WEBVTT 00:00:00.000 --> 00:00:00.016 The following content is provided under a Creative 00:00:00.016 --> 00:00:00.022 Commons license. 00:00:00.022 --> 00:00:00.038 Your support will help MIT OpenCourseWare continue to 00:00:00.038 --> 00:00:00.054 offer high quality educational resources for free. 00:00:00.054 --> 00:00:00.072 To make a donation or view additional materials from 00:00:00.072 --> 00:00:00.088 hundreds of MIT courses, visit MIT OpenCourseWare at 00:00:00.088 --> 00:00:00.110 ocw.mit.edu. 00:00:00.110 --> 00:00:23.575 PROFESSOR: -- that this is not a quick clicker question, so 00:00:23.575 --> 00:00:26.090 you actually need to maybe write something down to figure 00:00:26.090 --> 00:00:26.740 out the answer. 00:00:26.740 --> 00:00:30.520 So if you haven't clicked in yet, or if you want to change 00:00:30.520 --> 00:00:33.050 your answer, keep in mind that you might need to jot down, 00:00:33.050 --> 00:00:36.420 for example, a Lewis structure before you can answer this 00:00:36.420 --> 00:00:59.900 question. 00:00:59.900 --> 00:01:01.480 -- and get in your final answer 00:01:01.480 --> 00:01:03.030 to the clicker question. 00:01:03.030 --> 00:01:05.970 For those of you just walking in now, you might not have a 00:01:05.970 --> 00:01:08.770 chance to get all of the thought process that you need 00:01:08.770 --> 00:01:11.260 in on this clicker question, because it is based on a Lewis 00:01:11.260 --> 00:01:13.700 structure, so we will go over it. 00:01:13.700 --> 00:01:16.880 But for those of you that have been here for 30 seconds or 00:01:16.880 --> 00:01:19.480 longer, see if you can get the right answer in here. 00:01:19.480 --> 00:01:24.450 All right, so OK, it looks like we have a very mixed 00:01:24.450 --> 00:01:26.380 response in terms of the answer to the 00:01:26.380 --> 00:01:28.030 clicker question today. 00:01:28.030 --> 00:01:30.240 Raise your hand if you didn't have time to figure out the 00:01:30.240 --> 00:01:32.360 Lewis structure. 00:01:32.360 --> 00:01:34.740 OK, so that accounts for some of you. 00:01:34.740 --> 00:01:37.160 Let's go over the correct answer this question. 00:01:37.160 --> 00:01:39.000 So, who got the right answer -- 00:01:39.000 --> 00:01:40.890 31% of us. 00:01:40.890 --> 00:01:44.810 This is not the kind of percentages we're looking for, 00:01:44.810 --> 00:01:46.260 so let's go over this. 00:01:46.260 --> 00:01:52.150 In class on Monday, we did go over the geometries, and the 00:01:52.150 --> 00:01:55.530 geometries themselves are very straightforward, once you know 00:01:55.530 --> 00:01:58.400 what the Lewis structure is, but remember, you can't just 00:01:58.400 --> 00:02:00.300 always look at a molecule and automatically 00:02:00.300 --> 00:02:01.060 know the Lewis structure. 00:02:01.060 --> 00:02:02.960 We actually need to think about those valence electrons. 00:02:02.960 --> 00:02:08.500 So, here we're dealing with selenium hydride, so s e h 2. 00:02:08.500 --> 00:02:12.020 I told you that there's 6 valence electrons in selenium, 00:02:12.020 --> 00:02:16.310 so we have 6 there, plus 1 for each of the hydrogen. 00:02:16.310 --> 00:02:19.420 So what we should have is 8 valence electrons 00:02:19.420 --> 00:02:20.980 in our Lewis structure. 00:02:20.980 --> 00:02:25.050 How many electrons do we need to have full valence shells? 00:02:25.050 --> 00:02:26.470 STUDENT: [INAUDIBLE] 00:02:26.470 --> 00:02:27.010 PROFESSOR: 12, that's right. 00:02:27.010 --> 00:02:32.120 We need 8 plus 4 is 12 for full shells. 00:02:32.120 --> 00:02:41.300 That means that we need 12 minus 8, or 4 bonding 00:02:41.300 --> 00:02:44.870 electrons in our structure. 00:02:44.870 --> 00:02:46.990 So I tried to give you one that you could draw pretty 00:02:46.990 --> 00:02:49.170 quickly, it just has hydrogens in It. 00:02:49.170 --> 00:02:52.550 So we have s e h 2. 00:02:52.550 --> 00:02:55.600 We can do our 4 bonding electrons. 00:02:55.600 --> 00:02:57.660 How many valence electrons do we have left? 00:02:57.660 --> 00:02:59.500 STUDENT: [INAUDIBLE] 00:02:59.500 --> 00:03:00.220 PROFESSOR: 4, that's right. 00:03:00.220 --> 00:03:04.740 So, we need to fill our octet for selenium, so 1, 2, 3, 4. 00:03:04.740 --> 00:03:07.520 So, this is our Lewis structure here, hopefully you 00:03:07.520 --> 00:03:09.600 can see why it's not linear. 00:03:09.600 --> 00:03:13.570 If it were linear, which 32% of you seem have thought, that 00:03:13.570 --> 00:03:17.150 would have meant that our Lewis structure had no lone 00:03:17.150 --> 00:03:20.290 pairs in it, right, and that's not the case. 00:03:20.290 --> 00:03:23.330 We have two lone pairs, so if we thought about what the 00:03:23.330 --> 00:03:26.040 bonds were everywhere, it would be 109 . 00:03:26.040 --> 00:03:29.540 5, but it's bent because we're only looking at the bonds, 00:03:29.540 --> 00:03:31.930 we're not counting the Lewis structures in naming our 00:03:31.930 --> 00:03:34.450 geometry, but they do affect the angles. 00:03:34.450 --> 00:03:37.600 And it turns out that it's actually less than 109 . 00:03:37.600 --> 00:03:40.540 5, because those lone pairs are pushing the bonds even 00:03:40.540 --> 00:03:41.700 further away. 00:03:41.700 --> 00:03:44.590 So, does this make sense to everyone if you think 00:03:44.590 --> 00:03:47.450 about it this way? 00:03:47.450 --> 00:03:48.310 Pretty much, okay. 00:03:48.310 --> 00:03:52.570 So, we'll try another clicker question like this later. 00:03:52.570 --> 00:03:55.140 Some of these questions that look very straightforward just 00:03:55.140 --> 00:03:57.580 naming the geometry, you have to remember to do the first 00:03:57.580 --> 00:04:00.580 step before you jump in and go ahead with a naming. 00:04:00.580 --> 00:04:02.770 So you'll got plenty of practice with this on your 00:04:02.770 --> 00:04:04.340 problem-set if you haven't already. 00:04:04.340 --> 00:04:06.050 All right. 00:04:06.050 --> 00:04:09.030 So before we start in with today's notes, I do want to 00:04:09.030 --> 00:04:11.690 mention that this morning the Nobel Prize in 00:04:11.690 --> 00:04:13.420 chemistry was announced. 00:04:13.420 --> 00:04:17.200 This is an exciting week in science in general because we 00:04:17.200 --> 00:04:19.290 got to hear another Nobel Prize every 00:04:19.290 --> 00:04:21.300 morning pretty much. 00:04:21.300 --> 00:04:25.910 So, let's settle down for a second and start listening. 00:04:25.910 --> 00:04:26.230 All right. 00:04:26.230 --> 00:04:29.400 So, today we're going to be talking about molecular 00:04:29.400 --> 00:04:31.775 orbital theory, but first I wanted to just mention, in 00:04:31.775 --> 00:04:34.810 case some of you didn't hear what the Nobel Prize was this 00:04:34.810 --> 00:04:37.230 morning, and this was in chemistry, it went to three 00:04:37.230 --> 00:04:38.430 different chemists. 00:04:38.430 --> 00:04:47.600 Osamu Shimomura, who's a Japanese chemist, and then 00:04:47.600 --> 00:04:50.970 Martin Chalfi who's at Columbia, and Robert Chen 00:04:50.970 --> 00:04:52.880 who's at U. C. San Diego. 00:04:52.880 --> 00:04:55.670 The three of these chemists split the Nobel Prize this 00:04:55.670 --> 00:04:59.490 morning for their discovery and/or their application of 00:04:59.490 --> 00:05:01.840 using green fluorescent protein, which 00:05:01.840 --> 00:05:03.090 is also called GFP. 00:05:03.090 --> 00:05:05.970 How many of you have heard of GFP before? 00:05:05.970 --> 00:05:06.460 Oh, that's so great. 00:05:06.460 --> 00:05:07.070 OK. 00:05:07.070 --> 00:05:08.660 Many of you have heard of GFP. 00:05:08.660 --> 00:05:11.850 For some of you that haven't I'll just say that it's a 00:05:11.850 --> 00:05:16.130 protein, it's 238 amino acids, which means that it's about 00:05:16.130 --> 00:05:19.940 1,000, actually more than 1,000 atoms in size, and this 00:05:19.940 --> 00:05:21.600 protein is fluorescent. 00:05:21.600 --> 00:05:24.960 The protein was first discovered and first isolated 00:05:24.960 --> 00:05:26.760 from this jellyfish here. 00:05:26.760 --> 00:05:30.890 This was done by Shimomura, and he did this in 00:05:30.890 --> 00:05:32.090 the 60's and 70's. 00:05:32.090 --> 00:05:35.340 He actually recognized and, of course, many people recognized 00:05:35.340 --> 00:05:38.080 that this jellyfish was fluorescent, and he isolated 00:05:38.080 --> 00:05:41.020 the actual protein, and determined and proved that 00:05:41.020 --> 00:05:43.620 this protein was sufficient to cause this fluorescence. 00:05:43.620 --> 00:05:47.140 So, in terms of thinking about applications of why it's so 00:05:47.140 --> 00:05:49.360 exciting that you have this fluorescent protein, other 00:05:49.360 --> 00:05:51.670 than it's always really fun to look at things that are 00:05:51.670 --> 00:05:54.810 fluorescent, we can think about in terms of biology why 00:05:54.810 --> 00:05:58.080 it's so exciting, you can actually tag this protein to 00:05:58.080 --> 00:06:00.850 any other protein that you're studying and now you have a 00:06:00.850 --> 00:06:02.640 visual handle on what's going on. 00:06:02.640 --> 00:06:05.340 So, for example, if you were interested in some protein 00:06:05.340 --> 00:06:08.150 involved in cancer, you could tag it with GFP. 00:06:08.150 --> 00:06:11.240 You could watch where it localizes in the cell, there 00:06:11.240 --> 00:06:13.440 are fluorescent assays you could use to determine what 00:06:13.440 --> 00:06:15.400 other proteins it interacts with. 00:06:15.400 --> 00:06:18.190 You could see, for example, when it's expressed in a 00:06:18.190 --> 00:06:19.880 cancer cell, and where it's expressed. 00:06:19.880 --> 00:06:21.900 There are all sorts of things you can do once you can 00:06:21.900 --> 00:06:24.200 visualize something with fluorescence. 00:06:24.200 --> 00:06:27.510 The reason it is so exciting that it's a protein, and it's 00:06:27.510 --> 00:06:30.060 a protein, this is the structure here, it's a ribbon 00:06:30.060 --> 00:06:32.650 structure so you can kind of see what it looks like, it's 00:06:32.650 --> 00:06:35.150 made up of all natural amino acids. 00:06:35.150 --> 00:06:37.840 So this means we can code for it in DNA, you don't have to 00:06:37.840 --> 00:06:40.100 worry how am I going to get into the cell. 00:06:40.100 --> 00:06:43.370 All you have to do is mutate the DNA, which is very 00:06:43.370 --> 00:06:46.760 straightforward to do in molecular biology, and now you 00:06:46.760 --> 00:06:50.070 can tag absolutely any protein that you're interested in. 00:06:50.070 --> 00:06:53.150 So, as I said, this was first discovered and isolated from 00:06:53.150 --> 00:06:53.890 the jellyfish. 00:06:53.890 --> 00:06:56.750 This was done by Shimomura -- that was kind of the first 00:06:56.750 --> 00:07:00.550 step in this process of having it become such a useful tool. 00:07:00.550 --> 00:07:04.530 And then, many years later, not until 1994 did Martin 00:07:04.530 --> 00:07:08.810 Chalfi, at Columbia, show that yes, I can, in fact, take the 00:07:08.810 --> 00:07:11.260 DNA and put it into a different organism, and he put 00:07:11.260 --> 00:07:13.390 it into e coli, a bacteria. 00:07:13.390 --> 00:07:16.200 And what he could show was that it could be expressed, 00:07:16.200 --> 00:07:19.560 this is a picture from his 1994 science paper, in that e 00:07:19.560 --> 00:07:22.160 coli, and it is going to fluoresce green. 00:07:22.160 --> 00:07:24.510 Now, the first application tends to not be quite as 00:07:24.510 --> 00:07:27.060 exciting as, for example, all the other organisms people 00:07:27.060 --> 00:07:29.820 have put it in since then -- you can have flies, you see 00:07:29.820 --> 00:07:32.830 transgenic mice that are glowing green with this GFP. 00:07:32.830 --> 00:07:36.670 Of course, that's not the useful application for it, 00:07:36.670 --> 00:07:38.610 it's more of a proof of principle, but it does show 00:07:38.610 --> 00:07:42.240 you that you can put it in for studies in any organisms. 00:07:42.240 --> 00:07:45.160 And the field was really pushed forward by the 00:07:45.160 --> 00:07:49.550 discoveries of Robert Chen at UC San Diego, and what he did 00:07:49.550 --> 00:07:53.370 was he actually figured out how it was that this protein 00:07:53.370 --> 00:07:56.030 fluoresced, what caused the actual fluorescence. 00:07:56.030 --> 00:08:00.050 And once he did that, both he and many other scientists, 00:08:00.050 --> 00:08:02.250 could then, once they understood what caused the 00:08:02.250 --> 00:08:05.450 fluorescence, make little changes to the actual protein, 00:08:05.450 --> 00:08:07.300 and tune what the properties of that 00:08:07.300 --> 00:08:08.890 fluorescent protein were. 00:08:08.890 --> 00:08:11.630 So now, for example, there are a whole range, just a whole 00:08:11.630 --> 00:08:14.050 rainbow of fluorescent proteins that can be used. 00:08:14.050 --> 00:08:17.500 And I'm sure you can imagine that if you want to label onw 00:08:17.500 --> 00:08:20.250 protein green and one red and one yellow, now you can start 00:08:20.250 --> 00:08:23.630 looking at really complex biological processes. 00:08:23.630 --> 00:08:25.910 So, it's pretty rare that chemistry makes 00:08:25.910 --> 00:08:26.630 the every day news. 00:08:26.630 --> 00:08:29.470 So hopefully you'll all look in the normal papers today, 00:08:29.470 --> 00:08:31.550 not just the scientific journals, and get to read 00:08:31.550 --> 00:08:32.570 something about chemistry. 00:08:32.570 --> 00:08:35.430 It's always fun to see how its described in The New York 00:08:35.430 --> 00:08:37.540 Times or in The Boston Globe. 00:08:37.540 --> 00:08:39.520 The other thing I wanted to mention and I'm not sure if 00:08:39.520 --> 00:08:41.020 the exhibit's still there. 00:08:41.020 --> 00:08:43.340 But there was an exhibit of jellyfish, I know at least 00:08:43.340 --> 00:08:46.760 until last year, at the Boston Museum of Science, and all of 00:08:46.760 --> 00:08:48.370 you guys can get in there free. 00:08:48.370 --> 00:08:50.400 And it's neat to see the glowing jellyfish and think 00:08:50.400 --> 00:08:53.020 about the fluorescent protein that's in them. 00:08:53.020 --> 00:08:55.610 So, I encourage you to do that the next time you have some 00:08:55.610 --> 00:09:00.940 free time on your hands, maybe at IAP or some time like that. 00:09:00.940 --> 00:09:03.680 All right, so let's move into today's notes. 00:09:03.680 --> 00:09:06.480 Today we're talking about molecular orbital theory. 00:09:06.480 --> 00:09:10.510 This is a shift, this is a new topic that we're starting. 00:09:10.510 --> 00:09:13.990 So far we've exclusively been using Lewis structures any 00:09:13.990 --> 00:09:17.170 time we've tried to describe bonding within molecules. 00:09:17.170 --> 00:09:19.880 Lewis structures are really useful, we use them all the 00:09:19.880 --> 00:09:21.080 time in chemistry. 00:09:21.080 --> 00:09:23.550 And they're useful because, first of all, they're easy to 00:09:23.550 --> 00:09:27.320 depict, they're easy to draw -- relatively easy once we get 00:09:27.320 --> 00:09:28.550 all the rules down. 00:09:28.550 --> 00:09:31.730 And also they're accurate over 90% of the time. 00:09:31.730 --> 00:09:34.570 But they're not accurate all the time in predicting bonding 00:09:34.570 --> 00:09:37.970 within molecules, and the reason for this is because 00:09:37.970 --> 00:09:39.710 Lewis structures are not, in fact, 00:09:39.710 --> 00:09:41.720 based on quantum mechanics. 00:09:41.720 --> 00:09:45.410 So, molecular orbital theory, on the other hand, is based on 00:09:45.410 --> 00:09:46.640 quantum mechanics. 00:09:46.640 --> 00:09:49.760 And specifically, MO theory is the quantum mechanical 00:09:49.760 --> 00:09:53.780 description of wave functions within molecules. 00:09:53.780 --> 00:09:56.280 So, saying wave functions within molecules might sound a 00:09:56.280 --> 00:09:59.480 little confusing, but remember we spent a lot of time talking 00:09:59.480 --> 00:10:03.040 about wave functions within atoms, and we know how to 00:10:03.040 --> 00:10:05.320 describe that, we know that a wave function just means an 00:10:05.320 --> 00:10:06.000 atomic orbital. 00:10:06.000 --> 00:10:09.210 It's the same thing with molecules -- a molecular wave 00:10:09.210 --> 00:10:11.370 function just means a molecular orbital. 00:10:11.370 --> 00:10:13.600 So, we'll start today talking about the two kinds of 00:10:13.600 --> 00:10:15.910 molecular orbitals, we can talk about bonding or 00:10:15.910 --> 00:10:17.580 anti-bonding orbitals. 00:10:17.580 --> 00:10:20.250 Then we're going to actually use MO theory to describe 00:10:20.250 --> 00:10:22.830 bonding within these molecules, and we'll start 00:10:22.830 --> 00:10:25.740 with homonuclear diatomic molecules. 00:10:25.740 --> 00:10:30.070 Diatomic mean it's di atomic, it's made up of two atoms, and 00:10:30.070 --> 00:10:33.270 homonuclear means that those two are the same atoms. Then 00:10:33.270 --> 00:10:35.760 at the end, we'll look at an example with a heteronuclear 00:10:35.760 --> 00:10:37.330 diatomic molecules. 00:10:37.330 --> 00:10:40.480 So, again, the same thing, but now two different atoms. 00:10:40.480 --> 00:10:43.560 So, I will point out, in terms of MO theory, because it 00:10:43.560 --> 00:10:46.330 rigorously does take into account quantum mechanics, it 00:10:46.330 --> 00:10:48.650 starts to become complicated once we go 00:10:48.650 --> 00:10:50.830 beyond diatomic molecules. 00:10:50.830 --> 00:10:53.930 So we're going to limit in our discussion in 511-1 for 00:10:53.930 --> 00:10:56.760 molecular orbital theory to diatomic molecules. 00:10:56.760 --> 00:10:59.220 However, on Friday we will use a different approach so we can 00:10:59.220 --> 00:11:02.360 talk about bonding within atoms that have more than two 00:11:02.360 --> 00:11:06.920 atoms, molecules with more than two atoms. 00:11:06.920 --> 00:11:09.300 All right, so one thing that I first want to point out about 00:11:09.300 --> 00:11:11.730 MO theory that is a big difference from Lewis 00:11:11.730 --> 00:11:15.350 structures, is that in MO theory valence electrons are 00:11:15.350 --> 00:11:18.710 de-localized over the entire molecule. 00:11:18.710 --> 00:11:21.150 So, when we talked about Lewis structures, we actually 00:11:21.150 --> 00:11:24.330 assigned electrons to individual atoms or to 00:11:24.330 --> 00:11:25.670 individual bonds. 00:11:25.670 --> 00:11:28.280 Whereas in molecular orbital theory, what I'm telling you 00:11:28.280 --> 00:11:32.060 is instead we understand that the electrons are spread all 00:11:32.060 --> 00:11:34.780 over the molecule, they're not just associated with a single 00:11:34.780 --> 00:11:37.260 atom or a single bond. 00:11:37.260 --> 00:11:40.270 So specifically, what we do associate them instead is 00:11:40.270 --> 00:11:43.970 within molecular orbitals, and what we say is that they can 00:11:43.970 --> 00:11:45.770 be either in bonding or anti-bonding orbitals. 00:11:45.770 --> 00:11:49.210 And again, I want to point out that a molecular orbital, we 00:11:49.210 --> 00:11:50.740 can also call that a wave function, 00:11:50.740 --> 00:11:51.920 they're the same thing. 00:11:51.920 --> 00:11:55.370 And these orbitals arise from the combination of individual 00:11:55.370 --> 00:11:55.910 atomic orbital. 00:11:55.910 --> 00:11:59.310 So, if we have two atomic orbitals coming together from 00:11:59.310 --> 00:12:02.230 two different atoms and they combine, what we end up 00:12:02.230 --> 00:12:04.060 forming is a molecular orbital. 00:12:04.060 --> 00:12:06.460 The reason that we can talk about this is remember that 00:12:06.460 --> 00:12:08.490 we're talking about wave functions, we're talking about 00:12:08.490 --> 00:12:11.420 waves, so we can have constructive interference in 00:12:11.420 --> 00:12:16.300 which two different orbitals can constructively interfere, 00:12:16.300 --> 00:12:18.630 we can also have destructive interference. 00:12:18.630 --> 00:12:20.970 So, we'll start by taking a look at constructive 00:12:20.970 --> 00:12:24.030 interference, and another way to explain this is just to say 00:12:24.030 --> 00:12:26.540 again, molecular orbitals are a linear 00:12:26.540 --> 00:12:28.120 combination of atomic orbitals. 00:12:28.120 --> 00:12:31.970 So, let's start our discussion of a bonding orbital. 00:12:31.970 --> 00:12:34.730 Our simplest case that we can look at would be if we had two 00:12:34.730 --> 00:12:36.620 1 s orbitals coming together. 00:12:36.620 --> 00:12:39.160 So let's say, for example, in a hydrogen atom. 00:12:39.160 --> 00:12:42.800 So in hydrogen atom a, I'll depict that here where the 00:12:42.800 --> 00:12:46.500 nucleus is this dot, and then the circle is what I'm 00:12:46.500 --> 00:12:49.070 depicting as the wave function. 00:12:49.070 --> 00:12:51.740 It makes sense to draw the wave function as a circle, 00:12:51.740 --> 00:12:53.440 because we do know that 1 s orbitals 00:12:53.440 --> 00:12:55.220 are spherically symmetric. 00:12:55.220 --> 00:12:58.180 So, we can say that a circle is a good approximation for a 00:12:58.180 --> 00:12:59.810 1 s wave function. 00:12:59.810 --> 00:13:02.950 Similarly, with the second hydrogen atom, we've got the 00:13:02.950 --> 00:13:06.710 nucleus in the middle, and the 1 s b wave function around it. 00:13:06.710 --> 00:13:08.490 So these are atomic orbitals. 00:13:08.490 --> 00:13:11.040 What we're going to do in forming a molecule is just 00:13:11.040 --> 00:13:15.650 bring these two orbitals close together such that now we have 00:13:15.650 --> 00:13:18.920 their nucleus, the two nuclei, at a distance apart that's 00:13:18.920 --> 00:13:21.360 equal to the bond length. 00:13:21.360 --> 00:13:23.970 And what we end up forming is a molecular orbital, because 00:13:23.970 --> 00:13:27.610 as we bring these two atomic orbitals close together, the 00:13:27.610 --> 00:13:30.500 part between them, that wave function, constructively 00:13:30.500 --> 00:13:33.730 interferes such that in our molecular orbital, we actually 00:13:33.730 --> 00:13:39.440 have a lot of wave function in between the two nuclei. 00:13:39.440 --> 00:13:42.200 So we can go ahead and name our molecular orbital, just 00:13:42.200 --> 00:13:45.270 like we know how to name our atomic orbitals. 00:13:45.270 --> 00:13:47.710 And I'm going to name this sigma 1 s. 00:13:47.710 --> 00:13:50.530 The 1 s just comes from the fact that the molecular 00:13:50.530 --> 00:13:53.920 orbital is a combination of two 1 s atomic orbitals. 00:13:53.920 --> 00:13:56.450 And the sigma tells us something about the symmetry 00:13:56.450 --> 00:13:59.140 of this molecular orbital, specifically that it's 00:13:59.140 --> 00:14:01.770 cylindrically symmetric about the bond axis. 00:14:01.770 --> 00:14:05.340 So that is the bond axis -- it's just the axis between the 00:14:05.340 --> 00:14:06.470 two nuclei. 00:14:06.470 --> 00:14:09.340 Sometimes it's also called the internuclear axis. 00:14:09.340 --> 00:14:12.590 So any time you have two atoms bonding, the bond axis is just 00:14:12.590 --> 00:14:15.550 the axis that they're bonding along. 00:14:15.550 --> 00:14:18.520 Another thing I want to point out about every sigma orbital 00:14:18.520 --> 00:14:21.925 that you see, and it will make more sense when we contrast it 00:14:21.925 --> 00:14:23.050 with pi orbitals later. 00:14:23.050 --> 00:14:26.610 But in sigma orbitals, you have no nodal planes along the 00:14:26.610 --> 00:14:29.480 bond axis, so if we had a nodal plane here, we'd see an 00:14:29.480 --> 00:14:31.820 area where the wave function was equal to zero. 00:14:31.820 --> 00:14:32.780 We don't see that. 00:14:32.780 --> 00:14:35.110 It will make more sense when we can show you one where it 00:14:35.110 --> 00:14:36.400 does have that area. 00:14:36.400 --> 00:14:40.210 But keep in mind sigma orbitals have no nodal planes 00:14:40.210 --> 00:14:41.440 along the bond axis. 00:14:41.440 --> 00:14:43.160 All right. 00:14:43.160 --> 00:14:45.250 So, let's look at this in another way, sometimes it's 00:14:45.250 --> 00:14:47.040 hard to picture these waves combining. 00:14:47.040 --> 00:14:50.200 So let's think of them a little bit more by graphing 00:14:50.200 --> 00:14:53.210 the amplitude of the wave, and seeing how we can have this 00:14:53.210 --> 00:14:54.710 constructive interference. 00:14:54.710 --> 00:14:57.550 So again, if we think of a graph of the wave function, we 00:14:57.550 --> 00:15:01.180 had the wave function is at its highest amplitude when 00:15:01.180 --> 00:15:03.320 it's lined up with the nucleus, and then as we got 00:15:03.320 --> 00:15:07.300 further away from the nucleus, the amplitude of the wave 00:15:07.300 --> 00:15:11.700 function ends up tapering off until -- it never hits zero 00:15:11.700 --> 00:15:13.340 exactly, but it goes down very low. 00:15:13.340 --> 00:15:18.030 So we can draw that for 1 s a, we can also draw it for 1 s b, 00:15:18.030 --> 00:15:20.250 and what I'm saying for the molecular wave function is 00:15:20.250 --> 00:15:22.820 that we have the interference between the two, and we have a 00:15:22.820 --> 00:15:25.870 constructive interference, so we end up adding these two 00:15:25.870 --> 00:15:27.940 wave functions together. 00:15:27.940 --> 00:15:30.280 So, we're talking about wave functions and we know that 00:15:30.280 --> 00:15:35.140 means orbitals, but this is -- probably the better way to 00:15:35.140 --> 00:15:36.460 think about is the physical 00:15:36.460 --> 00:15:38.820 interpretation of the wave function. 00:15:38.820 --> 00:15:41.720 So what is the wave function squared going to be equal to? 00:15:41.720 --> 00:15:42.342 STUDENT: [INAUDIBLE] 00:15:42.342 --> 00:15:46.260 PROFESSOR: Probability density, yes. 00:15:46.260 --> 00:15:49.010 Probability density of finding an electron within that 00:15:49.010 --> 00:15:52.250 molecule in some given volume. 00:15:52.250 --> 00:15:54.630 So let's think about that instead, let's think about 00:15:54.630 --> 00:15:55.910 probability density. 00:15:55.910 --> 00:15:58.770 So if we're talking about probability density that's the 00:15:58.770 --> 00:16:00.450 wave function squared. 00:16:00.450 --> 00:16:03.290 But now we're talking not about an atomic wave function, 00:16:03.290 --> 00:16:05.500 we're talking about a molecular wave function. 00:16:05.500 --> 00:16:08.650 So to talk about it's squared, we're going to say it's sigma 00:16:08.650 --> 00:16:11.580 1 s squared. 00:16:11.580 --> 00:16:13.890 Oh, and actually before you skip your page in the notes, I 00:16:13.890 --> 00:16:17.090 realized I should write out for you what the addition is 00:16:17.090 --> 00:16:18.190 to start with. 00:16:18.190 --> 00:16:23.350 So, when we're combining two waves, what we have is 1 s a 00:16:23.350 --> 00:16:26.810 that we're adding together with 1 s for 00:16:26.810 --> 00:16:29.150 b, the second atom. 00:16:29.150 --> 00:16:32.450 And what we end up for our molecular wave 00:16:32.450 --> 00:16:34.740 function is sigma 1 s. 00:16:34.740 --> 00:16:38.020 So this is what we call our molecular orbital. 00:16:38.020 --> 00:16:41.780 All right, so that will now allow you to turn the page, I 00:16:41.780 --> 00:16:44.880 think, and we can take a look at the probability. 00:16:44.880 --> 00:16:48.500 So the probability again, that's just the orbital 00:16:48.500 --> 00:16:50.870 squared, the wave function squared. 00:16:50.870 --> 00:16:54.680 So when we write that out, we just write sigma 1 s squared, 00:16:54.680 --> 00:16:57.350 or we can break it up into its individual parts, there's no 00:16:57.350 --> 00:16:59.080 reason we can't do that as well. 00:16:59.080 --> 00:17:04.320 So just to say that it's 1 s squared plus 1 s b, all of 00:17:04.320 --> 00:17:07.030 that together squared. 00:17:07.030 --> 00:17:09.910 So if we write out every term individually, what we end up 00:17:09.910 --> 00:17:12.940 with is essentially just the probability density for the 00:17:12.940 --> 00:17:15.740 first atom, then the probability density for the 00:17:15.740 --> 00:17:19.900 second atom, and then we have this last term here, and this 00:17:19.900 --> 00:17:23.090 is what ends up being the interference term. 00:17:23.090 --> 00:17:25.990 So in this case where we're adding it together, this is 00:17:25.990 --> 00:17:27.970 going to be constructive interference. 00:17:27.970 --> 00:17:31.250 So in this case the cross term represents constructive 00:17:31.250 --> 00:17:37.250 interference between the two 1 s atomic wave functions. 00:17:37.250 --> 00:17:38.580 And this again is what we're going to 00:17:38.580 --> 00:17:41.710 call a bonding orbital. 00:17:41.710 --> 00:17:44.550 So it can often make a lot more sense if we think about 00:17:44.550 --> 00:17:45.900 things in terms of energy. 00:17:45.900 --> 00:17:49.010 We've been discussing energy diagrams a lot in this class, 00:17:49.010 --> 00:17:51.300 it's a very good way to visualize exactly 00:17:51.300 --> 00:17:52.510 what's going on. 00:17:52.510 --> 00:17:55.090 So, let's think of the energy of interaction when we're 00:17:55.090 --> 00:17:58.800 comparing atomic orbitals to molecular bonding orbitals. 00:17:58.800 --> 00:18:01.510 And what you find is when you have a bonding orbital, the 00:18:01.510 --> 00:18:05.480 energy decreases compared to the atomic orbitals. 00:18:05.480 --> 00:18:08.890 So you can see here in this slide we have the atomic 00:18:08.890 --> 00:18:12.370 orbitals for the two hydrogen atoms, each of them have one 00:18:12.370 --> 00:18:16.730 electron in them, hydrogen has one electron in a 1 s orbital. 00:18:16.730 --> 00:18:18.650 So, if we look at the molecular orbital, that's 00:18:18.650 --> 00:18:22.050 actually going to be lower in energy than either of the two 00:18:22.050 --> 00:18:23.080 atomic orbitals. 00:18:23.080 --> 00:18:26.160 So it's going to be favorable for the electrons instead to 00:18:26.160 --> 00:18:29.690 go to that lower energy state and be within 00:18:29.690 --> 00:18:31.170 the molecular orbital. 00:18:31.170 --> 00:18:35.700 So, let's draw in our electrons there, so we have 00:18:35.700 --> 00:18:40.080 our two electrons now in the molecular orbital. 00:18:40.080 --> 00:18:42.180 So any time that you're drawing these molecular 00:18:42.180 --> 00:18:45.070 orbital diagrams, you want to keep in mind that the number 00:18:45.070 --> 00:18:48.090 of electrons that you have in atomic orbitals, you need to 00:18:48.090 --> 00:18:49.620 add those together and put that many 00:18:49.620 --> 00:18:51.640 electrons into your molecule. 00:18:51.640 --> 00:18:54.890 Right, we had one from each atom, so that means we need a 00:18:54.890 --> 00:18:57.290 total of two in our molecular orbital. 00:18:57.290 --> 00:18:59.740 And what you can see directly from looking at this energy 00:18:59.740 --> 00:19:02.780 level diagram, is that the molecule that we have is now 00:19:02.780 --> 00:19:05.650 more stable in the individual atoms. That makes sense 00:19:05.650 --> 00:19:07.710 because we're lower in energy, the electrons are 00:19:07.710 --> 00:19:09.810 now lower in energy. 00:19:09.810 --> 00:19:13.450 So that's the idea of a bonding molecular orbital. 00:19:13.450 --> 00:19:16.100 Since we're talking about wave functions, since we're talking 00:19:16.100 --> 00:19:19.110 about the properties of waves, we don't only have 00:19:19.110 --> 00:19:21.780 constructive interference, we can also imagine a case where 00:19:21.780 --> 00:19:24.130 we would have destructive interference. 00:19:24.130 --> 00:19:27.090 Just like we see destructive interference with water waves 00:19:27.090 --> 00:19:29.410 or with light waves, we can also see destructive 00:19:29.410 --> 00:19:30.870 interference with orbitals. 00:19:30.870 --> 00:19:33.420 So, let's think about what that would look like. 00:19:33.420 --> 00:19:37.640 So in this case we would have 1 s a and 1 s b, and instead 00:19:37.640 --> 00:19:41.380 we would subtract one from the other, and what we would see 00:19:41.380 --> 00:19:44.850 is that instead of having additional, more wave function 00:19:44.850 --> 00:19:47.370 in the middle here, we've actually cancelled out the 00:19:47.370 --> 00:19:50.180 wave function and we end up with a node. 00:19:50.180 --> 00:19:53.100 So we can also name this orbital, and this orbital 00:19:53.100 --> 00:19:56.320 we're going to call sigma 1 s star. 00:19:56.320 --> 00:20:00.210 So if we name this orbital, this is an anti-bonding 00:20:00.210 --> 00:20:00.880 molecular orbital. 00:20:00.880 --> 00:20:03.160 So we had bonding and now we're talking about 00:20:03.160 --> 00:20:04.520 anti-bonding. 00:20:04.520 --> 00:20:08.360 When we talk about anti-bonding, essentially 00:20:08.360 --> 00:20:14.570 we're taking 1 s a and now we're subtracting 1 s b, and 00:20:14.570 --> 00:20:18.520 what we end up with again is sigma 1 s, and the important 00:20:18.520 --> 00:20:21.400 thing to remember is to write this star here. 00:20:21.400 --> 00:20:23.110 So any time you see a star that means an 00:20:23.110 --> 00:20:27.700 anti-bonding orbital. 00:20:27.700 --> 00:20:30.600 Again we can look at this in terms of thinking about a 00:20:30.600 --> 00:20:33.510 picture this way, in terms of drawing the wave function out 00:20:33.510 --> 00:20:34.730 on an axis. 00:20:34.730 --> 00:20:38.270 So we have 1 s a, and we're drawing this as having a 00:20:38.270 --> 00:20:41.300 positive amplitude, but since we have destructive 00:20:41.300 --> 00:20:45.030 interference we're going to draw 1 s b as having the 00:20:45.030 --> 00:20:47.580 opposite sign, so we have a plus and a 00:20:47.580 --> 00:20:49.380 minus in terms of signs. 00:20:49.380 --> 00:20:51.780 So that should make it very easy to picture that this is 00:20:51.780 --> 00:20:53.440 being cancelled out in the middle. 00:20:53.440 --> 00:20:57.600 If we overlay what the actual molecular orbital is on top of 00:20:57.600 --> 00:21:00.490 it, what you see is that in the center you end up 00:21:00.490 --> 00:21:03.650 cancelling out the wave function entirely. 00:21:03.650 --> 00:21:08.480 So this is the 1 s star, sigma 1 s star orbital, and what you 00:21:08.480 --> 00:21:12.390 have in the center here is a node, right in the center 00:21:12.390 --> 00:21:15.060 between the two nuclei. 00:21:15.060 --> 00:21:17.670 So again if we look at this in terms of its physical 00:21:17.670 --> 00:21:21.170 interpretation or probability density, what we need to do is 00:21:21.170 --> 00:21:22.960 square the wave function. 00:21:22.960 --> 00:21:27.970 So if we square sigma 1 s star, we flip the amplitude so 00:21:27.970 --> 00:21:31.280 it's all positive now, but again we still have this node 00:21:31.280 --> 00:21:32.400 right in the middle. 00:21:32.400 --> 00:21:34.680 So if we talk about the probability density and we 00:21:34.680 --> 00:21:38.630 write that in, it's going to be sigma 1 s star squared, so 00:21:38.630 --> 00:21:42.730 now we're talking about 1 s a minus 1 s b, all 00:21:42.730 --> 00:21:44.670 of that being squared. 00:21:44.670 --> 00:21:47.480 And again, if we write out what all the terms are, we 00:21:47.480 --> 00:21:52.270 again have 1 s a squared plus 1 s b squared, but now what 00:21:52.270 --> 00:21:54.510 we're doing is we're actually subtracting the 00:21:54.510 --> 00:21:56.200 interference term. 00:21:56.200 --> 00:21:59.110 So if we're subtracting the interference term, what we 00:21:59.110 --> 00:22:04.860 have here now is destructive interference. 00:22:04.860 --> 00:22:07.900 So let's think about the energy of interaction here. 00:22:07.900 --> 00:22:11.020 When we were talking about constructive interference, we 00:22:11.020 --> 00:22:14.350 had more electron density in between the 2 nuclei. 00:22:14.350 --> 00:22:17.810 So that lowered the energy of the molecular orbital. 00:22:17.810 --> 00:22:20.360 So, bonding orbitals are down here. 00:22:20.360 --> 00:22:22.910 But when we think about where anti-bonding orbitals should 00:22:22.910 --> 00:22:25.820 be, it should be higher in energy. 00:22:25.820 --> 00:22:29.070 It's increased compared to the atomic orbitals. 00:22:29.070 --> 00:22:33.240 So we would label our anti-bonding orbital higher in 00:22:33.240 --> 00:22:37.110 energy than our 1 s atomic orbitals. 00:22:37.110 --> 00:22:39.190 So, let's think a little bit about what this means. 00:22:39.190 --> 00:22:42.380 First of all, again to repeat, any time we see the star, 00:22:42.380 --> 00:22:46.240 sigma 1 s star, that's an anti-bonding orbital. 00:22:46.240 --> 00:22:48.610 When we talk about that, basically what we're saying, 00:22:48.610 --> 00:22:51.440 and you can see that because of that negative interference, 00:22:51.440 --> 00:22:55.490 we actually have less electron density between the nuclei 00:22:55.490 --> 00:22:58.470 than we did when they were two separate atoms. So you can see 00:22:58.470 --> 00:23:01.670 that this is non-bonding, this is even worse than 00:23:01.670 --> 00:23:03.550 non-bonding, it's anti-bonding, because we're 00:23:03.550 --> 00:23:06.520 actually getting rid of electron density between the 00:23:06.520 --> 00:23:07.200 two nuclei. 00:23:07.200 --> 00:23:09.870 And we know that it's electron density between the nuclei 00:23:09.870 --> 00:23:13.290 that holds two atoms together in a bond. 00:23:13.290 --> 00:23:15.770 So what I want to point out is that it creates an effect that 00:23:15.770 --> 00:23:18.080 is exactly opposite of a bond. 00:23:18.080 --> 00:23:20.590 You might have thought before we started talking about 00:23:20.590 --> 00:23:23.370 molecular orbital theory that non-bonding was the opposite 00:23:23.370 --> 00:23:26.840 of bonding, it's not, anti-bonding is the opposite 00:23:26.840 --> 00:23:29.960 of bonding, and anti-bonding is not non-bonding. 00:23:29.960 --> 00:23:32.680 We can see that if we just look at this picture here. 00:23:32.680 --> 00:23:35.170 Here is bonding, and here is non-bonding. 00:23:35.170 --> 00:23:40.140 Anti-bonding is even higher in energy than non-bonding. 00:23:40.140 --> 00:23:43.260 And the other thing to point out is that the energy that an 00:23:43.260 --> 00:23:47.650 anti-bonding orbital is raised by, is the same amount as a 00:23:47.650 --> 00:23:49.640 bonding orbital is lowered by. 00:23:49.640 --> 00:23:52.990 So any time I draw these molecular orbitals, I do my 00:23:52.990 --> 00:23:55.460 best, and I'm not always perfect, yet trying to make 00:23:55.460 --> 00:23:59.110 this energy different exactly the same for the anti-bonding 00:23:59.110 --> 00:24:01.220 orbital being raised, versus the bonding 00:24:01.220 --> 00:24:02.560 orbital being lowered. 00:24:02.560 --> 00:24:07.730 So those should be raised and lowered by the same energy. 00:24:07.730 --> 00:24:09.995 So now let's take a look at some of -- is there 00:24:09.995 --> 00:24:16.130 a question up there? 00:24:16.130 --> 00:24:17.930 STUDENT: Why would two atoms decide to [INAUDIBLE]. 00:24:17.930 --> 00:24:18.100 PROFESSOR: Well, they don't want to. 00:24:18.100 --> 00:24:19.860 It's a higher energy situation. 00:24:19.860 --> 00:24:22.930 So we'll start to look at molecules and we'll see if we 00:24:22.930 --> 00:24:27.180 take two atoms and we fill in our molecular orbital and it 00:24:27.180 --> 00:24:29.750 turns out that they have more anti-bonding orbitals than 00:24:29.750 --> 00:24:33.610 bonding, that's -- a diatomic molecule we'll never see. 00:24:33.610 --> 00:24:37.060 So it helps us predict, will we see this, for example, h 2, 00:24:37.060 --> 00:24:40.830 which we're going to be about to do, we'll see is stabilized 00:24:40.830 --> 00:24:42.850 because it has more bonding than anti-bonding. 00:24:42.850 --> 00:24:44.730 So we'll predict, yes, there's a bond here. 00:24:44.730 --> 00:24:45.850 That's a really good question. 00:24:45.850 --> 00:24:51.480 So, let's go ahead and do this and take a look at some of the 00:24:51.480 --> 00:24:54.640 actual atoms that we can think about and think 00:24:54.640 --> 00:24:56.280 about them in molecules. 00:24:56.280 --> 00:24:58.900 So our simplest case that we started talking about was 00:24:58.900 --> 00:25:00.190 molecular hydrogen. 00:25:00.190 --> 00:25:03.230 I want to finish this discussion by including the 00:25:03.230 --> 00:25:05.880 anti-bonding orbital, and this is a tip for you when you're 00:25:05.880 --> 00:25:09.890 drawing your molecular orbital diagrams, any time you draw a 00:25:09.890 --> 00:25:12.080 bonding orbital, there is also an anti-bonding 00:25:12.080 --> 00:25:13.490 orbital that exists. 00:25:13.490 --> 00:25:15.700 It might not have any electrons in it, but it still 00:25:15.700 --> 00:25:18.960 exists, so you need to draw these into your molecular 00:25:18.960 --> 00:25:20.020 orbital diagram. 00:25:20.020 --> 00:25:22.330 So I wanted to make sure you have a complete set for 00:25:22.330 --> 00:25:23.740 hydrogen in your notes. 00:25:23.740 --> 00:25:24.940 So let's take a look at this. 00:25:24.940 --> 00:25:29.440 Hydrogen, we can first draw in our atomic electrons. 00:25:29.440 --> 00:25:32.850 So there's one electron in each hydrogen atom. 00:25:32.850 --> 00:25:36.030 And then this means we'll have a total of two electrons in 00:25:36.030 --> 00:25:39.910 our hydrogen molecule, so we can fill both of those into 00:25:39.910 --> 00:25:43.260 the sigma 1 s orbital, the bonding orbital. 00:25:43.260 --> 00:25:46.460 We don't have to put anything into the anti-bonding orbital, 00:25:46.460 --> 00:25:47.330 so that's great. 00:25:47.330 --> 00:25:51.180 What we've seen is we have a net lowering of energy of the 00:25:51.180 --> 00:25:56.330 molecule versus the individual atoms. 00:25:56.330 --> 00:26:00.090 So let's draw the electron configuration of hydrogen, the 00:26:00.090 --> 00:26:02.480 molecule, molecular hydrogen. 00:26:02.480 --> 00:26:05.200 What you saw, what we've done a lot of is drawing the 00:26:05.200 --> 00:26:08.520 electron configurations for different atoms, we can do the 00:26:08.520 --> 00:26:10.430 same thing for a molecule. 00:26:10.430 --> 00:26:13.850 So, if we take h 2, and we want to draw the electron 00:26:13.850 --> 00:26:15.900 configuration, it's very short. 00:26:15.900 --> 00:26:20.500 All it is sigma 1 s, and then we have two electrons in it, 00:26:20.500 --> 00:26:23.890 so it's sigma 1 s squared. 00:26:23.890 --> 00:26:25.990 So this is our electron configuration. 00:26:25.990 --> 00:26:27.620 Let's take a look at another example. 00:26:27.620 --> 00:26:30.700 Let's draw the molecular diagram for h e 2 now. 00:26:30.700 --> 00:26:35.880 So again, we can fill in our atomic orbitals here, there's 00:26:35.880 --> 00:26:39.490 going to be two electrons in each of our atomic orbitals. 00:26:39.490 --> 00:26:42.240 So now let's go ahead and fill in our molecular orbitals. 00:26:42.240 --> 00:26:45.950 We need to fill in a total of four electrons. 00:26:45.950 --> 00:26:49.280 So we have two electrons in our bonding orbital, but 00:26:49.280 --> 00:26:53.130 because we use the same rules to fill up molecular orbitals 00:26:53.130 --> 00:26:56.810 as we do atomic orbitals, so the Pauli exclusion principle 00:26:56.810 --> 00:26:58.760 tells us we can't have more than two electrons per 00:26:58.760 --> 00:27:00.910 orbital, so we have to go up to our 00:27:00.910 --> 00:27:02.870 anti-bonding orbital here. 00:27:02.870 --> 00:27:06.130 So this means that we have two of the electrons are lowered 00:27:06.130 --> 00:27:09.690 in energy, but two are raised in energy. 00:27:09.690 --> 00:27:12.470 So would this be a stabilized molecule then? 00:27:12.470 --> 00:27:14.520 STUDENT: [INAUDIBLE] 00:27:14.520 --> 00:27:15.320 PROFESSOR: No. 00:27:15.320 --> 00:27:18.050 So, compared to the atoms, it should be somewhat the same 00:27:18.050 --> 00:27:20.940 energy, we shouldn't get any extra stabilization from 00:27:20.940 --> 00:27:21.730 forming the molecule. 00:27:21.730 --> 00:27:25.100 So lets go ahead and write what the electron 00:27:25.100 --> 00:27:31.680 configuration would be of h e 2. 00:27:31.680 --> 00:27:34.660 And again, we're just filling in the different orbitals, so 00:27:34.660 --> 00:27:39.060 we have sigma 1 s, that's going to be squared, and now 00:27:39.060 --> 00:27:44.730 we have sigma 1 s star squared. 00:27:44.730 --> 00:27:48.440 So we can compare the two electron configurations, and 00:27:48.440 --> 00:27:52.220 we can actually think about -- what we figure out from them, 00:27:52.220 --> 00:27:55.320 we see that two are lowered in energy, two electrons are 00:27:55.320 --> 00:27:58.930 raised in energy, so we have no net gain or no net loss in 00:27:58.930 --> 00:28:01.830 energy for h e 2. 00:28:01.830 --> 00:28:04.810 And there's actually a way that we can make predictions 00:28:04.810 --> 00:28:07.630 here, and what I'll tell you is molecular orbital theory 00:28:07.630 --> 00:28:10.970 predicts that h e 2 does not exist because it's not 00:28:10.970 --> 00:28:14.830 stabilized in terms of forming the molecule. 00:28:14.830 --> 00:28:17.070 The way that we can figure this out is using something 00:28:17.070 --> 00:28:21.260 called bond order, and bond order is equal to 1/2 times 00:28:21.260 --> 00:28:23.990 the number of bonding electrons, minus the number of 00:28:23.990 --> 00:28:25.550 anti-bonding electrons. 00:28:25.550 --> 00:28:28.350 And the bond order you get out will either be, for example, 00:28:28.350 --> 00:28:31.165 zero, which would mean that you have no bond, or you could 00:28:31.165 --> 00:28:33.330 have 1, a single bond, 1 . 00:28:33.330 --> 00:28:37.490 5, a 1 and 1/2 bond, 2, a double bond, and so on. 00:28:37.490 --> 00:28:42.130 So let's figure out the bond order for our two molecules 00:28:42.130 --> 00:28:45.670 here that we figured out the electron configuration for. 00:28:45.670 --> 00:28:47.220 So I guess we'll start with helium 2. 00:28:47.220 --> 00:28:53.900 So the bond order is going to be equal to 1/2, and then it 00:28:53.900 --> 00:28:56.400 will be 2 minus 2. 00:28:56.400 --> 00:29:00.250 So our bond order for h e 2 is going to be equal to 0. 00:29:00.250 --> 00:29:04.330 So it has a 0 bond, there's no bond in h e 2. 00:29:04.330 --> 00:29:06.120 Let's look for hydrogen. 00:29:06.120 --> 00:29:14.260 For hydrogen our bond order is going to equal 1/2, 2 minus 0. 00:29:14.260 --> 00:29:16.850 So we would predict a bond order of 1. 00:29:16.850 --> 00:29:19.590 What kind of a bond is a bond order of 1? 00:29:19.590 --> 00:29:23.780 Yeah, we'd expect to see a single bond in hydrogen. 00:29:23.780 --> 00:29:27.660 So what actually turns out the reality is that h e 2 does 00:29:27.660 --> 00:29:31.300 exist, but it exists as the weakest chemical bond known, 00:29:31.300 --> 00:29:35.370 and it wasn't, in fact, even found to exist until 1993, so 00:29:35.370 --> 00:29:39.000 I can assure you this is not a bond that you see very often 00:29:39.000 --> 00:29:42.210 in nature, and it is a very, very weak bond. 00:29:42.210 --> 00:29:45.320 It only has a dissociation energy of 0 . 00:29:45.320 --> 00:29:47.180 1 kilojoules per mole. 00:29:47.180 --> 00:29:50.210 So that should make sense, because we saw no energy 00:29:50.210 --> 00:29:53.780 difference between the actual atoms and the molecules. 00:29:53.780 --> 00:29:57.330 Molecular orbital theory, even at this very basic level, 00:29:57.330 --> 00:30:00.340 allowed us to predict that no, we're not going to see a true 00:30:00.340 --> 00:30:02.220 bond here, a strong bond. 00:30:02.220 --> 00:30:06.930 In contrast, the dissociation energy of a bond for hydrogen, 00:30:06.930 --> 00:30:10.710 and molecular hydrogen is everywhere around us, we see 00:30:10.710 --> 00:30:12.720 432 kilojoules per mole. 00:30:12.720 --> 00:30:16.880 All right, so we can now see a little bit of what the power 00:30:16.880 --> 00:30:20.180 of molecular orbital theory is in predicting what kind of 00:30:20.180 --> 00:30:23.110 bonds we're going to see in molecules, or whether or not 00:30:23.110 --> 00:30:25.610 we'll see this bonding occur at all. 00:30:25.610 --> 00:30:28.540 So let's look at another example, let's take lithium 2 00:30:28.540 --> 00:30:30.710 and see what we can figure out here. 00:30:30.710 --> 00:30:34.430 In lithium 2, we have two atoms of lithium, each have 00:30:34.430 --> 00:30:36.450 three electrons in them. 00:30:36.450 --> 00:30:40.670 So now we have to include both the 1 s orbitals and also the 00:30:40.670 --> 00:30:42.250 2 s orbitals. 00:30:42.250 --> 00:30:45.390 So any time in a molecular orbital diagram you draw in 00:30:45.390 --> 00:30:46.790 orbitals, you need to draw the 00:30:46.790 --> 00:30:49.630 corresponding molecular orbitals. 00:30:49.630 --> 00:30:54.450 So, this means we need to have sigma 1 s, sigma 1 s star, and 00:30:54.450 --> 00:30:58.210 now sigma 2 s and sigma 2 s star. 00:30:58.210 --> 00:31:01.490 Something I'll also point out as you see these dashed line 00:31:01.490 --> 00:31:04.370 that tell you where the individual molecular orbitals 00:31:04.370 --> 00:31:08.050 are arising from, as you get to higher and higher atomic 00:31:08.050 --> 00:31:12.380 numbers of molecules that you're making, it makes a lot 00:31:12.380 --> 00:31:14.760 more sense to look at a diagram when you draw these 00:31:14.760 --> 00:31:16.460 dotted lines in, because they can start to get 00:31:16.460 --> 00:31:17.510 a little bit confusing. 00:31:17.510 --> 00:31:20.010 So when you go ahead and draw these on your problem-sets or 00:31:20.010 --> 00:31:22.820 on your exams, it's a good idea to put these dashed lines 00:31:22.820 --> 00:31:25.670 in, both for you and for people reading it to see 00:31:25.670 --> 00:31:29.050 exactly where your molecular orbitals are coming from. 00:31:29.050 --> 00:31:32.390 So, this means we have a total of six electrons that we need 00:31:32.390 --> 00:31:34.550 to put into molecular orbitals. 00:31:34.550 --> 00:31:37.260 So again we just start filling those up -- we have two in the 00:31:37.260 --> 00:31:42.050 1 s, two in the sigma 1 s star, and then we have two in 00:31:42.050 --> 00:31:44.220 the sigma 2 s. 00:31:44.220 --> 00:31:46.890 So we should be able to also calculate the bond order, just 00:31:46.890 --> 00:31:49.330 like we did for hydrogen and helium. 00:31:49.330 --> 00:31:52.120 First we can do that by knowing the electron 00:31:52.120 --> 00:31:56.070 configuration, we can write it out just by going up the table 00:31:56.070 --> 00:31:58.560 here, up the energy levels. 00:31:58.560 --> 00:32:01.270 And you can go ahead and tell me what you think the bond 00:32:01.270 --> 00:32:22.730 order is going to be for this molecule. 00:32:22.730 --> 00:32:22.920 All right. 00:32:22.920 --> 00:32:36.460 Let's take 10 more seconds on this. 00:32:36.460 --> 00:32:37.960 OK, good, we're back on track a little bit 00:32:37.960 --> 00:32:39.170 with our clicker answers. 00:32:39.170 --> 00:32:46.180 So it's selection three or one is the bond order. 00:32:46.180 --> 00:32:49.250 So let's switch back to our class notes and look at what 00:32:49.250 --> 00:32:49.900 this means. 00:32:49.900 --> 00:32:54.010 So we know that it's 1, because we have 1, 2, 3, 4 00:32:54.010 --> 00:32:58.000 bonding, minus 2 anti-bonding, and 1/2 of that is a bond 00:32:58.000 --> 00:32:58.900 order of 1. 00:32:58.900 --> 00:33:01.800 We would predict to see a single bond between lithium, 00:33:01.800 --> 00:33:04.000 and it turns out that's what we see. 00:33:04.000 --> 00:33:07.060 And so you have for a reference, the dissociation 00:33:07.060 --> 00:33:10.680 energy of lithium 2 is 105 kilojoules per mole. 00:33:10.680 --> 00:33:14.040 So let's keep moving along the periodic table and keep 00:33:14.040 --> 00:33:16.440 applying our molecular orbitals. 00:33:16.440 --> 00:33:22.100 For example now, with b e 2, so beryllium 2 has four 00:33:22.100 --> 00:33:24.840 electrons in terms of each atom. 00:33:24.840 --> 00:33:28.040 So you can start by filling those in, and now we can fill 00:33:28.040 --> 00:33:30.110 in our molecular orbitals as well. 00:33:30.110 --> 00:33:34.090 This means we need a total of eight electrons in our 00:33:34.090 --> 00:33:35.480 molecular orbitals. 00:33:35.480 --> 00:33:40.220 So we have two in 1 s, two in the sigma 1 s star, two in the 00:33:40.220 --> 00:33:44.460 sigma 2 s, and two in the sigma 2 s star. 00:33:44.460 --> 00:33:48.270 So let's go ahead and figure out the bonding order for 00:33:48.270 --> 00:33:57.030 beryllium here. 00:33:57.030 --> 00:34:00.720 So when we figure it out for beryllium -- let's see if I 00:34:00.720 --> 00:34:06.610 wrote in your notes what the actual -- electron 00:34:06.610 --> 00:34:08.830 configuration, OK that's already in your notes for you. 00:34:08.830 --> 00:34:12.450 So let's go right to the bond order for beryllium. 00:34:12.450 --> 00:34:16.210 So for the bond order we want to take 1/2 of the total 00:34:16.210 --> 00:34:20.140 number of bonding electrons, so that's going to be 4 minus 00:34:20.140 --> 00:34:24.660 anti-bonding is 4, so we end up getting a bond order that's 00:34:24.660 --> 00:34:25.940 equal to 0. 00:34:25.940 --> 00:34:28.530 So what I want to point out with this case in beryllium is 00:34:28.530 --> 00:34:31.450 that you don't have to use all of the electrons to figure out 00:34:31.450 --> 00:34:35.320 the bond order, and in fact, once you get to molecules that 00:34:35.320 --> 00:34:39.240 are from atoms with atomic numbers of 8 or 10, you're not 00:34:39.240 --> 00:34:42.190 going to want to maybe draw out the full 00:34:42.190 --> 00:34:44.010 molecular orbital diagram. 00:34:44.010 --> 00:34:46.600 So what I want to tell you is we also always get the same 00:34:46.600 --> 00:34:49.050 bond order if we instead only deal 00:34:49.050 --> 00:34:50.810 with the valence electrons. 00:34:50.810 --> 00:34:53.620 So let's just prove that to ourselves and figure out the 00:34:53.620 --> 00:34:57.030 bond order just using valence electrons. 00:34:57.030 --> 00:34:59.940 So this would mean the bond order is equal to 1/2, and in 00:34:59.940 --> 00:35:02.370 terms of valence electrons, how many bonding valence 00:35:02.370 --> 00:35:02.990 electrons do we have? 00:35:02.990 --> 00:35:03.440 STUDENT: [INAUDIBLE] 00:35:03.440 --> 00:35:06.690 PROFESSOR: All right, what about anti-bonding? 00:35:06.690 --> 00:35:07.840 STUDENT: [INAUDIBLE] 00:35:07.840 --> 00:35:08.270 PROFESSOR: Two. 00:35:08.270 --> 00:35:08.630 OK, good. 00:35:08.630 --> 00:35:11.780 So again, we're going to see that we have a 00:35:11.780 --> 00:35:13.820 bonding order of 0. 00:35:13.820 --> 00:35:18.330 So we would not predict to see a b e 2 bond. 00:35:18.330 --> 00:35:23.150 So what we see is a bond order of 0, and again, the bond is 00:35:23.150 --> 00:35:24.180 very, very weak. 00:35:24.180 --> 00:35:26.320 Essentially we're not going to see this, it's 9 00:35:26.320 --> 00:35:27.450 kilojoules per mole. 00:35:27.450 --> 00:35:29.990 All right. 00:35:29.990 --> 00:35:33.060 So, so far we've looked only at molecules that involve 00:35:33.060 --> 00:35:36.110 atoms that have only s orbitals in them. 00:35:36.110 --> 00:35:38.560 I'm sure you're thinking well, what do we do in the case of p 00:35:38.560 --> 00:35:40.900 orbitals, and, in fact, we can do the same thing. 00:35:40.900 --> 00:35:43.480 Again, we're going to take the linear combination of those p 00:35:43.480 --> 00:35:47.700 atomic orbitals and make what are called pi or some more 00:35:47.700 --> 00:35:49.990 sigma molecular orbitals. 00:35:49.990 --> 00:35:52.670 So let's look at the first case where we have either the 00:35:52.670 --> 00:35:57.200 2 p x or 2 p y type of orbitals that we're combining. 00:35:57.200 --> 00:35:59.760 So they're the same shape, this is the shape of the 00:35:59.760 --> 00:36:03.090 orbital or the shape of the wave function, and we can call 00:36:03.090 --> 00:36:07.840 this either 2 p x a being combined with 2 p x b, or we 00:36:07.840 --> 00:36:11.085 could say since it's the same shape, it's 2 p y a being 00:36:11.085 --> 00:36:13.780 combined with 2 p y b. 00:36:13.780 --> 00:36:16.530 And in either case if we first talk about constructive 00:36:16.530 --> 00:36:19.310 interference, what again we're going to see is that where 00:36:19.310 --> 00:36:22.380 these two orbitals come together, we're going to see 00:36:22.380 --> 00:36:25.430 increased wave function in that area, so we saw 00:36:25.430 --> 00:36:27.530 constructive interference. 00:36:27.530 --> 00:36:31.740 So again, we can name these molecular orbitals and these 00:36:31.740 --> 00:36:35.220 we're going to call -- also to point out there is now a bond 00:36:35.220 --> 00:36:38.650 axis along this nodal plane, which is something we didn't 00:36:38.650 --> 00:36:41.600 see before when we were combining the s orbitals. 00:36:41.600 --> 00:36:43.670 So when we go ahead and name these, we're going to call 00:36:43.670 --> 00:36:45.260 these pi orbitals. 00:36:45.260 --> 00:36:49.520 We'll call it either pi 2 p x, if we're combining the x 00:36:49.520 --> 00:36:53.910 orbitals, or pi 2 p y. 00:36:53.910 --> 00:36:57.280 The reason that I wanted to point out this nodal plane 00:36:57.280 --> 00:37:00.840 here is because this is why it is called a pi orbital. 00:37:00.840 --> 00:37:04.630 Pi orbitals are a molecular orbital that have a nodal 00:37:04.630 --> 00:37:07.220 plane through the bond axis. 00:37:07.220 --> 00:37:10.750 Remember this is our bond axis here, and you can see there is 00:37:10.750 --> 00:37:13.640 this area where the wave function is equal to zero all 00:37:13.640 --> 00:37:16.190 along that plane, that's a nodal plane. 00:37:16.190 --> 00:37:18.290 So that's why these are pi orbitals 00:37:18.290 --> 00:37:20.420 instead of sigma orbitals. 00:37:20.420 --> 00:37:23.410 So again, we can think about the probability density in 00:37:23.410 --> 00:37:25.480 terms of squaring the wave function. 00:37:25.480 --> 00:37:28.410 So now what it is that we're squaring is if we're talking 00:37:28.410 --> 00:37:34.390 about x orbital, it's pi 2 p x squared, and this is just 00:37:34.390 --> 00:37:42.980 equal to the 2 p x a plus the 2 p x b all squared, or if we 00:37:42.980 --> 00:37:48.360 write out all of the terms we have 2 p x a squared plus 2 p 00:37:48.360 --> 00:37:52.330 x b squared, and then this term here, and again, this is 00:37:52.330 --> 00:37:53.760 our interference term. 00:37:53.760 --> 00:37:56.200 In this case is it constructive or destructive 00:37:56.200 --> 00:37:57.000 interference? 00:37:57.000 --> 00:37:57.336 STUDENT: [INAUDIBLE] 00:37:57.336 --> 00:37:59.410 PROFESSOR: Constructive interference. 00:37:59.410 --> 00:38:02.030 We're seeing that the wave function's adding together and 00:38:02.030 --> 00:38:06.680 giving us more wave function in the center here. 00:38:06.680 --> 00:38:07.010 All right. 00:38:07.010 --> 00:38:09.390 So we see constructive interference, of course, we 00:38:09.390 --> 00:38:12.060 can also see destructive interference. 00:38:12.060 --> 00:38:15.490 So I changed the colors here to show that these are 2 p 00:38:15.490 --> 00:38:19.150 orbitals with an opposite phase or an opposite sign. 00:38:19.150 --> 00:38:24.490 So what happens when we add a 2 p a and we subtract from it 00:38:24.490 --> 00:38:29.970 a 2 p x b, or the same with a 2 p y a subtracting a 2 p y b, 00:38:29.970 --> 00:38:33.290 is that we're actually going to cancel out the wave 00:38:33.290 --> 00:38:36.830 function in the center, so we now have 2 nodal planes. 00:38:36.830 --> 00:38:39.530 So again, this is an anti-bonding orbital, and what 00:38:39.530 --> 00:38:43.470 you see is that there is now less electron density between 00:38:43.470 --> 00:38:49.040 the two nuclei than there was when you had non-bonding. 00:38:49.040 --> 00:38:53.320 So we're going to call this the sigma 2 p x star, or if 00:38:53.320 --> 00:38:58.400 we're talking about the 2 p y orbitals we'll call this the 00:38:58.400 --> 00:39:05.880 pi 2 p x star, and the pi 2 p y star. 00:39:05.880 --> 00:39:09.200 And the pi star orbitals result from any time you have 00:39:09.200 --> 00:39:12.600 destructive interference from 2 p orbitals that are either 00:39:12.600 --> 00:39:16.370 the p x or the p y. 00:39:16.370 --> 00:39:19.030 So now we can move on to an example where we do, in fact, 00:39:19.030 --> 00:39:23.790 have to use some p orbitals, so this would be b 2. 00:39:23.790 --> 00:39:26.990 How many electrons are in boron? 00:39:26.990 --> 00:39:27.590 Five. 00:39:27.590 --> 00:39:29.590 I see some hands going up. 00:39:29.590 --> 00:39:32.740 There's five electrons So what you'll notice here is that I 00:39:32.740 --> 00:39:35.240 only filled in 3 electrons. 00:39:35.240 --> 00:39:37.140 What do these electrons represent? 00:39:37.140 --> 00:39:38.750 STUDENT: Valence. 00:39:38.750 --> 00:39:39.740 PROFESSOR: Valence electrons. 00:39:39.740 --> 00:39:41.910 OK, sometimes you're going to be asked to draw a molecular 00:39:41.910 --> 00:39:44.790 orbital diagram where you're asked to include all 00:39:44.790 --> 00:39:48.080 electrons, and sometimes it will specifically say only 00:39:48.080 --> 00:39:50.110 include valence electrons. 00:39:50.110 --> 00:39:53.190 That happens because of space issues that you were asked to 00:39:53.190 --> 00:39:55.880 do that, because you can always assume that all of the 00:39:55.880 --> 00:39:59.050 core orbitals are already going to be filled. 00:39:59.050 --> 00:40:01.310 So, in this case, we're just drawing the molecular orbital 00:40:01.310 --> 00:40:03.940 diagram for the valence electrons, so we 00:40:03.940 --> 00:40:05.320 have three for each. 00:40:05.320 --> 00:40:09.330 And what we see here is now when we're combining the p, we 00:40:09.330 --> 00:40:13.200 have our 2 p x and our 2 p y orbitals that are lower in 00:40:13.200 --> 00:40:16.900 energy, and then our pi anti-bonding orbitals that are 00:40:16.900 --> 00:40:18.580 higher in energy. 00:40:18.580 --> 00:40:22.090 You might be asking where the 2 p z orbital is and we'll get 00:40:22.090 --> 00:40:24.410 to that soon once we need it. 00:40:24.410 --> 00:40:28.170 Let's just first fill in this for the b 2 case. 00:40:28.170 --> 00:40:32.360 So we can start at the bottom, two electrons in sigma 2 s, 00:40:32.360 --> 00:40:35.700 two electrons in sigma 2 s star. 00:40:35.700 --> 00:40:40.220 Now we need to jump up to using these pi orbitals, and 00:40:40.220 --> 00:40:43.910 what we're going to do is put one electron into each of our 00:40:43.910 --> 00:40:47.790 pi 2 p x and 2 p y orbitals. 00:40:47.790 --> 00:40:50.690 So again you can see as we're filling up our molecular 00:40:50.690 --> 00:40:53.750 orbitals, we're using the exact same principle we used 00:40:53.750 --> 00:40:55.110 to fill up atomic orbitals. 00:40:55.110 --> 00:41:00.530 So let's think about what the valence electron 00:41:00.530 --> 00:41:03.170 configuration is here. 00:41:03.170 --> 00:41:07.980 So now we're looking at the case of b 2. 00:41:07.980 --> 00:41:11.500 And what we're looking at is a valence electron molecular 00:41:11.500 --> 00:41:13.640 orbital diagram, so let's just draw the electron 00:41:13.640 --> 00:41:16.880 configuration for the valence orbitals, so that will be 00:41:16.880 --> 00:41:25.940 sigma 2 s 2, sigma 2 s star 2, and now we start in with our 00:41:25.940 --> 00:41:34.350 pi 2 p x 1, and our pi 2 p y 1. 00:41:34.350 --> 00:41:36.440 So this is our valence electron 00:41:36.440 --> 00:41:38.800 configuration for b 2. 00:41:38.800 --> 00:41:41.250 All right. 00:41:41.250 --> 00:41:48.670 So what would you expect the bonding order for b 2 to be? 00:41:48.670 --> 00:41:50.030 Shout it out if you know. 00:41:50.030 --> 00:41:51.440 STUDENT: one. 00:41:51.440 --> 00:41:55.220 PROFESSOR: And I didn't write up there but it is one, and we 00:41:55.220 --> 00:42:00.200 can see that it's 1, because it's 1/2 of 2, 4 minus 2, so 00:42:00.200 --> 00:42:04.130 1/2 of 2, the bonding order is going to be equal to one. 00:42:04.130 --> 00:42:06.900 So let's move on to another example, let's talk about 00:42:06.900 --> 00:42:07.680 carbon here. 00:42:07.680 --> 00:42:10.230 Again, we're just talking about the valence electrons. 00:42:10.230 --> 00:42:13.660 So carbon has four valence electrons, so if we talk about 00:42:13.660 --> 00:42:17.220 c 2, again we're going to start filling in our molecular 00:42:17.220 --> 00:42:21.100 orbitals, and now we're going to have eight electrons to 00:42:21.100 --> 00:42:22.400 fill into our molecular orbitals. 00:42:22.400 --> 00:42:27.130 So, we'll put two in the sigma 2 s, two in the sigma 2 s 00:42:27.130 --> 00:42:30.870 star, and now we're going to fill one and one into each of 00:42:30.870 --> 00:42:35.540 our pi 2 p x and 2 p y, but we still have two electrons left, 00:42:35.540 --> 00:42:38.560 so what we're going to do is double up in terms of our 2 p 00:42:38.560 --> 00:42:40.120 x and our 2 p y. 00:42:40.120 --> 00:42:43.640 So let's think about what this valence electron configuration 00:42:43.640 --> 00:42:48.230 is for c 2. 00:42:48.230 --> 00:42:51.270 And again, I want you to have practiced drawing these out in 00:42:51.270 --> 00:42:54.460 the form -- you always need to start with the sigma and then 00:42:54.460 --> 00:42:56.710 write the number of the orbital. 00:42:56.710 --> 00:43:02.170 So, sigma 2 s has two electrons, sigma 2 s star with 00:43:02.170 --> 00:43:06.560 two electrons, and now we have sigma 2 p x -- how many 00:43:06.560 --> 00:43:07.630 electrons here? 00:43:07.630 --> 00:43:09.760 STUDENT: Two. 00:43:09.760 --> 00:43:10.560 PROFESSOR: Two. 00:43:10.560 --> 00:43:15.710 And sigma 2 p y, two electrons here. 00:43:15.710 --> 00:43:20.960 Oh excuse me, pi 2 p y, thank you -- pi 2 p x and pi 2 p y. 00:43:20.960 --> 00:43:23.540 So let's talk about what the bonding order is 00:43:23.540 --> 00:43:25.110 going to be for c 2. 00:43:25.110 --> 00:43:30.640 So what's the bonding order for c 2? 00:43:30.640 --> 00:43:31.460 STUDENT: Two. 00:43:31.460 --> 00:43:32.320 PROFESSOR: two? 00:43:32.320 --> 00:43:40.880 OK, so we have 2, 4, 6 minus 2, so we have 1/2 of 6 minus 00:43:40.880 --> 00:43:45.390 2, so that's 1/2 half 4, so we have a bonding order of two 00:43:45.390 --> 00:43:46.870 for carbon 2. 00:43:46.870 --> 00:43:50.330 So we would expect to see a double bond for a c 2 where we 00:43:50.330 --> 00:43:54.680 would expect to see a -- double bond for c 2 and a 00:43:54.680 --> 00:43:58.060 single bond for b 2. 00:43:58.060 --> 00:44:01.810 And that is, in fact, what we can surmise if we look at the 00:44:01.810 --> 00:44:04.940 different dissociation energies for the two bonds. 00:44:04.940 --> 00:44:08.490 So for b 2, which is a single bond, that's 289 kilojoules 00:44:08.490 --> 00:44:12.130 per mole to break it, and it takes us more energy to break 00:44:12.130 --> 00:44:14.690 this double bond for carbon, which is 599 00:44:14.690 --> 00:44:17.000 kilojoules per mole. 00:44:17.000 --> 00:44:20.080 So, in general what we see, and this is always true if 00:44:20.080 --> 00:44:22.420 we're comparing the same atom, and in general, if we're 00:44:22.420 --> 00:44:25.470 comparing different types of molecules, but we know that a 00:44:25.470 --> 00:44:27.950 single bond is always weaker than a double bond, which is 00:44:27.950 --> 00:44:29.490 weaker than a triple bond. 00:44:29.490 --> 00:44:33.380 And obviously, no bond is the weakest of all is not bonding. 00:44:33.380 --> 00:44:34.470 All right. 00:44:34.470 --> 00:44:37.790 So let's look now at the case where we do have 2 p z 00:44:37.790 --> 00:44:39.570 orbitals that we're talking about. 00:44:39.570 --> 00:44:41.850 So again, what we're talking about is the linear 00:44:41.850 --> 00:44:45.710 combination of atomic 2 p orbitals, and now we're 00:44:45.710 --> 00:44:47.440 talking about 2 p z. 00:44:47.440 --> 00:44:50.680 So if we have constructive interference between the two, 00:44:50.680 --> 00:44:54.610 what we're going to see is our molecular orbital looks 00:44:54.610 --> 00:44:56.570 something like this. 00:44:56.570 --> 00:44:59.790 Do you predict that this will be a sigma or a pi orbital? 00:44:59.790 --> 00:45:02.420 STUDENT: [INAUDIBLE] 00:45:02.420 --> 00:45:03.613 PROFESSOR: All right, I'm hearing a little of both, but 00:45:03.613 --> 00:45:05.640 I'm very encouraged to hear quite a few 00:45:05.640 --> 00:45:07.310 people saying sigma. 00:45:07.310 --> 00:45:10.230 This is, in fact, a sigma 2 p z orbital is what 00:45:10.230 --> 00:45:12.210 this orbital is called. 00:45:12.210 --> 00:45:15.270 The reason that it's sigma is if you look at the bonding 00:45:15.270 --> 00:45:18.410 axis here, is that there is no nodal plane 00:45:18.410 --> 00:45:20.820 along the bonding axis. 00:45:20.820 --> 00:45:25.430 Also, it is cylindrically symmetric around the bonding 00:45:25.430 --> 00:45:28.390 axis, so this is how we know that it's a sigma orbital. 00:45:28.390 --> 00:45:32.660 So some p orbitals form pi molecular orbitals, and some 00:45:32.660 --> 00:45:34.540 form sigma p orbitals. 00:45:34.540 --> 00:45:38.030 Specifically, it's always the z that forms the sigma 00:45:38.030 --> 00:45:41.600 orbital, and the reason is at least at a minimum for this 00:45:41.600 --> 00:45:45.740 class we always define the internuclear axis as the z 00:45:45.740 --> 00:45:50.290 axis, so this is always the z axis, so it's always going to 00:45:50.290 --> 00:45:53.440 be the 2 p z's that are coming together head-on. 00:45:53.440 --> 00:45:56.370 The reason that there is increased electron density 00:45:56.370 --> 00:45:59.490 here is you can see that these two orbitals come together and 00:45:59.490 --> 00:46:02.450 constructively interfere. 00:46:02.450 --> 00:46:05.210 We can also talk about anti-bonding orbitals where we 00:46:05.210 --> 00:46:07.190 have destructive interference. 00:46:07.190 --> 00:46:10.250 So instead, these would be canceling out wave functions 00:46:10.250 --> 00:46:13.820 between the two, so we would end up with a nodal plane down 00:46:13.820 --> 00:46:15.190 the center. 00:46:15.190 --> 00:46:18.390 Would this be a sigma or a pi? 00:46:18.390 --> 00:46:19.840 It's still sigma. 00:46:19.840 --> 00:46:22.670 So even though we see a nodal plane down the center, I just 00:46:22.670 --> 00:46:25.110 want to really point out that it's only when we have a nodal 00:46:25.110 --> 00:46:27.940 plane in the internuclear or the bond axis that we're 00:46:27.940 --> 00:46:30.660 calling that a pi orbital. 00:46:30.660 --> 00:46:32.360 So this is still a sigma -- it's a 00:46:32.360 --> 00:46:35.360 sigma 2 p z star orbital. 00:46:35.360 --> 00:46:38.370 We have destructive interference here. 00:46:38.370 --> 00:46:41.270 So now let's look at an example where we talk about 00:46:41.270 --> 00:46:45.210 using these 2 p z orbitals, so let's look at oxygen. 00:46:45.210 --> 00:46:48.280 So the first thing I want to point out is that the 2 p z, 00:46:48.280 --> 00:46:53.400 the sigma 2 p z is even lower in energy than the pi orbitals 00:46:53.400 --> 00:46:57.340 here, and the anti-bonding sigma orbital is going to be 00:46:57.340 --> 00:47:03.010 higher in energy than the pi 2 p orbitals that we have here. 00:47:03.010 --> 00:47:05.690 So in oxygen again, this is just showing the valence 00:47:05.690 --> 00:47:09.570 electrons, so we end up having six valence electrons from 00:47:09.570 --> 00:47:11.070 each oxygen atom. 00:47:11.070 --> 00:47:14.380 We can fill right up our table just like we did before, but 00:47:14.380 --> 00:47:18.610 now we have included our 2 p z orbital here. 00:47:18.610 --> 00:47:23.080 So we have two electrons in sigma 2 s, two in sigma 2 s 00:47:23.080 --> 00:47:29.730 star, in sigma 2 p z we have two -- those are filled first, 00:47:29.730 --> 00:47:33.780 and now we're going to put one into pi 2 p x, and 00:47:33.780 --> 00:47:37.480 one into pi 2 p y. 00:47:37.480 --> 00:47:41.860 So we can write out what the electron configuration is 00:47:41.860 --> 00:47:44.250 here, and I think that I have already written that out for 00:47:44.250 --> 00:47:45.890 you in your notes. 00:47:45.890 --> 00:47:50.400 What is the bond order of o 2? 00:47:50.400 --> 00:47:54.200 It's two. 00:47:54.200 --> 00:47:56.090 Oh excuse me, I didn't fill in all of my electrons. 00:47:56.090 --> 00:47:57.140 All right. 00:47:57.140 --> 00:48:00.220 So we had a total of 2, 4, 6, 8. 00:48:00.220 --> 00:48:01.990 So we had a total of 12. 00:48:01.990 --> 00:48:07.640 So we filled in four here -- we need to keep going. 00:48:07.640 --> 00:48:10.630 All right, so I did this not at all purposely, but this can 00:48:10.630 --> 00:48:13.570 point out for you that you need to make sure that the 00:48:13.570 --> 00:48:17.480 number of electrons that you have in your molecular orbital 00:48:17.480 --> 00:48:19.840 does match up with the total number that you have in your 00:48:19.840 --> 00:48:21.170 atomic orbitals. 00:48:21.170 --> 00:48:24.160 So I did not do any counting up here, you should make sure 00:48:24.160 --> 00:48:25.910 you do counting, I apologize. 00:48:25.910 --> 00:48:29.850 So we need to fill all the way up to the pi 2 p x, 00:48:29.850 --> 00:48:31.220 and the pi 2 p y. 00:48:31.220 --> 00:48:34.760 All right, so the bonding order, you're correct, should 00:48:34.760 --> 00:48:38.040 be 2, if we subtract the number of bonding minus 00:48:38.040 --> 00:48:42.380 anti-bonding electrons and take that in 1/2. 00:48:42.380 --> 00:48:45.560 And what I want to point out that we just figured out for 00:48:45.560 --> 00:48:49.120 molecular orbital theory, is that o 2 is a biradical, 00:48:49.120 --> 00:48:51.180 because remember, the definition of a radical is 00:48:51.180 --> 00:48:53.550 when we have an unpaired electron. 00:48:53.550 --> 00:48:57.680 You can see that we have two unpaired electrons in this 00:48:57.680 --> 00:49:02.880 molecule here -- one in the pi 2 p x star, and one in the pi 00:49:02.880 --> 00:49:05.020 2 p y star orbital. 00:49:05.020 --> 00:49:07.570 This was something we could not predict using Lewis 00:49:07.570 --> 00:49:11.520 structures, but we can predict using MO theory that we have a 00:49:11.520 --> 00:49:13.190 radical species here. 00:49:13.190 --> 00:49:15.850 So that's a really important type of an application that we 00:49:15.850 --> 00:49:18.440 can use MO theory for that we weren't able to do with our 00:49:18.440 --> 00:49:20.340 Lewis structures. 00:49:20.340 --> 00:49:23.380 All right, I want to do one more at homonuclear example 00:49:23.380 --> 00:49:25.520 here, and this is n 2. 00:49:25.520 --> 00:49:28.710 The first thing that I need to point out is you can actually 00:49:28.710 --> 00:49:33.440 see an n 2 versus o 2 that we flip-flopped the energy of the 00:49:33.440 --> 00:49:36.590 sigma and the pi 2 p orbitals. 00:49:36.590 --> 00:49:39.610 So this is a glitch, just like sometimes we had glitches in 00:49:39.610 --> 00:49:41.040 filling up our atomic orbitals. 00:49:41.040 --> 00:49:43.100 This is something that you need to remember. 00:49:43.100 --> 00:49:47.670 And what you need to remember is if the z is equal to eight 00:49:47.670 --> 00:49:51.370 or greater, such as oxygen being the cut-off point, this 00:49:51.370 --> 00:49:56.030 sigma 2 p orbital is actually lower in energy than the pi 2 00:49:56.030 --> 00:49:57.650 p orbitals, the molecular orbitals. 00:49:57.650 --> 00:50:01.660 But for anything 7 or less, so what is the 00:50:01.660 --> 00:50:03.220 atomic number for nitrogen? 00:50:03.220 --> 00:50:05.400 STUDENT: Five. 00:50:05.400 --> 00:50:07.330 PROFESSOR: five -- there's five valence electrons, but 00:50:07.330 --> 00:50:09.990 the atomic number is actually seven. 00:50:09.990 --> 00:50:13.950 So z equals 7 -- this is the cut-off where, in fact, the 00:50:13.950 --> 00:50:18.450 sigma orbital is going to be higher in energy than the pi 2 00:50:18.450 --> 00:50:19.410 p orbitals. 00:50:19.410 --> 00:50:21.330 This is something that you just need to remember. 00:50:21.330 --> 00:50:24.120 I wrote it down your notes, if you can put a big star next to 00:50:24.120 --> 00:50:25.890 it so you don't forget this. 00:50:25.890 --> 00:50:27.930 This is something you're going to be responsible for in 00:50:27.930 --> 00:50:29.850 drawing out your molecular orbitals. 00:50:29.850 --> 00:50:32.650 So let's fill it out in this way, keeping in mind that 00:50:32.650 --> 00:50:36.630 we're going to fill out the pi 2 p's before the sigma. 00:50:36.630 --> 00:50:42.410 So we have a total of 2, 4, 6, 8, 10 valence electrons, so 00:50:42.410 --> 00:50:44.590 I'll make sure I count to 10 as we fill up our molecular 00:50:44.590 --> 00:50:45.760 orbitals here. 00:50:45.760 --> 00:50:48.050 We have two, then we have four. 00:50:48.050 --> 00:50:51.710 Now we're going to start in with that pi 2 p orbitals, 00:50:51.710 --> 00:50:55.960 which gives us 1 each, and then two each in those, and 00:50:55.960 --> 00:51:00.490 then after that, we'll go up to our sigma 2 p z orbital. 00:51:00.490 --> 00:51:04.210 So this is going to be our molecular orbital diagram. 00:51:04.210 --> 00:51:06.340 And again, I've written for you, but you can figure out 00:51:06.340 --> 00:51:08.320 what the electron configuration is just by 00:51:08.320 --> 00:51:10.940 writing up in this order here. 00:51:10.940 --> 00:51:13.480 And what is the bond order going to be n 2? 00:51:13.480 --> 00:51:15.280 STUDENT: [INAUDIBLE] 00:51:15.280 --> 00:51:16.190 PROFESSOR: It's going to be three. 00:51:16.190 --> 00:51:18.850 So, you can go ahead and calculate that, if you can't 00:51:18.850 --> 00:51:20.390 see that right away. 00:51:20.390 --> 00:51:22.370 So we'll end here, we'll finish up with the 00:51:22.370 --> 00:51:25.230 heteronuclear example on Friday.