --> 25:47.239 So that would tend to pull them together, all the way, 25:47.239 --> 25:48.299 to distance zero. 25:48.299 --> 25:50.729 Why don't they? 25:50.730 --> 25:51.400 Elizabeth? 25:51.400 --> 25:52.300 Student: The protons repel. 25:52.298 --> 25:54.258 Prof: Because the protons will repel one another. 25:54.259 --> 25:56.339 That depends on 1/r. 25:56.339 --> 25:56.879 Right? 25:56.880 --> 25:59.580 And that increases much more dramatically. 25:59.578 --> 26:04.338 In fact, the amount by which the electrons become more stable 26:04.343 --> 26:07.923 is 650 kcal/mole, or would become more stable. 26:07.915 --> 26:08.705 Right? 26:08.710 --> 26:13.200 But the nuclear repulsion increases by that much by the 26:13.195 --> 26:18.265 time they get to 0.3 angstroms, let alone the last little bit, 26:18.265 --> 26:21.085 when 1/r gets enormous. 26:21.089 --> 26:21.619 Okay? 26:21.619 --> 26:24.999 So it's not worth it; unless you have glue to hold 26:25.003 --> 26:26.443 the neutrons together. 26:26.444 --> 26:26.974 Right? 26:26.970 --> 26:31.120 So on the sun you can take deuterium and fuse it into -- 26:31.118 --> 26:33.668 to make a helium -- you have neutrons there to hold the 26:33.667 --> 26:36.527 protons together -- and then you get 200 million 26:36.532 --> 26:38.332 kcal/mole; which is, of course, 26:38.327 --> 26:40.387 nuclear energy, not electronic energy. 26:40.390 --> 26:43.420 It is possible, but not under the chemical 26:43.423 --> 26:46.463 circumstances that we're talking about. 26:46.460 --> 26:49.730 Okay, so here's the Morse potential. 26:49.730 --> 26:51.120 Yes, Lucas? 26:51.118 --> 26:54.328 Student: Have we been taking proton-proton repulsion 26:54.325 --> 26:56.765 into account before, with all our energies? 26:56.769 --> 27:00.969 Prof: No, or only sort of subliminally. 27:00.971 --> 27:01.721 Right? 27:01.720 --> 27:05.120 Because if you take -- at first glance there's going to be 27:05.118 --> 27:07.918 nuclear-nuclear repulsion, and electron-electron 27:07.922 --> 27:12.122 repulsion, between the atoms; nuclear-electron attraction; 27:12.119 --> 27:13.739 nuclear-electron attraction. 27:13.740 --> 27:17.000 So to first approximation, those will all cancel out. 27:16.998 --> 27:17.498 Right? 27:17.500 --> 27:21.350 But then you get -- on top of that you have a little change 27:21.348 --> 27:24.338 from the fact that the nuclear-nuclear goes as 27:24.336 --> 27:27.926 1/r and gets quite big, when they get really close, 27:27.933 --> 27:30.723 and that the electrons are coming down because of overlap. 27:30.720 --> 27:33.400 And we've been focusing on this overlap thing that causes the 27:33.396 --> 27:36.116 bonding, but obviously things aren't going to collapse because 27:36.118 --> 27:37.188 of the nuclear part. 27:37.190 --> 27:40.490 But we haven't been talking about it explicitly; 27:40.487 --> 27:41.537 you're right. 27:41.538 --> 27:44.358 Okay, so anyhow this is the form of the bonding potential, 27:44.358 --> 27:47.308 the Morse potential, which was just cobbled together 27:47.313 --> 27:50.383 artificially to make it convenient to calculate things 27:50.382 --> 27:53.222 and to have reasonable properties for a bond. 27:53.220 --> 27:57.390 But now we understand why it should look like that. 27:57.390 --> 27:59.490 This first part, the attractive part, 27:59.492 --> 28:02.532 is because the electron pair becomes more stable with 28:02.529 --> 28:05.509 increasing overlap, as the atoms come together. 28:05.509 --> 28:09.099 And then the nuclear repulsion becomes dominant, 28:09.103 --> 28:11.093 when it becomes too close. 28:11.090 --> 28:11.780 Right? 28:11.779 --> 28:15.179 So all this is Coulomb's Law. 28:15.180 --> 28:16.550 There's nothing special. 28:16.548 --> 28:18.378 There's not ‘correlation 28:18.383 --> 28:21.193 energy', which is some completely new physical 28:21.189 --> 28:21.819 phenomenon. 28:21.818 --> 28:22.448 Right? 28:22.450 --> 28:24.720 It's all Coulombic. 28:24.720 --> 28:28.480 Correlation energy is just, remember, an excuse for the 28:28.482 --> 28:31.482 error you're making, or a way to hide it. 28:31.480 --> 28:35.220 Okay, so it all comes from Coulomb's Law for potential 28:35.223 --> 28:35.863 energy. 28:35.858 --> 28:39.408 But the funny thing was the kinetic energy of the electrons, 28:41.218 --> 28:41.758 Right? 28:41.759 --> 28:44.569 Because as you make things -- as you concentrate things, 28:44.570 --> 28:46.360 you change the curvature as well. 28:46.358 --> 28:48.628 So you have to take that into account. 28:48.630 --> 28:54.180 But this curve provides the potential for studying molecular 28:54.180 --> 28:57.200 vibration; that is, once you know the form 28:57.195 --> 28:59.615 of this curve, then you can use quantum 28:59.616 --> 29:02.086 mechanics for the motion of the atoms -- 29:02.088 --> 29:03.968 not of the electrons but of the atoms -- 29:03.970 --> 29:06.120 and figure out how atoms vibrate; 29:06.118 --> 29:09.168 which we've already done, when we were doing Erwin 29:09.170 --> 29:10.520 Meets Goldilocks. 29:10.519 --> 29:14.079 Okay, but here, finally we understand the 29:14.078 --> 29:15.858 atom-atom force law. 29:15.858 --> 29:16.658 Right? 29:16.660 --> 29:18.210 That's what we've been doing the whole time, 29:18.210 --> 29:21.010 for four weeks or five weeks or whatever it's been, 29:21.009 --> 29:24.679 is trying to understand where -- what the force law is. 29:24.680 --> 29:26.040 Wouldn't Newton be happy? 29:26.038 --> 29:27.948 Remember, he said, "There are therefore 29:27.952 --> 29:30.362 agents in Nature able to make particles of bodies stick 29:30.355 --> 29:32.175 together by very strong attractions, 29:32.180 --> 29:34.760 and it's the business of Experimental Philosophy to find 29:34.760 --> 29:35.560 them out." 29:35.559 --> 29:37.599 And now we've found it out. 29:37.598 --> 29:42.678 Now, can we use this understanding then to gain 29:42.682 --> 29:46.222 greater purchase on chemistry? 29:46.220 --> 29:47.460 So we've looked at overlap. 29:47.460 --> 29:50.620 But there's one other thing we have to look at, 29:50.618 --> 29:53.638 in order to apply it, and that's what we call 29:53.642 --> 29:54.812 energy-match. 29:54.808 --> 29:57.888 I don't think anybody else talks about energy-match, 29:57.885 --> 29:58.605 but we do. 29:58.608 --> 30:01.748 Okay, so here's what we talked about already. 30:01.749 --> 30:02.319 Right? 30:02.318 --> 30:05.828 And we have this splitting, which is about proportional to 30:05.833 --> 30:06.453 overlap. 30:06.450 --> 30:09.420 It's not numerically strictly proportional to overlap, 30:09.423 --> 30:12.513 but it certainly is close to proportional to overlap. 30:12.509 --> 30:16.649 Okay, now what would happen if the two atoms you started with 30:16.650 --> 30:19.890 were not the same, if one was a better place for 30:19.894 --> 30:25.924 electrons to be than the other; like there for example? 30:25.920 --> 30:29.250 So why would you -- remember what happened is you mix these. 30:29.250 --> 30:32.000 You get A+B and A-B. 30:32.000 --> 30:35.460 But why would you put any A together 30:35.455 --> 30:38.625 with B, if B is already much better than A? 30:38.630 --> 30:41.540 If they're equal, you don't care where it is, 30:41.544 --> 30:43.734 then fine, use a 50/50 mixture. 30:43.730 --> 30:49.000 But if one's better than the other, why use any of the 30:48.998 --> 30:50.488 inferior one? 30:50.490 --> 30:53.580 Why not just use the one that's good? 30:53.578 --> 30:58.618 So we already actually saw this in the case of the 1s 30:58.616 --> 31:01.796 atomic orbitals, which did remain pure and 31:01.797 --> 31:05.347 unmixed, when we made the molecular orbitals of that funny 31:05.346 --> 31:09.606 molecule last time, the fluoroethanol. 31:09.609 --> 31:10.549 Remember, it looked like that. 31:10.548 --> 31:12.888 One of them was just an s orbital on F; 31:12.890 --> 31:15.410 another one was an s orbital on O; 31:15.410 --> 31:17.890 s orbital on one carbon, s orbital on the other 31:17.887 --> 31:18.257 carbon. 31:18.259 --> 31:23.459 The didn't mix. Right? 31:23.460 --> 31:27.500 So the compact 1s core orbitals did remain pure and 31:27.500 --> 31:31.610 unmixed, but the valence level atomic orbitals were heavily 31:31.611 --> 31:32.321 mixed. 31:32.318 --> 31:35.008 For example, the next one was biggest on 31:35.009 --> 31:39.149 fluorine, but also substantial on oxygen, and carbon even got 31:39.147 --> 31:40.937 into the act a little bit. 31:40.941 --> 31:41.701 Right? 31:41.700 --> 31:47.970 Now why is it that the core orbitals didn't mix and the 31:47.972 --> 31:51.112 valence orbitals did mix? 31:51.109 --> 31:54.389 What's different? 31:54.390 --> 31:58.830 The core orbitals are very small, very compact. 31:58.829 --> 32:00.409 These orbitals are bigger. 32:00.410 --> 32:02.590 So what happens? 32:02.589 --> 32:05.309 They overlap. Right? 32:05.308 --> 32:09.858 So it's overlap that causes things to mix. 32:09.858 --> 32:11.718 If there's no overlap they don't mix. 32:11.720 --> 32:15.150 If they overlap they mix. 32:15.150 --> 32:17.930 So why use any of an inferior orbital? 32:17.930 --> 32:21.050 Well suppose the energy of A is much higher, less favorable, 32:21.046 --> 32:22.416 than that of B. Right? 32:22.420 --> 32:25.540 So now we make a sum, a weighted sum, 32:25.540 --> 32:29.010 a parts of A, b parts of B, 32:29.009 --> 32:30.829 and we square it. 32:30.828 --> 32:34.418 So we get a^2^( )parts of the A density, 32:34.416 --> 32:38.936 b^2^( )parts of the B density, and also this overlap 32:38.942 --> 32:40.582 term, 2ab. 32:40.578 --> 32:44.988 Now, can you profit from shifting electron density toward 32:44.990 --> 32:49.560 the inter-nuclear AB region, without paying too much of the 32:49.560 --> 32:51.610 high energy cost of A? 32:51.608 --> 32:55.168 That is, A^2^( )is higher energy than B^2. 32:55.173 --> 32:55.873 Right? 32:55.868 --> 32:58.928 The electron density around A is higher energy than the 32:58.930 --> 33:00.460 electron density about B. 33:00.460 --> 33:04.540 And if you mix A with B, you're going to get a certain 33:04.540 --> 33:07.010 amount of that bad, or less good, 33:07.005 --> 33:08.695 distribution, A^2. 33:08.700 --> 33:12.840 But at the same time you're going to get some of AB, 33:12.838 --> 33:17.708 which puts stuff in the middle, at the expense of outside. 33:17.710 --> 33:19.200 That's good. Right? 33:19.200 --> 33:24.080 At a certain distance from the nuclei, you'd rather be between 33:24.078 --> 33:27.678 the two nuclei than out beyond one of them. 33:27.680 --> 33:31.190 So as you increase a, you increase -- oops sorry 33:31.194 --> 33:33.284 > 33:33.278 --> 33:37.248 -- you increase this bad part, but you also increase that good 33:37.249 --> 33:37.899 part. 33:37.900 --> 33:41.710 Can it be worthwhile to make a non-0? 33:41.710 --> 33:43.150 Which one is going to help? 33:43.150 --> 33:44.630 But notice this. 33:44.630 --> 33:49.430 If you put only a small amount of A in, then the amount of 33:49.431 --> 33:52.881 A^2^( )probability density, this bit here, 33:52.884 --> 33:57.084 is a^2 parts of that; really, really tiny, 33:57.082 --> 33:58.662 if a is tiny. 33:58.660 --> 34:02.250 But the amount of ab you put in is a times 34:02.250 --> 34:03.880 b, not a^2. 34:03.882 --> 34:04.472 Right? 34:04.470 --> 34:05.430 So it's much bigger. 34:05.430 --> 34:12.240 So you get this good stuff, without getting very much of 34:12.244 --> 34:14.104 this bad stuff. 34:14.103 --> 34:15.223 Right? 34:15.219 --> 34:17.869 For example, suppose you used, 34:17.873 --> 34:21.723 a was 0.03 and b was 0.98. 34:21.719 --> 34:23.909 So you square them, to find out how much -- 34:23.909 --> 34:26.269 <> 34:26.266 --> 34:29.296 -- you square them, and you find out that the 34:29.304 --> 34:32.044 amount of a^2 you get is only 0.001. 34:32.039 --> 34:34.669 The amount of b^2 is 0.96. 34:34.670 --> 34:37.270 And the amount of 2ab is 0.06. 34:37.268 --> 34:41.448 So you're getting sixty times as much of ab as you get 34:41.454 --> 34:42.574 of a^2. 34:42.570 --> 34:45.680 So that's why it can be useful to put a little bit in. 34:45.679 --> 34:49.559 And if you're pedantic, you can look at the footnote 34:49.561 --> 34:50.171 there. 34:50.170 --> 34:53.580 So let's look at Erwin Meets Goldilocks in the case where 34:53.577 --> 34:56.877 the two wells are not matched, where the energies are a little 34:56.876 --> 34:58.966 bit different; because that's what we're 34:58.974 --> 34:59.654 talking about. 34:59.650 --> 35:04.380 So here are non-degenerate atomic orbitals. 35:04.380 --> 35:07.850 So the one on the left is a little bit lower than the one on 35:07.849 --> 35:09.849 the right, but only a teeny bit. 35:09.849 --> 35:11.049 Okay? 35:11.050 --> 35:13.260 Now we're going to look at the wave functions here. 35:13.260 --> 35:16.010 So there's the lowest energy wave function. 35:16.005 --> 35:16.525 Right? 35:16.530 --> 35:20.690 And notice it's the sum, it's a weighted sum, 35:20.688 --> 35:22.198 with no nodes. 35:22.199 --> 35:25.719 But there's almost no mixing at all, just a really, 35:25.715 --> 35:28.525 really, really tiny amount of A in it. 35:28.530 --> 35:32.690 So essentially it's just the solution you'd get in the left 35:32.693 --> 35:33.053 well. 35:33.052 --> 35:33.702 Right? 35:33.699 --> 35:36.769 There'd be one with one node as well. 35:36.768 --> 35:41.048 What will it look like, can you guess? 35:41.050 --> 35:43.970 This is the one with zero nodes. 35:43.969 --> 35:46.489 What's the wave function with one node look like? 35:46.489 --> 35:49.999 Any guesses? 35:50.000 --> 35:51.370 Yes, Josh? 35:51.369 --> 35:53.159 Student: It'll just have a node in the middle of 35:53.164 --> 35:55.194 that first potential and then be straight on the second one. 35:55.190 --> 35:56.000 Prof: And be what? 35:56.000 --> 36:00.270 Student: And be sort of straight on the second one. 36:00.268 --> 36:01.328 Prof: Right. 36:01.326 --> 36:03.096 So the first one, the lowest one, 36:03.103 --> 36:04.553 is the one on the left. 36:04.550 --> 36:06.580 The second one, the next highest energy 36:06.576 --> 36:09.666 orbital, is the one on the right, with just a little bit of 36:09.670 --> 36:12.790 the one on the left in it; negligible amount of mixing. 36:12.789 --> 36:13.169 Right? 36:13.170 --> 36:16.160 And their energies, you might think their energies 36:16.159 --> 36:19.089 would be the same, because they're not mixing. 36:19.090 --> 36:24.980 But the green one is in this well, and the red one is in that 36:24.983 --> 36:28.033 well, and that well's higher. 36:28.030 --> 36:28.730 Okay? 36:28.730 --> 36:30.220 So it's got to be higher in energy. 36:30.219 --> 36:33.909 That spitting is due only to the original offset between the 36:33.909 --> 36:34.409 wells. 36:34.409 --> 36:37.029 There's no shift of it. Right? 36:37.030 --> 36:39.890 It's just you have A or you have B, and you have what you 36:39.885 --> 36:41.105 would expect for them. 36:41.110 --> 36:46.730 Now suppose we increase the overlap between these. 36:46.730 --> 36:52.030 What do you think is going to happen? 36:52.030 --> 36:55.790 You should get a little more mixing because AB is going to 36:55.786 --> 36:58.286 count for more, if you have overlap. 36:58.289 --> 36:59.779 Okay, so here they are close together. 36:59.780 --> 37:03.440 You still don't have very much mixing, just a little bit, 37:03.443 --> 37:06.653 and you haven't seen any appreciable change in the 37:06.648 --> 37:07.498 energies. 37:07.500 --> 37:10.620 You still have that same splitting that's due to the 37:10.619 --> 37:11.719 original offset. 37:11.719 --> 37:12.279 Okay? 37:12.280 --> 37:15.220 Now we'll bring them still closer together. 37:15.219 --> 37:18.999 And now it's getting worthwhile to put it in the wrong well, 37:19.003 --> 37:21.253 because the AB term is so important. 37:21.248 --> 37:21.888 Right? 37:21.889 --> 37:24.779 So the antibonding energy is rising, 37:24.780 --> 37:27.560 the bonding energy is falling -- that's why they're 37:27.561 --> 37:31.901 antibonding and bonding -- and if we bring them still 37:31.902 --> 37:35.672 closer together, we get that. Right? 37:35.670 --> 37:40.840 Which, if you looked at it casually, they look like a 37:40.838 --> 37:42.228 single well. 37:42.230 --> 37:46.270 But notice that they're still quite unsymmetrical, 37:46.271 --> 37:48.171 they're still biased. 37:48.170 --> 37:52.210 The one without any nodes is still mostly in the left well, 37:52.213 --> 37:55.983 and the one with a node is mostly in the right well. 37:55.980 --> 37:57.610 But they're heavily mixed. 37:57.610 --> 37:58.050 Right? 37:58.050 --> 38:00.890 So what's happening is this increasing overlap, 38:00.887 --> 38:04.337 as you bring them together, is fighting the effect of the 38:04.344 --> 38:06.324 difference in the two wells. 38:06.320 --> 38:10.300 So when we had the core electrons in fluoroethanol, 38:10.295 --> 38:13.715 if we had tiny orbitals that didn't overlap, 38:13.715 --> 38:15.465 then they stayed pure. 38:15.465 --> 38:16.335 Right? 38:16.340 --> 38:18.810 But once we went to the valence level orbitals, 38:18.809 --> 38:21.279 that were much bigger, so that they overlapped, 38:21.280 --> 38:23.430 then they started mixing, like this. 38:23.429 --> 38:29.859 Okay, now what if one partner is lower in energy than A? 38:29.860 --> 38:31.510 That's the case we're dealing with. 38:31.510 --> 38:34.020 But what will these ultimate energies be, 38:34.018 --> 38:37.578 when you have this competition between overlap, 38:37.579 --> 38:41.759 which is trying to mix them, and energy mismatch, 38:41.760 --> 38:44.760 which is trying to keep them separate from one another? 38:44.760 --> 38:47.820 So here's what you get. 38:47.820 --> 38:51.770 You get again splitting, but not as much shift as you 38:51.771 --> 38:52.761 got before. 38:52.760 --> 38:55.960 The lower level will look mostly like C, 38:55.960 --> 38:58.340 because C is better than A. 38:58.340 --> 39:00.860 The antibonding will look mostly like A, 39:00.862 --> 39:03.192 with just a little bit of C in it. 39:03.190 --> 39:07.880 And if they had had the same energy, you'd get a big energy 39:07.876 --> 39:10.056 shift because of overlap. 39:10.059 --> 39:13.229 But now you get a smaller energy shift, 39:13.228 --> 39:16.318 because the mismatch is fighting that. 39:16.315 --> 39:17.145 Right? 39:17.150 --> 39:20.660 You don't want to -- you lose as you try to mix, 39:20.663 --> 39:23.733 because of the difference between A and C, 39:23.728 --> 39:24.998 in this case. 39:25.000 --> 39:30.660 Now, so that one looks mostly like C, both in shape and in 39:30.655 --> 39:31.545 energy. 39:31.550 --> 39:35.070 That one looks mostly like A, both in shape and energy. 39:35.070 --> 39:38.150 But it's a little worse than A, and the first one is a little 39:38.148 --> 39:38.968 better than C. 39:38.969 --> 39:46.069 Now how much smaller is that bonding shift? 39:46.070 --> 39:48.620 When they were mismatched, they didn't shift as much with 39:48.623 --> 39:49.493 the same overlap. 39:49.489 --> 39:51.259 How much less? 39:51.260 --> 39:52.710 Exactly where does it end up? 39:52.710 --> 39:55.400 Well that's not so crucially important to you, 39:55.400 --> 39:58.390 but there's a neat trick you can do to see that. 39:58.389 --> 40:02.359 Suppose we have that much energy mismatch. 40:02.360 --> 40:02.940 Okay? 40:02.940 --> 40:06.680 And the red dot is halfway between B and C, 40:06.681 --> 40:10.691 or between A and C, since A and B are the same 40:10.690 --> 40:11.670 energy. 40:11.670 --> 40:14.260 Now, so when they were perfectly matched, 40:14.264 --> 40:17.574 A and B perfectly matched in energy, that's how much 40:17.574 --> 40:20.824 splitting you got from that amount of overlap. 40:20.820 --> 40:24.010 So these are the two factors that go into it: 40:24.012 --> 40:28.152 how much splitting you get when they have the same energy, 40:28.146 --> 40:31.626 and how different the original energies are. 40:31.630 --> 40:36.220 How can you put those together, to find out how much shift you 40:36.221 --> 40:37.351 actually get? 40:37.349 --> 40:40.579 Well what we do is slide that over, 40:40.579 --> 40:48.109 and then bend down the blue one, so it's perpendicular to 40:48.105 --> 40:51.925 that, and make a rectangle around it, 40:51.929 --> 40:53.969 and draw the diagonal. 40:53.969 --> 40:59.679 And that diagonal will be the new energy difference between 40:59.677 --> 41:01.347 the new levels. 41:01.349 --> 41:02.119 Okay? 41:02.119 --> 41:04.569 You say, why do I make this construction? 41:04.570 --> 41:07.160 It's because there's a quadratic formula that comes in. 41:07.159 --> 41:11.569 So the diagonal is the square root of the squares of the two 41:11.574 --> 41:15.244 sides, the sum of the squares of the two sides. 41:15.239 --> 41:18.979 Okay, so we can rotate that; put a tack in there and rotate 41:18.981 --> 41:19.291 it. 41:19.289 --> 41:23.019 And that's going to be the new energy difference. 41:23.019 --> 41:23.859 Okay? 41:23.860 --> 41:27.000 And it's bigger than the original energy difference, 41:26.996 --> 41:30.806 because the diagonal has to be bigger than one of the sides. 41:30.809 --> 41:32.719 But because of the normalization, 41:32.721 --> 41:35.471 because one of them is a little less than -- 41:35.469 --> 41:38.559 one of them is a little smaller and one's a little greater -- 41:38.559 --> 41:42.379 that was the less than/greater than √2, 41:42.380 --> 41:45.470 1/√2 thing -- it's going to shift up a little bit, 41:45.469 --> 41:48.029 both levels will shift up a little bit, like that. 41:48.030 --> 41:48.450 Right? 41:48.449 --> 41:49.689 I'll do it again so you see it. 41:49.690 --> 41:50.970 Both will shift up. 41:50.969 --> 41:53.679 So there are the new levels. 41:53.679 --> 41:56.009 That's how you do it. 41:56.010 --> 41:57.100 Okay? 41:57.099 --> 42:03.289 Now, so for a given overlap, the bonding shift, 42:03.289 --> 42:06.499 how much the electrons changed when the atoms came together, 42:06.500 --> 42:10.680 is reduced if the energies aren't well matched, 42:10.679 --> 42:13.059 if you have the same overlap. 42:13.059 --> 42:16.969 You don't get as strong a bond, from that point of view. 42:16.969 --> 42:20.769 The energies didn't shift down as much, or up as much. 42:20.768 --> 42:29.258 But still A+C will be lower in energy than the original one 42:29.259 --> 42:30.869 was, A+B. 42:30.869 --> 42:31.679 Okay? 42:31.679 --> 42:35.569 And we had that construction, which shows us an interesting 42:35.574 --> 42:38.034 thing, which is the splitting is not 42:38.034 --> 42:41.494 very sensitive to the one of these contributions that's 42:41.485 --> 42:42.185 smaller. 42:42.190 --> 42:45.350 There are two contributions: the overlap part, 42:45.349 --> 42:47.719 that's the black arrow -- or pardon me, 42:47.719 --> 42:51.859 that's the blue arrow -- and the energy difference, 42:51.860 --> 42:55.110 the energy mismatch, which is the black arrow. 42:55.110 --> 42:59.310 But if one of those is very small, like here, 42:59.311 --> 43:01.991 the mismatch, which is black, 43:01.987 --> 43:04.657 is very big, and the overlap, 43:04.661 --> 43:07.911 the blue one, is very small. 43:07.909 --> 43:11.649 But you can see that the length of the diagonal is not going to 43:11.652 --> 43:14.252 be very sensitive to what the overlap is. 43:14.250 --> 43:18.660 You could increase that blue overlap, the width of the 43:18.661 --> 43:23.491 rectangle, which wouldn't change the diagonal very much. 43:23.489 --> 43:26.739 So it's sensitive to the one that's bigger. 43:26.739 --> 43:29.149 Okay, don't worry too much about that part. 43:29.150 --> 43:31.910 I just think it's fun. 43:31.909 --> 43:34.519 Okay, so we can generalize from this. 43:34.518 --> 43:38.168 Mixing two overlapping orbitals gives one composite orbital 43:38.172 --> 43:41.512 that's lower in energy than either of the parents, 43:41.510 --> 43:45.100 and one that's higher in energy than either of the parents. 43:45.099 --> 43:45.649 Okay? 43:45.650 --> 43:48.810 The lower energy combination looks -- that is, 43:48.813 --> 43:52.473 its shape -- is most like the lower energy parent; 43:52.469 --> 43:54.579 and the same is true for energy. 43:54.576 --> 43:55.116 Right? 43:55.119 --> 43:58.979 And the higher one looks like the higher parent. 43:58.980 --> 44:02.400 For a given overlap, increasing energy mismatch 44:02.396 --> 44:06.926 decreases the amount of mixing, and decreases the magnitude of 44:06.925 --> 44:08.555 the energy shifts. 44:08.559 --> 44:11.549 Now what does this have to do with bonding? 44:11.550 --> 44:16.660 Okay, the AC electrons are clearly lower in energy. 44:16.659 --> 44:19.189 But that's not really what we're interested in. 44:19.190 --> 44:22.330 We're interested in the change of energy 44:22.329 --> 44:25.589 that comes when you break the bond, or make the bond. 44:25.590 --> 44:29.950 So which bond is stronger, AB or AC? 44:29.949 --> 44:34.159 How many think AB is stronger, given this scheme? 44:34.159 --> 44:36.619 How many think AC is stronger? 44:36.619 --> 44:40.069 It's clearly got lower energy electrons, AC. 44:40.070 --> 44:44.210 But this is a classic example of "compared to what?" 44:44.210 --> 44:45.130 Okay? 44:45.130 --> 44:47.870 How are we going to break the bond? 44:47.869 --> 44:51.489 Suppose what we're going to do is break it, to put two 44:51.485 --> 44:54.625 electrons in C, because that's the lower energy 44:54.625 --> 44:56.805 atom; or in the other case, 44:56.809 --> 44:58.829 to put two electrons in B. 44:58.829 --> 44:59.219 Okay? 44:59.219 --> 45:01.499 So both electrons go the same way. 45:01.500 --> 45:04.710 Can you see anything bad about that? 45:04.710 --> 45:08.330 Why might it be better to put one electron each way? 45:08.329 --> 45:10.369 Kevin? 45:10.369 --> 45:13.559 Student: Well in terms of spin, they have to be -- 45:13.559 --> 45:14.419 Prof: Not spin. 45:14.420 --> 45:16.960 You can put two electrons in an orbital with opposite spin. 45:16.960 --> 45:20.790 So spin's not a problem, if you only have two. 45:20.789 --> 45:23.619 If you had three it would be a problem, but with two, 45:23.621 --> 45:24.931 spin is not a problem. 45:24.929 --> 45:27.349 But there's an obvious problem with having both the electrons 45:27.346 --> 45:27.826 go to one. 45:27.829 --> 45:28.599 Dana? 45:28.599 --> 45:29.149 Student: They'll repel each other. 45:29.150 --> 45:30.360 Prof: They'll repel each other. 45:30.360 --> 45:31.620 If you could put them on opposite ones, 45:31.619 --> 45:32.249 so much the better. 45:32.251 --> 45:32.551 Right? 45:32.550 --> 45:36.580 But it would be possible to do this, and it might plausible in 45:36.581 --> 45:39.621 the case of AC, where C is lower in energy than 45:39.623 --> 45:41.853 A; although the repulsion might 45:41.847 --> 45:44.717 make it better to go one on C and one on A. 45:44.719 --> 45:46.849 Okay, but anyhow, suppose you break it this way. 45:46.849 --> 45:48.639 Which one would be easier to break? 45:48.639 --> 45:52.119 Which requires less energy, red or blue? 45:52.119 --> 45:52.959 Students: Red. 45:52.960 --> 45:54.890 Prof: Red requires less energy. 45:54.889 --> 45:59.359 Okay, so AB is stronger, if you're forming A^+ B^-, 45:59.364 --> 46:03.304 if both the electrons are going the same way. 46:03.304 --> 46:04.204 Right? 46:04.199 --> 46:08.649 So mismatch aids heterolysis. 46:08.650 --> 46:11.110 Heterolysis, (uneven breaking) is to put 46:11.108 --> 46:14.448 them both on the same side, rather than one on each side 46:14.445 --> 46:17.545 (that's called homolysis, as you'll see in a second). 46:17.550 --> 46:21.300 So if you put them both on one side, then it's easier to break 46:21.302 --> 46:22.782 if they're mismatched. 46:22.780 --> 46:25.710 The bond is stronger if they're well matched. 46:25.710 --> 46:26.910 Okay? 46:26.909 --> 46:28.719 That's because that. 46:28.719 --> 46:34.619 But now suppose you do homolysis and put one on each. 46:34.619 --> 46:37.579 Now which one's easier? 46:37.579 --> 46:38.189 Student: The blue one. 46:38.190 --> 46:42.690 Prof: Now the blue is less energy than the red. 46:42.690 --> 46:43.410 Okay? 46:43.409 --> 46:47.319 So now the AC is going to be stronger. 46:47.320 --> 46:51.470 So mismatch hinders homolysis. 46:51.471 --> 46:52.441 Right? 46:52.440 --> 46:55.290 So you can't really say which bond is stronger, 46:55.293 --> 46:58.033 unless you say, "Compared to what -- how 46:58.025 --> 47:00.255 are you breaking it apart?" 47:00.260 --> 47:00.670 Okay? 47:00.670 --> 47:03.270 Is all this true? 47:03.268 --> 47:06.238 So I've been weaving this fairytale for you, 47:06.237 --> 47:09.477 for the last couple of weeks, but is it true? 47:09.480 --> 47:11.870 Well, we can check it with experiment. 47:11.869 --> 47:14.629 For example, compare HH with HF. 47:14.630 --> 47:19.130 HH has perfect matching between the two atoms. 47:19.130 --> 47:22.480 In HF, there's a much bigger nuclear charge on F; 47:22.480 --> 47:25.970 electrons in the valence orbital are lower in energy on F 47:25.969 --> 47:27.279 than they are on H. 47:27.280 --> 47:29.800 Okay, so if we look at the σ orbital, 47:29.800 --> 47:31.540 the valence σ orbital, 47:31.539 --> 47:35.229 it's symmetrical in the case of H_2 and quite unsymmetrical in 47:35.231 --> 47:36.261 the case of HF. 47:36.260 --> 47:40.650 It's big on F and small on H, just as we were speaking of. 47:40.650 --> 47:43.880 That's the σ, big on F. Right? 47:43.880 --> 47:48.270 But there's also an antibonding orbital, σ, 47:48.271 --> 47:49.791 which has a node. 47:49.789 --> 47:54.279 So that one is the contrary; it's big on H, small on F. 47:54.280 --> 47:57.310 This is just what we were talking about a few minutes ago. 47:57.309 --> 48:00.019 And the electrons, of course, are only in the 48:00.023 --> 48:02.863 σ*, not in the σ*; 48:02.860 --> 48:05.310 there are only two electrons and that one's empty. 48:05.309 --> 48:09.779 And the * means that it's antibonding. 48:09.782 --> 48:10.752 Right? 48:10.750 --> 48:14.600 So it has the node between the nuclei, planar in the 48:14.597 --> 48:18.067 symmetrical case and bent in the case of HF; 48:18.070 --> 48:20.390 but it's still the node. 48:20.389 --> 48:23.529 Now, how about the experiment? 48:23.530 --> 48:25.880 Heterolysis, where you break, 48:25.882 --> 48:28.912 in order to get H^+ H^-, in one case, 48:28.907 --> 48:31.677 or H^+ F^- in the other case. 48:31.679 --> 48:34.719 In the case of HH, it costs 400 kilocalories to 48:34.717 --> 48:35.837 break the bond. 48:35.840 --> 48:39.760 In the case of HF, it costs only 373. 48:39.760 --> 48:41.960 Incidentally, this is a lot of energy, 48:41.960 --> 48:44.930 to break this bond, because you're putting both the 48:44.934 --> 48:46.664 electrons the same place. 48:46.659 --> 48:49.569 It can happen in solution, but it's not so easy in the gas 48:49.572 --> 48:51.772 phase, which is what we're talking about. 48:51.768 --> 48:57.178 Okay, so indeed we were right, that mismatch weakens the bond; 48:57.179 --> 49:01.679 for heterolysis, the HF bond is weaker. 49:01.679 --> 49:04.699 That's why you call it hydrofluoric acid, 49:04.704 --> 49:06.894 because it can easily break off an H. 49:06.889 --> 49:12.549 You don't call H_2 hydrogenic acid or something like that. 49:12.545 --> 49:13.335 Right? 49:13.340 --> 49:17.340 But if you break it into two atoms, 49:17.344 --> 49:22.444 two H atoms or an H atom and an F atom, then it costs only 104 49:22.436 --> 49:24.686 for HH, but 136 for HF. 49:24.690 --> 49:28.320 So the HF bond is stronger, if you're breaking to atoms. 49:28.320 --> 49:30.230 So that's the first verification, 49:30.226 --> 49:33.446 experimental verification, of what I've been talking to 49:33.445 --> 49:34.275 you about. 49:34.280 --> 49:37.520 And we're going to go on next time to talk about XH_3, 49:37.516 --> 49:40.876 which will have lots of experimental data that will show 49:40.875 --> 49:42.825 that this stuff is sensible. 49:42.829 --> 49:48.999