1 00:00:01 --> 00:00:04 The following content is provided by MIT OpenCourseWare 2 00:00:04 --> 00:00:06 under a Creative Commons license. 3 00:00:06 --> 00:00:10 Additional information about our license and MIT 4 00:00:10 --> 00:00:15 OpenCourseWare in general is available at ocw.mit.edu. 5 00:00:15 --> 00:00:18 At the end of last hour, we had just gotten to the point 6 00:00:18 --> 00:00:22 of having developed the molecular orbital energy level 7 00:00:22 --> 00:00:27 diagram for the BH three molecule, this trigonal planar 8 00:00:27 --> 00:00:29 entity. And I had not had time last 9 00:00:29 --> 00:00:33 hour to show you what these molecular orbitals look like in 10 00:00:33 --> 00:00:38 their calculated form. And so, I am going to start off 11 00:00:38 --> 00:00:41 today by doing that, and then will proceed to answer 12 00:00:41 --> 00:00:45 a quadrangle of questions that we can attack regarding diatomic 13 00:00:45 --> 00:00:48 molecules using molecular orbital theory. 14 00:00:48 --> 00:00:51 Remember that the BH three MO problem is a seven 15 00:00:51 --> 00:00:55 orbital problem. And so, we will go through and 16 00:00:55 --> 00:00:58 just look at these seven molecular orbitals in ascending 17 00:00:58 --> 00:01:02 energy from the lowest energy on up. 18 00:01:02 --> 00:01:06 This one is the lowest energy molecular orbital for BH three 19 00:01:06 --> 00:01:12 as calculated using a modern quantum chemical package. 20 00:01:12 --> 00:01:16 And what you can see is that since we are indicating the 21 00:01:16 --> 00:01:21 phase of the wave function by color, there is only one phase 22 00:01:21 --> 00:01:24 to be seen. This, of course, 23 00:01:24 --> 00:01:27 is a characteristic property of an s orbital. 24 00:01:27 --> 00:01:31 Remember that? And what we have here, 25 00:01:31 --> 00:01:36 at the center of the molecule, is the 2s orbital on boron. 26 00:01:36 --> 00:01:40 And in this molecular orbital theory, effectively what is 27 00:01:40 --> 00:01:44 happening is that 2s orbital on boron is reaching out and 28 00:01:44 --> 00:01:49 simultaneously overlapping with the three 1s orbitals on each of 29 00:01:49 --> 00:01:52 the hydrogens. And the way that we have 30 00:01:52 --> 00:01:57 orthogonalized it and normalized it amounts to a single molecular 31 00:01:57 --> 00:02:00 orbital that can, if you will, 32 00:02:00 --> 00:02:03 house a pair of electrons in this orbital that is 33 00:02:03 --> 00:02:10 simultaneously bonding between boron and the three hydrogens. 34 00:02:10 --> 00:02:12 You have one electron pair in here. 35 00:02:12 --> 00:02:17 Two of the six electrons in the valance shell of this molecule 36 00:02:17 --> 00:02:21 are in this lowest lying, most tightly held, 37 00:02:21 --> 00:02:24 most electronegative molecular orbital. 38 00:02:24 --> 00:02:28 Let's look now at the next one. 39 00:02:28 --> 00:02:40 40 00:02:40 --> 00:02:44 You should be thinking in your mind just what was the next 41 00:02:44 --> 00:02:49 highest lying orbital that we had, and you will realize that 42 00:02:49 --> 00:02:53 this is an orbital formed from one of the boron p orbitals and 43 00:02:53 --> 00:02:59 a linear combination of two of the hydrogen wave functions. 44 00:02:59 --> 00:03:04 And let's see if you can recognize it based on what we 45 00:03:04 --> 00:03:08 did last time. Maybe I can reorient it to help 46 00:03:08 --> 00:03:12 in that regard. Here is a molecular orbital 47 00:03:12 --> 00:03:17 that can house a pair of electrons, one spin-up and one 48 00:03:17 --> 00:03:22 spin-down, and that is simultaneously bonding from that 49 00:03:22 --> 00:03:27 boron to this hydrogen, up here. 50 00:03:27 --> 00:03:29 And then there is a nodal surface, here, 51 00:03:29 --> 00:03:33 that is coincident with the nodal surfaces of the boron 2px 52 00:03:33 --> 00:03:36 orbital, using the same coordinate system that we were 53 00:03:36 --> 00:03:39 using last time. And so, the wave function 54 00:03:39 --> 00:03:42 changes sign as you pass through the boron. 55 00:03:42 --> 00:03:46 And then the opposite phase lobe of the boron 2px orbital is 56 00:03:46 --> 00:03:49 able to overlap with these two hydrogens, here. 57 00:03:49 --> 00:03:52 If you will remember, when I wrote down the 58 00:03:52 --> 00:03:55 normalization constants for this molecular orbital, 59 00:03:55 --> 00:03:58 we had double the coefficient on the hydrogen up here as 60 00:03:58 --> 00:04:03 compared with the two hydrogens down here. 61 00:04:03 --> 00:04:07 And they were opposite in sign. And that leads to a really nice 62 00:04:07 --> 00:04:11 overlap, as you can see here. This is BH bonding here, 63 00:04:11 --> 00:04:13 and BH bonding, down here. 64 00:04:13 --> 00:04:16 And it involves that boron 2px orbital. 65 00:04:16 --> 00:04:20 One way you can think about this molecular orbital theory is 66 00:04:20 --> 00:04:25 that this 2px orbital on the central atom is reaching out 67 00:04:25 --> 00:04:29 with its intrinsic plus-minus phase combination that is 68 00:04:29 --> 00:04:33 intrinsic to a 2px orbital simultaneously reaching out and 69 00:04:33 --> 00:04:38 bonding with all three hydrogens in the only way that it can, 70 00:04:38 --> 00:04:43 being a 2px orbital. And so, we created that linear 71 00:04:43 --> 00:04:46 combination with that idea in mind. 72 00:04:46 --> 00:04:50 And then, if we go up one more in energy, strike that. 73 00:04:50 --> 00:04:55 Not one up more in energy, but to the other orbital in the 74 00:04:55 --> 00:04:58 molecule that is at the same energy. 75 00:04:58 --> 00:05:02 What we will find is that we are involving, 76 00:05:02 --> 00:05:06 now, the 2py orbital. And it will reach out and 77 00:05:06 --> 00:05:10 interact with hydrogens in the only way it can, 78 00:05:10 --> 00:05:14 given its intrinsic nodal properties as a 2py orbital. 79 00:05:14 --> 00:05:18 Remember that a 2py orbital has the x,z-plane as a nodal 80 00:05:18 --> 00:05:21 surface. And there is a hydrogen up here 81 00:05:21 --> 00:05:24 on that x,z-plane, namely the one that lies on the 82 00:05:24 --> 00:05:27 plus x-axis. And because it lies on the 83 00:05:27 --> 00:05:32 intrinsic nodal surface of this 2py orbital, it can contribute 84 00:05:32 --> 00:05:36 nothing to this molecular orbital. 85 00:05:36 --> 00:05:40 All we are seeing up here at the top is an arbitrarily sized 86 00:05:40 --> 00:05:44 sphere, just to show the location of that nucleus, 87 00:05:44 --> 00:05:47 the hydrogen nucleus that is on the plus x-axis. 88 00:05:47 --> 00:05:50 And then here, what you see is the 2py orbital 89 00:05:50 --> 00:05:55 oriented along y and overlapping simultaneously with a plus 1s 90 00:05:55 --> 00:05:59 wave function here and minus 1s wave function here so that you 91 00:05:59 --> 00:06:03 see a beautiful bonding molecular orbital that is at the 92 00:06:03 --> 00:06:08 same energy at the one we just looked at. 93 00:06:08 --> 00:06:11 And so, as you step up in energy, looking at the energy 94 00:06:11 --> 00:06:14 level diagram for BH three from last time, 95 00:06:14 --> 00:06:17 that is what you see. We have now six electrons in 96 00:06:17 --> 00:06:20 the molecule, two in this orbital and two 97 00:06:20 --> 00:06:24 each in the two orbitals we just looked at that provide the three 98 00:06:24 --> 00:06:27 BH bonds that we represent in the valance bond theory as 99 00:06:27 --> 00:06:32 electron pair bonds. But this is a totally different 100 00:06:32 --> 00:06:36 way of looking at the electronic structure that is very appearing 101 00:06:36 --> 00:06:41 because it just takes advantage of the atomic orbital properties 102 00:06:41 --> 00:06:44 that you would calculate for your central atom. 103 00:06:44 --> 00:06:48 Now, let's go up one more. The very next one, 104 00:06:48 --> 00:06:51 I will skip showing to you for purposes of saving time, 105 00:06:51 --> 00:06:56 here, but you know that the next orbital up is simply the 106 00:06:56 --> 00:07:00 2pz orbital on the boron, which is our lowest unoccupied 107 00:07:00 --> 00:07:03 molecular orbital, as well as being an atomic 108 00:07:03 --> 00:07:07 orbital in this system and responsible for the Lewis acid 109 00:07:07 --> 00:07:12 characteristics of this species. And one up above that, 110 00:07:12 --> 00:07:16 one higher in energy than the LUMO is the orbital that I did 111 00:07:16 --> 00:07:20 show you last time, the out-of-phase combination of 112 00:07:20 --> 00:07:24 the boron 2s with the three hydrogens all with the same 113 00:07:24 --> 00:07:26 sign. It is sort of a round nodal 114 00:07:26 --> 00:07:30 surface intersection each of the BH bonds. 115 00:07:30 --> 00:07:34 And then, finally, orbitals number six and seven 116 00:07:34 --> 00:07:40 are the antibonding counterparts to the ones that I just showed 117 00:07:40 --> 00:07:45 you involving boron's 2px and 2py wave functions. 118 00:07:45 --> 00:07:49 Here is what these look like. And this one, 119 00:07:49 --> 00:07:53 you will see, involves the 2px orbital. 120 00:07:53 --> 00:07:58 Here is our x-axis pointing up. And the blue lobe of 2px, 121 00:07:58 --> 00:08:02 the positive lobe here, as you can see, 122 00:08:02 --> 00:08:07 is squished out and down. These pictures can be a little 123 00:08:07 --> 00:08:11 bit more complicated than what we are used to looking at from 124 00:08:11 --> 00:08:14 just sketching it out on the board or the qualitative 125 00:08:14 --> 00:08:16 pictures that you sometimes see in your textbook. 126 00:08:16 --> 00:08:20 But what we do find here that is the important feature is that 127 00:08:20 --> 00:08:22 as we go from the 1s contribution on this hydrogen 128 00:08:22 --> 00:08:26 over here to the positive lobe of 2px we are going through a 129 00:08:26 --> 00:08:28 nodal surface. And that is antibonding in 130 00:08:28 --> 00:08:31 character. And you can see that this 131 00:08:31 --> 00:08:35 deformation of this lobe of the p orbital, of course, 132 00:08:35 --> 00:08:38 looks like a high energy type of phenomena. 133 00:08:38 --> 00:08:41 And indeed it is. This is one of the two highest 134 00:08:41 --> 00:08:45 energy orbitals in the energy level diagram for the BH three 135 00:08:45 --> 00:08:47 molecule. And then, similarly, 136 00:08:47 --> 00:08:51 here is the other lobe of the 2px orbital, the minus lobe. 137 00:08:51 --> 00:08:55 And, as you try to go from it to the adjacent hydrogens, 138 00:08:55 --> 00:08:59 remember, in the bonding one we were allowing this to overlap 139 00:08:59 --> 00:09:03 with the same sign on the hydrogens. 140 00:09:03 --> 00:09:06 Now we have the opposite sign on the hydrogens, 141 00:09:06 --> 00:09:10 so that we have a beautiful antibonding node indicated here 142 00:09:10 --> 00:09:15 and here between the minus phase lobe of 2px and the adjacent 143 00:09:15 --> 00:09:17 hydrogens. So, this antibonding orbital 144 00:09:17 --> 00:09:22 has lots of internuclear nodes, nodes that appear between 145 00:09:22 --> 00:09:26 nuclei and indicate that we are not getting overlapped and 146 00:09:26 --> 00:09:30 bonding, but rather we are getting a high frequency orbital 147 00:09:30 --> 00:09:36 that is likewise high in energy. Finally, I will show you the 148 00:09:36 --> 00:09:39 counterpart to this one, that involves 2py. 149 00:09:39 --> 00:09:44 It is a little easier to understand from inspecting it. 150 00:09:44 --> 00:09:51 151 00:09:51 --> 00:09:55 And it also evinces the internuclear nodes that you 152 00:09:55 --> 00:10:00 would expect for an antibonding molecular orbital. 153 00:10:00 --> 00:10:04 And I am orienting it so that you will be able to understand 154 00:10:04 --> 00:10:07 it with reference to our coordinate system as introduced 155 00:10:07 --> 00:10:10 last time. And so, you have the boron and 156 00:10:10 --> 00:10:12 the hydrogen along x, up here. 157 00:10:12 --> 00:10:15 Here is our 2py. It is sort of bending away from 158 00:10:15 --> 00:10:19 these two hydrogens whose wave functions have opposite sign to 159 00:10:19 --> 00:10:23 the lobes that are directed into their vicinity. 160 00:10:23 --> 00:10:27 You can see that we have here a nodal surface between boron and 161 00:10:27 --> 00:10:30 this hydrogen wherein the bonding counterpart that we 162 00:10:30 --> 00:10:35 looked at had the same sign and a nice bond. 163 00:10:35 --> 00:10:38 And then over here, once again, the mirror image. 164 00:10:38 --> 00:10:42 So, this is one of our final orbitals in looking at the BH 165 00:10:42 --> 00:10:44 three energy level diagram. 166 00:10:44 --> 00:10:47 It is the case that if you start to put electrons into 167 00:10:47 --> 00:10:51 antibonding orbitals, they will cancel the bonding 168 00:10:51 --> 00:10:53 properties of the bonding counterparts. 169 00:10:53 --> 00:10:57 And we will explore that in quite a bit more detail here 170 00:10:57 --> 00:11:02 shortly. Let me leave that up there for 171 00:11:02 --> 00:11:09 now and tell you what quadrangle of problems it is that I hope to 172 00:11:09 --> 00:11:15 answer for you today using more MO theory ideas. 173 00:11:15 --> 00:11:22 First of these will be why He two is so stable? 174 00:11:22 --> 00:11:27 175 00:11:27 --> 00:11:33 And so, today's lecture is predominantly devoted to 176 00:11:33 --> 00:11:39 diatomic molecules. And He two will be the 177 00:11:39 --> 00:11:44 first of these. Let's make this unstable. 178 00:11:44 --> 00:11:52 Let's do stable here in just a moment, but first let's say, 179 00:11:52 --> 00:12:00 next, why does O two have unpaired electrons? 180 00:12:00 --> 00:12:07 181 00:12:07 --> 00:12:11 Certainly, if we draw the valance bond picture for O two, 182 00:12:11 --> 00:12:14 like that, it does not give us any 183 00:12:14 --> 00:12:19 indication that this diatomic molecule would have unpaired 184 00:12:19 --> 00:12:22 electrons. And so, we are going to see how 185 00:12:22 --> 00:12:26 MO theory can shed some light on this issue. 186 00:12:26 --> 00:12:30 And then, the final two questions that I will fold into 187 00:12:30 --> 00:12:36 one line here given the way I am using up space on this board is, 188 00:12:36 --> 00:12:40 why is N two so stable -- 189 00:12:40 --> 00:12:45 190 00:12:45 --> 00:12:47 -- and CO poison? 191 00:12:47 --> 00:12:52 192 00:12:52 --> 00:12:55 MO theory can shed very clear light on all of these questions. 193 00:12:55 --> 00:12:59 And so, that is what we will work on for the rest of the 194 00:12:59 --> 00:13:01 hour. In MO theory, 195 00:13:01 --> 00:13:05 there are a couple things you should keep in mind when trying 196 00:13:05 --> 00:13:11 to grasp all the subtleties of a given energy level diagram with 197 00:13:11 --> 00:13:15 which you may be confronted in your textbook or on an exam or 198 00:13:15 --> 00:13:20 just through reading papers in the Journal of the American 199 00:13:20 --> 00:13:25 Chemical Society, wherever you may find these. 200 00:13:25 --> 00:13:31 You should keep in mind that, number one, interaction is 201 00:13:31 --> 00:13:36 strong. That is, when atomic orbitals 202 00:13:36 --> 00:13:43 interact to form molecular orbitals, the AO interaction is 203 00:13:43 --> 00:13:45 strong -- 204 00:13:45 --> 00:13:57 205 00:13:57 --> 00:14:04 -- when there is good spatial overlap. 206 00:14:04 --> 00:14:11 207 00:14:11 --> 00:14:15 Overlap is a central concept in molecular orbital theory. 208 00:14:15 --> 00:14:19 The idea is that if you have atoms that are far apart from 209 00:14:19 --> 00:14:23 each other in space, then their wave functions have 210 00:14:23 --> 00:14:27 dropped off exponentially and are not interacting much and 211 00:14:27 --> 00:14:32 there is not good overlap. But when orbitals are close in 212 00:14:32 --> 00:14:36 space and if their orbitals are directed in space toward one 213 00:14:36 --> 00:14:40 another, then there may be overlap that leads to good 214 00:14:40 --> 00:14:43 bonding. And also I can echo this first 215 00:14:43 --> 00:14:47 part, AO interaction is strong when, and say two, 216 00:14:47 --> 00:14:50 AOs are close in energy. The interacting orbitals are 217 00:14:50 --> 00:14:53 close in energy. 218 00:14:53 --> 00:15:13 219 00:15:13 --> 00:15:17 When I talk about where atomic orbitals are in energy, 220 00:15:17 --> 00:15:21 I am going to really want you to think about your periodic 221 00:15:21 --> 00:15:26 table and the properties that appear with periodicity and are 222 00:15:26 --> 00:15:30 organized and collated in the periodic table. 223 00:15:30 --> 00:15:33 We are going to be talking about properties like 224 00:15:33 --> 00:15:37 electronegativity as it relates to the energy. 225 00:15:37 --> 00:15:42 And I will get to that a little bit on the next board, 226 00:15:42 --> 00:15:45 but let's first make a small MO diagram here. 227 00:15:45 --> 00:15:51 And this will be a diagram that we may use both for H two 228 00:15:51 --> 00:15:55 or He two. This is the simplest of all MO 229 00:15:55 --> 00:16:01 diagrams and one with which you should be quite familiar. 230 00:16:01 --> 00:16:07 We have a bonding molecular orbital at low-end energy. 231 00:16:07 --> 00:16:14 And notice that if this is a 1s orbital over here and this is a 232 00:16:14 --> 00:16:20 1s orbital over here for H two or He two 233 00:16:20 --> 00:16:25 systems, then when these come together and bond, 234 00:16:25 --> 00:16:30 here are your two nuclei, -- 235 00:16:30 --> 00:16:33 -- and here is a probability density isosurface that I am 236 00:16:33 --> 00:16:37 drawing around that shows in-phase combination of those 237 00:16:37 --> 00:16:42 two 1s orbitals merging with each other, giving good overlap, 238 00:16:42 --> 00:16:45 and the interacting AOs being of the same energy. 239 00:16:45 --> 00:16:49 Because the H two and He two molecules have such 240 00:16:49 --> 00:16:52 symmetry we have a good bonding orbital. 241 00:16:52 --> 00:16:55 And then, up here, we must find there to be an 242 00:16:55 --> 00:16:59 internuclear node in that corresponding antibonding 243 00:16:59 --> 00:17:03 orbital. And so, it will look something 244 00:17:03 --> 00:17:05 like this. And, therefore, 245 00:17:05 --> 00:17:10 I am going to associate with this high-lying orbital an 246 00:17:10 --> 00:17:14 asterisk to indicate the antibonding character, 247 00:17:14 --> 00:17:18 the presence of this internuclear node, 248 00:17:18 --> 00:17:23 the change of sign as we go from one nucleus to the other, 249 00:17:23 --> 00:17:27 the absence of bonding character. 250 00:17:27 --> 00:17:30 Here we have the buildup of electron density in the 251 00:17:30 --> 00:17:34 internuclear region, electrons being stabilized by 252 00:17:34 --> 00:17:38 being held simultaneously by more than one nucleus that is 253 00:17:38 --> 00:17:42 positively charged. And here, the exact inverse of 254 00:17:42 --> 00:17:47 that, constructive interference and destructive interference in 255 00:17:47 --> 00:17:50 the H two or He two systems. 256 00:17:50 --> 00:17:54 And then we can ask, how many electrons do we have 257 00:17:54 --> 00:18:00 to put into the diagram? If it is the H two case, 258 00:18:00 --> 00:18:04 then, to figure out the bond order, -- 259 00:18:04 --> 00:18:14 260 00:18:14 --> 00:18:18 -- what we do is populate the diagram according to the same 261 00:18:18 --> 00:18:23 kind of Aufbau principle that you would for generating the 262 00:18:23 --> 00:18:27 energy level diagram for an atom, and taking into account 263 00:18:27 --> 00:18:32 things like Hund's rule. If it is H two, 264 00:18:32 --> 00:18:37 we have two electrons that we can put in, which in here with 265 00:18:37 --> 00:18:39 opposing spin, like that. 266 00:18:39 --> 00:18:43 That is our bonding molecular orbital. 267 00:18:43 --> 00:18:48 We have two bonding electrons. Zero antibonding electrons 268 00:18:48 --> 00:18:52 divided by two equals a bond order of one. 269 00:18:52 --> 00:18:57 We have an H-H single bond in the case of the H two 270 00:18:57 --> 00:19:02 molecule. But if we have He two, 271 00:19:02 --> 00:19:07 then in the He two system, we have two more electrons, 272 00:19:07 --> 00:19:12 and the only place they can go is up here in the antibonding 273 00:19:12 --> 00:19:16 molecular orbital. We have two bonding minus two 274 00:19:16 --> 00:19:22 antibonding over two is equal to zero for a bond order of zero. 275 00:19:22 --> 00:19:27 And so, the idea is that if two He atoms collide with each 276 00:19:27 --> 00:19:31 other, when they do so, their orbitals may overlap and 277 00:19:31 --> 00:19:36 give rise to bonding. But, simultaneously, 278 00:19:36 --> 00:19:40 you get antibonding. And the net bond order is zero, 279 00:19:40 --> 00:19:44 and so He two is not bound, but these atoms just 280 00:19:44 --> 00:19:47 bounce off each other. There is no stabilization. 281 00:19:47 --> 00:19:51 And you can certainly understand that if we were in 282 00:19:51 --> 00:19:55 the middle somewhere, as we would be if we had He two 283 00:19:55 --> 00:19:58 plus, missing one electron up here, 284 00:19:58 --> 00:20:02 then our bond order would be one-half. 285 00:20:02 --> 00:20:06 It is going to get a lot more complicated than this, 286 00:20:06 --> 00:20:11 but this you have to know because this is a really nice 287 00:20:11 --> 00:20:16 starting point for thinking about bonding in all kinds of 288 00:20:16 --> 00:20:20 scenarios where you may need to consider it. 289 00:20:20 --> 00:20:24 And so, let's look at some periodic properties. 290 00:20:24 --> 00:20:30 This will be with reference, again, to energy. 291 00:20:30 --> 00:20:36 And I am interested in how some of the properties of the atoms 292 00:20:36 --> 00:20:41 vary as we go across the periodic table, 293 00:20:41 --> 00:20:48 lithium to beryllium to boron to carbon to nitrogen to oxygen 294 00:20:48 --> 00:20:52 and over to fluorine. And I will stop there. 295 00:20:52 --> 00:21:00 We won't worry about any more of the noble gases today. 296 00:21:00 --> 00:21:03 As we go from left to right, one of the things that you know 297 00:21:03 --> 00:21:07 from your study of the periodic table is that electronegativity 298 00:21:07 --> 00:21:08 increases. 299 00:21:08 --> 00:21:21 300 00:21:21 --> 00:21:24 This increases from left to right across the Periodic Table 301 00:21:24 --> 00:21:27 in concert with increasing Z. 302 00:21:27 --> 00:21:34 303 00:21:34 --> 00:21:36 That is, the increasing atomic number. 304 00:21:36 --> 00:21:41 That is, the increasing number of positively charged protons in 305 00:21:41 --> 00:21:46 our nucleus, as we go across. Each time we are adding more 306 00:21:46 --> 00:21:50 protons to that nucleus. The nucleus is becoming more 307 00:21:50 --> 00:21:53 and more positively charged as we go across. 308 00:21:53 --> 00:21:58 And an important consequence of that has to do with the fact 309 00:21:58 --> 00:22:03 that s orbitals don't have a node at the nucleus. 310 00:22:03 --> 00:22:08 Whereas, p orbitals do. Since these elements are in the 311 00:22:08 --> 00:22:12 so-called p block of our periodic table, 312 00:22:12 --> 00:22:18 well, lithium in the s block, but we will consider the 313 00:22:18 --> 00:22:24 properties all the way across. And the energy issue up here 314 00:22:24 --> 00:22:29 that I am going to be concerned with is the energy of the atomic 315 00:22:29 --> 00:22:33 2s versus 2p orbitals as we go from left to right across the 316 00:22:33 --> 00:22:37 periodic table, systematically adding to the 317 00:22:37 --> 00:22:42 number of protons in our nucleus in a way that does not affect 2s 318 00:22:42 --> 00:22:46 orbitals the same way that it affects 2p orbitals. 319 00:22:46 --> 00:22:50 It turns out that by the time we get over to fluorine, 320 00:22:50 --> 00:22:55 where we have essentially our most electronegative element, 321 00:22:55 --> 00:23:00 the 2s orbital has sunk to a very low energy. 322 00:23:00 --> 00:23:05 And the 2p orbital has gone down in energy as well, 323 00:23:05 --> 00:23:12 but just not by nearly as much. And so, it is nearly an 324 00:23:12 --> 00:23:15 isotonic function as we go across. 325 00:23:15 --> 00:23:22 2p is decreasing in energy in response to this increased Z, 326 00:23:22 --> 00:23:27 but not as much as 2s is decreasing in energy, 327 00:23:27 --> 00:23:34 having to do with the fact that 2s electrons see much more of 328 00:23:34 --> 00:23:41 the nucleus than 2p electrons do because 2s electrons don't have 329 00:23:41 --> 00:23:47 a node there. They spend a lot more time in 330 00:23:47 --> 00:23:52 close to the nucleus than do your 2p electrons. 331 00:23:52 --> 00:23:57 This has a really important influence on that set of 332 00:23:57 --> 00:24:02 diatomic molecule MO theory problems, eight orbital 333 00:24:02 --> 00:24:09 problems, that we call homo or heteronuclear diatomic molecules 334 00:24:09 --> 00:24:14 of these elements. And that has to do with the 335 00:24:14 --> 00:24:20 fact that in between nitrogen and oxygen, a fundamental change 336 00:24:20 --> 00:24:24 takes place in the energy level diagram. 337 00:24:24 --> 00:24:28 And that change, that results from the atomic 338 00:24:28 --> 00:24:33 structure of the elements, ends up with the result that 339 00:24:33 --> 00:24:38 the MO diagram is much easier to draw for oxygen, 340 00:24:38 --> 00:24:41 O two, and fluorine, 341 00:24:41 --> 00:24:45 F two, than it is for the earlier 342 00:24:45 --> 00:24:48 ones. And it is much easier to 343 00:24:48 --> 00:24:53 understand for O two and F two than it is for N 344 00:24:53 --> 00:24:55 two, C two, B two, Be two, Li two. 345 00:24:55 --> 00:24:57 346 00:24:57 --> 00:25:00 So, let's just see what that means. 347 00:25:00 --> 00:25:11 348 00:25:11 --> 00:25:14 First of all, when we are going to draw an 349 00:25:14 --> 00:25:17 energy level diagram for a diatomic molecule, 350 00:25:17 --> 00:25:23 if it is a homonuclear diatomic molecule, meaning the two atoms 351 00:25:23 --> 00:25:27 that are going to be bonded together are the same, 352 00:25:27 --> 00:25:31 that means that the atomic orbitals for the contributing 353 00:25:31 --> 00:25:36 atoms are the same. Here, on the left, 354 00:25:36 --> 00:25:44 what I am drawing is, let's say, an F or an O atom. 355 00:25:44 --> 00:25:49 We have the 2s and the 2p, x-y-z. 356 00:25:49 --> 00:25:58 That is four of the eight orbitals in our problem. 357 00:25:58 --> 00:26:03 And then, over here, we have the other identical F 358 00:26:03 --> 00:26:10 or O atom, with its 2p x-y-z and 2s orbitals at exactly the same 359 00:26:10 --> 00:26:15 energy as for the counterpart, over here. 360 00:26:15 --> 00:26:18 So, this is another F or O atom. 361 00:26:18 --> 00:26:25 And then we are going to ask, how can these atomic orbitals 362 00:26:25 --> 00:26:31 combine to give molecular orbitals in these diatomic 363 00:26:31 --> 00:26:35 molecules? This is unlike the BH three 364 00:26:35 --> 00:26:40 problem because there is no atom at the center of gravity 365 00:26:40 --> 00:26:43 of our system, but the ideas are the same. 366 00:26:43 --> 00:26:47 And the ideas are very much the same as what we have here for H 367 00:26:47 --> 00:26:51 two, where also we could make molecular orbitals despite 368 00:26:51 --> 00:26:56 the fact that there was no atom at the center of our system. 369 00:26:56 --> 00:27:00 We can pretend that there is, and we can use that pretend 370 00:27:00 --> 00:27:05 atom to identify what linear combinations we should make. 371 00:27:05 --> 00:27:09 A simpler way to do it, at this point, 372 00:27:09 --> 00:27:14 would be to say that our molecule has the two nuclei 373 00:27:14 --> 00:27:20 oriented along the z-axis. And then you have x and y 374 00:27:20 --> 00:27:25 perpendicular to z. And so, if we take this choice 375 00:27:25 --> 00:27:32 of coordinate system that the molecule is oriented along z, 376 00:27:32 --> 00:27:39 the two nuclei lie one on plus z, one on minus z. 377 00:27:39 --> 00:27:47 Then we can immediately classify our atomic orbitals as 378 00:27:47 --> 00:27:55 being either sigma or pi with respect to the z-axis. 379 00:27:55 --> 00:28:02 I will say AO is sigma or pi with respect to z, 380 00:28:02 --> 00:28:10 which is the molecular axis. And remember what that means in 381 00:28:10 --> 00:28:15 terms of the nodal properties. If something is sigma with 382 00:28:15 --> 00:28:19 respect to z, that means if you view it down 383 00:28:19 --> 00:28:25 z it will look like a cylinder. It will look like a sphere, 384 00:28:25 --> 00:28:28 actually. It will be cylindrically 385 00:28:28 --> 00:28:32 symmetric about the z-axis. If it is sigma then, 386 00:28:32 --> 00:28:37 if you are viewing down z, you see that. 387 00:28:37 --> 00:28:43 That could be either an s orbital or it could be a pz 388 00:28:43 --> 00:28:47 orbital. They would look the same if you 389 00:28:47 --> 00:28:52 were viewing right down z. And then pi, 390 00:28:52 --> 00:28:56 viewing down z, would look like this. 391 00:28:56 --> 00:29:03 And that would be a px or a py orbital perpendicular to the 392 00:29:03 --> 00:29:07 z-axis. And this would be an s orbital 393 00:29:07 --> 00:29:11 or a pz orbital. What I can say right away is 394 00:29:11 --> 00:29:15 that we can separate out the molecular orbitals that we are 395 00:29:15 --> 00:29:20 going to form from these atomic orbitals into their sigma or pi 396 00:29:20 --> 00:29:24 characteristics relative to the z-axis. 397 00:29:24 --> 00:29:28 And because we are in the O or F atom case, very far on the 398 00:29:28 --> 00:29:33 right-hand side the periodic table, we have a large gap. 399 00:29:33 --> 00:29:36 This gap is large. 400 00:29:36 --> 00:29:42 401 00:29:42 --> 00:29:47 We can make the approximation that this 2s orbital here, 402 00:29:47 --> 00:29:53 which could in principle form a sigma bond with this 2pz orbital 403 00:29:53 --> 00:29:59 over here, that would be an interaction looking like that, 404 00:29:59 --> 00:30:02 -- -- that that does not occur. 405 00:30:02 --> 00:30:07 Because remember here I said you get strong interaction when 406 00:30:07 --> 00:30:10 the interacting AOs are close in energy. 407 00:30:10 --> 00:30:15 When you are talking about these very electronegative 408 00:30:15 --> 00:30:20 elements, the s manifold of orbitals is very well separated 409 00:30:20 --> 00:30:25 in energy from the p manifold. That leads to simplicity in the 410 00:30:25 --> 00:30:30 case of the diagram that we are about to draw. 411 00:30:30 --> 00:30:34 Because we say that this interacts with this in a sigma 412 00:30:34 --> 00:30:39 fashion, giving rise to bonding and antibonding interactions 413 00:30:39 --> 00:30:43 that look exactly like what we have drawn over there. 414 00:30:43 --> 00:30:46 I will draw the bonding orbital here. 415 00:30:46 --> 00:30:51 Actually, the antibonding orbital here and the bonding 416 00:30:51 --> 00:30:54 orbital here. And I will show the parentage 417 00:30:54 --> 00:30:59 of this molecular orbitals in this way. 418 00:30:59 --> 00:31:03 And you will recognize that this is our in-phase combination 419 00:31:03 --> 00:31:08 and this is our out-of-phase combination, analogous to the H 420 00:31:08 --> 00:31:12 two problem. This is like the H two 421 00:31:12 --> 00:31:16 problem built into the F two or the O two 422 00:31:16 --> 00:31:19 problem. And next what we find is that 423 00:31:19 --> 00:31:24 we can also make a sigma bond by interaction of pz with pz. 424 00:31:24 --> 00:31:27 This is going to be a nice strong directed bonding 425 00:31:27 --> 00:31:32 interaction that will look like this. 426 00:31:32 --> 00:31:38 427 00:31:38 --> 00:31:42 You see we have overlap here in the center, a nice strong 428 00:31:42 --> 00:31:47 bonding interaction in the center with 2pz orbitals that 429 00:31:47 --> 00:31:52 are directed at each other. And this is a sigma bond 430 00:31:52 --> 00:31:57 because you view that down z, it is going to look like a 431 00:31:57 --> 00:32:02 round thing. You are not going to see any 432 00:32:02 --> 00:32:06 nodal surfaces. And then it has up here a 433 00:32:06 --> 00:32:11 corresponding antibonding orbital right there. 434 00:32:11 --> 00:32:14 So far I have -- 435 00:32:14 --> 00:32:21 436 00:32:21 --> 00:32:27 -- two pair-wise combinations that give us two sigma bonding 437 00:32:27 --> 00:32:34 orbitals and two sigma star antibonding orbitals. 438 00:32:34 --> 00:32:37 So, that is pretty straightforward. 439 00:32:37 --> 00:32:40 And, once again, I can say that we have the H 440 00:32:40 --> 00:32:46 two problem built into this energy level diagram twice, 441 00:32:46 --> 00:32:50 with the s interactions, with the pz interactions. 442 00:32:50 --> 00:32:56 The only thing I have left is to do my px and py interactions. 443 00:32:56 --> 00:33:00 And we can make a pair of pi bonds and a pair of pi 444 00:33:00 --> 00:33:06 anti-bonds that corresponds to those pi bonds. 445 00:33:06 --> 00:33:08 This one is pi. This one is pi star. 446 00:33:08 --> 00:33:12 And what do they look like? Well, they look like 447 00:33:12 --> 00:33:16 side-to-side bonds between pairs of p orbitals. 448 00:33:16 --> 00:33:21 This is just like what I showed you for the ethylene molecule. 449 00:33:21 --> 00:33:25 The pi bond, in fact, has this nice overlap 450 00:33:25 --> 00:33:28 on one side and up here on the other. 451 00:33:28 --> 00:33:33 There is your pi bond. And you have one of those that 452 00:33:33 --> 00:33:38 lie in the x,z-plane and one of those that lie in the y,z-plane. 453 00:33:38 --> 00:33:43 You have two of them, and they are at equal energy 454 00:33:43 --> 00:33:44 here. And then up here, 455 00:33:44 --> 00:33:47 what does the pi star look like? 456 00:33:47 --> 00:33:51 Well, the same, except we turn around one of 457 00:33:51 --> 00:33:54 the p orbitals, introducing a nodal surface, 458 00:33:54 --> 00:33:59 like that. And we have two of those. 459 00:33:59 --> 00:34:04 And here is our nodal surface. Now it is an internuclear 460 00:34:04 --> 00:34:09 between the nuclei nodal surface, indicating antibonding 461 00:34:09 --> 00:34:14 character there. That is the easy case because s 462 00:34:14 --> 00:34:18 and p are very well separated. What you can see, 463 00:34:18 --> 00:34:23 though, is that type of interaction of a 2s on our left 464 00:34:23 --> 00:34:29 atom with a pz on the right atom, that might start to become 465 00:34:29 --> 00:34:34 important as you are over here in this part of the diagram, 466 00:34:34 --> 00:34:41 where s and p are pretty close together in energy. 467 00:34:41 --> 00:34:43 And that is what happens, in fact. 468 00:34:43 --> 00:34:48 And that is what happens as soon as you go to the left of 469 00:34:48 --> 00:34:53 oxygen and to nitrogen or anything lighter than nitrogen. 470 00:34:53 --> 00:34:57 Suddenly, you cannot ignore interactions of s on one side 471 00:34:57 --> 00:35:00 with p on the other. 472 00:35:00 --> 00:35:09 473 00:35:09 --> 00:35:14 And so, I am going to draw here the diagram that you would use, 474 00:35:14 --> 00:35:17 say, for N two. And, for simplicity, 475 00:35:17 --> 00:35:21 I am just going to draw the middle part. 476 00:35:21 --> 00:35:26 This part here in the middle is that which corresponds to the 477 00:35:26 --> 00:35:29 molecule. This one is what you would use 478 00:35:29 --> 00:35:33 for O two or F two. 479 00:35:33 --> 00:35:39 And let's just go ahead and draw that diagram for the 480 00:35:39 --> 00:35:44 molecule. This one would be this set of 481 00:35:44 --> 00:35:49 energy levels corresponding to, for example, N two. 482 00:35:49 --> 00:35:54 And we have increasing energy 483 00:35:54 --> 00:36:00 on the vertical axis. We are going to find that 484 00:36:00 --> 00:36:07 again, we have a sigma and a sigma star. 485 00:36:07 --> 00:36:12 And then, the difference comes right here where we find that as 486 00:36:12 --> 00:36:17 we go up in energy we next get to our pi bonds. 487 00:36:17 --> 00:36:22 And then, the next sigma orbital is slightly higher in 488 00:36:22 --> 00:36:29 energy than the pi system rather than slightly lower in energy. 489 00:36:29 --> 00:36:34 And then we will encounter up here our pi star. 490 00:36:34 --> 00:36:38 And then, finally, that highest in energy, 491 00:36:38 --> 00:36:41 sigma star. This switch, 492 00:36:41 --> 00:36:48 this sigma going up relative to that pi is really a consequence 493 00:36:48 --> 00:36:55 of all of the sigma orbitals being responsive to the value of 494 00:36:55 --> 00:37:02 the electronegativity of the 2s orbital of the atom. 495 00:37:02 --> 00:37:06 You can really almost consider the pi system independent from 496 00:37:06 --> 00:37:09 the sigma. These four sigma orbitals, 497 00:37:09 --> 00:37:12 sigma, sigma star, sigma, sigma star, 498 00:37:12 --> 00:37:16 I can call them one sigma, two, three, four, 499 00:37:16 --> 00:37:20 just to show you that we have, in ascending order, 500 00:37:20 --> 00:37:22 four orbitals of sigma symmetry. 501 00:37:22 --> 00:37:26 That whole manifold, when you can start mixing a 502 00:37:26 --> 00:37:31 little bit of very low energy s into it, sinks down relative to 503 00:37:31 --> 00:37:34 pi. In the case over here, 504 00:37:34 --> 00:37:39 we are basically pulling down the four sigma orbitals relative 505 00:37:39 --> 00:37:42 to pi. And here, because our s 506 00:37:42 --> 00:37:47 orbitals are higher in energy relative to our p orbitals, 507 00:37:47 --> 00:37:51 they go up a little bit and bumps three sigma up over pi. 508 00:37:51 --> 00:37:56 And what it means is that these orbitals are not so simple 509 00:37:56 --> 00:37:59 anymore. Any one of them is a linear 510 00:37:59 --> 00:38:02 combination of four atomic orbitals. 511 00:38:02 --> 00:38:06 This orbital here, one sigma, will not look like 512 00:38:06 --> 00:38:09 it looks in the H two problem, anymore. 513 00:38:09 --> 00:38:12 This one sigma will have some p mixed into it. 514 00:38:12 --> 00:38:16 And so, one way we can represent that through a simple 515 00:38:16 --> 00:38:19 drawing is like this. 516 00:38:19 --> 00:38:25 517 00:38:25 --> 00:38:29 You see the difference between that sigma bonding orbital and 518 00:38:29 --> 00:38:33 the one up there? We have some extra little nodes 519 00:38:33 --> 00:38:37 in here that are an inherent characteristic of the 520 00:38:37 --> 00:38:40 contribution of 2pz orbitals into this. 521 00:38:40 --> 00:38:45 This is a linear combination of the 2s and the 2pz orbitals on 522 00:38:45 --> 00:38:49 the two atoms we have. There are four atomic orbitals 523 00:38:49 --> 00:38:54 that go in with different coefficients to these different 524 00:38:54 --> 00:38:57 parts of the sigma manifold. And then up here, 525 00:38:57 --> 00:39:03 the other bonding orbital, we can draw it this way. 526 00:39:03 --> 00:39:08 527 00:39:08 --> 00:39:11 And this molecular orbital, this one here, 528 00:39:11 --> 00:39:14 three sigma, has diminished bonding 529 00:39:14 --> 00:39:20 character between the two nuclei and enhanced character on the 530 00:39:20 --> 00:39:25 outside, the part of the p orbital that is contributing to 531 00:39:25 --> 00:39:30 it that points away from the other atom. 532 00:39:30 --> 00:39:34 And so, while this has bonding character, it also has what we 533 00:39:34 --> 00:39:37 might think of as lone pair characteristics. 534 00:39:37 --> 00:39:40 In MO theory, some orbitals are not that 535 00:39:40 --> 00:39:42 simple. They might be at the same time 536 00:39:42 --> 00:39:46 a little bit bonding and a little bit lone pair in 537 00:39:46 --> 00:39:49 character. Let's look at a couple of 538 00:39:49 --> 00:39:52 orbitals like that, briefly. 539 00:39:52 --> 00:40:04 540 00:40:04 --> 00:40:08 And here I have done this for the C two molecule. 541 00:40:08 --> 00:40:12 I have done the calculation for C two, 542 00:40:12 --> 00:40:17 so now we are over here on the left-hand side of that dividing 543 00:40:17 --> 00:40:20 line where s and p are a big closer together. 544 00:40:20 --> 00:40:25 And I am opening up this orbital, this one down here. 545 00:40:25 --> 00:40:30 It is a little more complicated than the way I drew it on the 546 00:40:30 --> 00:40:35 board, but what you should be able to see is -- 547 00:40:35 --> 00:40:37 Think back, now, to the first orbital I showed 548 00:40:37 --> 00:40:41 you today, which was the lowest lying orbital in the BH three 549 00:40:41 --> 00:40:43 molecule. You remember, 550 00:40:43 --> 00:40:46 no matter which way we turned it, we only saw blue, 551 00:40:46 --> 00:40:48 which was the positive wave function. 552 00:40:48 --> 00:40:50 It looked like an s orbital, everywhere. 553 00:40:50 --> 00:40:53 It had the same sign everywhere, and you could not 554 00:40:53 --> 00:40:56 see any nodal properties. Well, that would be true also 555 00:40:56 --> 00:41:00 for this one down here in the case of O two or F two 556 00:41:00 --> 00:41:04 because it is not mixing in p character. 557 00:41:04 --> 00:41:07 Because the atomic s and p orbitals are so far away in 558 00:41:07 --> 00:41:09 energy. But now, when they are closer 559 00:41:09 --> 00:41:13 in energy, this orbital down here, the s over here sees the p 560 00:41:13 --> 00:41:15 over here and they mix in, and vice versa. 561 00:41:15 --> 00:41:19 And, if I turn this around, what you are going to see are 562 00:41:19 --> 00:41:22 these little negative lobes here that I am indicating that are 563 00:41:22 --> 00:41:24 mixing in. But this is hugely bonding 564 00:41:24 --> 00:41:27 orbital, still, because look at how much of the 565 00:41:27 --> 00:41:32 orbital is centered in the region between the nuclei. 566 00:41:32 --> 00:41:37 This is a very strongly bonding orbital in this system. 567 00:41:37 --> 00:41:44 Let's now visualize the three sigma, the third sigma symmetry 568 00:41:44 --> 00:41:50 orbital, as we ascend in energy. And it will look hopefully 569 00:41:50 --> 00:41:56 something like what I drew here. There it is. 570 00:41:56 --> 00:42:04 571 00:42:04 --> 00:42:07 You see this is a sigma orbital, because as we look down 572 00:42:07 --> 00:42:11 the z-axis, it looks just round. But it certainly has a lot of p 573 00:42:11 --> 00:42:15 orbital character because as we go from outside the molecule 574 00:42:15 --> 00:42:18 through the nucleus, we get a change in sign. 575 00:42:18 --> 00:42:21 And then there is overlap in here, but the amount of the 576 00:42:21 --> 00:42:25 overlap in here is small compared to the amount of this 577 00:42:25 --> 00:42:29 lobe out here that is just nonbonding in character because 578 00:42:29 --> 00:42:33 it is pointing out into space. It is like a lone pair of 579 00:42:33 --> 00:42:37 electrons at the same time as it is a bonding orbital. 580 00:42:37 --> 00:42:41 If this molecule actually had enough electrons to fill up 581 00:42:41 --> 00:42:46 through three sigma and no higher, than you would recognize 582 00:42:46 --> 00:42:50 that this orbital that we are looking at would be the highest 583 00:42:50 --> 00:42:55 occupied molecular orbital. And it would be responsible for 584 00:42:55 --> 00:42:58 the basicity and the nucleophilicity of the molecule 585 00:42:58 --> 00:43:02 -- -- because any Lewis acid that 586 00:43:02 --> 00:43:07 came in would want to come in on the z-axis to interact with this 587 00:43:07 --> 00:43:10 lone pair electron density out there. 588 00:43:10 --> 00:43:15 So, that is how our three sigma orbital now looks when we are on 589 00:43:15 --> 00:43:20 the left side of that red dotted line to the lighter elements. 590 00:43:20 --> 00:43:25 I will leave that up there for a moment while we consider a 591 00:43:25 --> 00:43:30 couple of interesting points. One of the things that you will 592 00:43:30 --> 00:43:34 often be asked to do is to write down the configuration. 593 00:43:34 --> 00:43:40 594 00:43:40 --> 00:43:45 And I want to finish these two questions here of O two, 595 00:43:45 --> 00:43:49 why does it have unpaired electrons? 596 00:43:49 --> 00:43:54 In the case of O two, we are over on this diagram, 597 00:43:54 --> 00:43:58 we have 12 valance electrons. We can go two, 598 00:43:58 --> 00:44:02 four, six, eight, ten, and then 11 and 12, 599 00:44:02 --> 00:44:08 two electrons up here in the pi star manifold. 600 00:44:08 --> 00:44:11 We are completely filled up through pi. 601 00:44:11 --> 00:44:16 And then, we have a half-filled pi star with 12 electrons 602 00:44:16 --> 00:44:19 populating the O two diagram. 603 00:44:19 --> 00:44:24 Let's represent that this way. We have our one sigma with two 604 00:44:24 --> 00:44:27 electrons in. We have our second sigma, 605 00:44:27 --> 00:44:32 which is antibonding with two electrons. 606 00:44:32 --> 00:44:36 Then we have our third sigma with two electrons. 607 00:44:36 --> 00:44:40 And then, as we go up in energy, the next is our first pi 608 00:44:40 --> 00:44:44 orbital bonding. That accommodates four 609 00:44:44 --> 00:44:47 electrons. And then we have next our 610 00:44:47 --> 00:44:51 second pi type orbital. It is antibonding and has two 611 00:44:51 --> 00:44:55 electrons in it. And then all the other orbitals 612 00:44:55 --> 00:45:00 are empty, so I won't indicate them. 613 00:45:00 --> 00:45:04 This is the configuration for the O two molecule. 614 00:45:04 --> 00:45:08 That means, we come back over here, by Hund's rule of maximum 615 00:45:08 --> 00:45:11 multiplicity, we have two spin-up electrons 616 00:45:11 --> 00:45:16 in the O two molecule with all these other orbitals 617 00:45:16 --> 00:45:20 down here being filled. That configuration that I wrote 618 00:45:20 --> 00:45:24 down for the O two molecule over there is a very shorthand way of 619 00:45:24 --> 00:45:29 representing the MO energy level diagram -- 620 00:45:29 --> 00:45:32 -- because I started here at the lowest energy, 621 00:45:32 --> 00:45:35 and I went up in energy like this. 622 00:45:35 --> 00:45:38 And what you can see is sigma star cancels sigma, 623 00:45:38 --> 00:45:42 so no bonding there. We have here three electron 624 00:45:42 --> 00:45:45 pairs in bonding orbitals, sigma and 2pi, 625 00:45:45 --> 00:45:49 but we have two electrons that are unpaired electrons, 626 00:45:49 --> 00:45:53 responsible for the paramagnetism of the O two 627 00:45:53 --> 00:45:56 molecule, that cancel some of the bonding 628 00:45:56 --> 00:46:01 down here. When we want to write that down 629 00:46:01 --> 00:46:04 in terms of our bond order convention, we have six bonding 630 00:46:04 --> 00:46:08 electrons minus two antibonding electrons over two, 631 00:46:08 --> 00:46:11 which is going to be equal to a bond order of two. 632 00:46:11 --> 00:46:14 That is our bond order for O two. 633 00:46:14 --> 00:46:18 While the bond order is what we expect to find based on that 634 00:46:18 --> 00:46:21 valance bond representation of O two up there, 635 00:46:21 --> 00:46:25 what we find out is that the representation of O two up there 636 00:46:25 --> 00:46:29 in the valance bond terminology would not tell us that the 637 00:46:29 --> 00:46:32 molecule should actually have two electrons that are not 638 00:46:32 --> 00:46:36 paired in the molecule, -- 639 00:46:36 --> 00:46:39 -- that it should have paramagnetism due to the lack of 640 00:46:39 --> 00:46:42 pairing up of all the electrons, spin pairing in the molecule. 641 00:46:42 --> 00:46:46 And it has to do with this high symmetry of the O two molecule. 642 00:46:46 --> 00:46:48 And it cannot distort from high 643 00:46:48 --> 00:46:51 symmetry because it has just two atoms. 644 00:46:51 --> 00:46:53 It has very few degrees of freedom. 645 00:46:53 --> 00:46:56 It cannot bend or something to get those electrons to pair up, 646 00:46:56 --> 00:47:01 and so they are unpaired. And that is why dioxegen has 647 00:47:01 --> 00:47:04 unpaired electrons. And then, if we go to nitrogen, 648 00:47:04 --> 00:47:09 the order that we write these things down in is a little 649 00:47:09 --> 00:47:13 different because the energy level diagram is different 650 00:47:13 --> 00:47:16 because now s and p are closer together. 651 00:47:16 --> 00:47:19 And what we have is one sigma with two electrons, 652 00:47:19 --> 00:47:22 or two sigma star with two electrons. 653 00:47:22 --> 00:47:25 And then, next, we have our one pi with its 654 00:47:25 --> 00:47:29 four electrons. And then next, 655 00:47:29 --> 00:47:32 we have our three sigma with its two electrons. 656 00:47:32 --> 00:47:35 And that is it. We have two less electrons in 657 00:47:35 --> 00:47:38 the system than we do in O two. 658 00:47:38 --> 00:47:41 That is N two. And our bond order now is 659 00:47:41 --> 00:47:43 three. That is in accord with our 660 00:47:43 --> 00:47:48 Lewis structure of N two, but it is a triple bond. 661 00:47:48 --> 00:47:52 And it is a triple bond in a molecule that is completely 662 00:47:52 --> 00:47:54 non-polar. And it is one of the strongest 663 00:47:54 --> 00:47:58 chemical bonds known. That triple bond is worth about 664 00:47:58 --> 00:48:03 226 kilocalories per mole. And it makes N two a 665 00:48:03 --> 00:48:06 very fascinating molecule. And, of course, 666 00:48:06 --> 00:48:09 it is the major constituent of our atmosphere. 667 00:48:09 --> 00:48:13 And it is very inert, due to the stability associated 668 00:48:13 --> 00:48:16 with having this diagram populated up all through the 669 00:48:16 --> 00:48:19 bonding orbitals, and then no more antibonding 670 00:48:19 --> 00:48:23 electrons present in the system. So, that is pretty interesting. 671 00:48:23 --> 00:48:27 And given the time, I think I will leave you after 672 00:48:27 --> 00:48:31 the following. I just want to show you one 673 00:48:31 --> 00:48:36 more picture as a prelude to where I will start next time. 674 00:48:36 --> 00:48:41 And that has to do with what happens when the two atoms that 675 00:48:41 --> 00:48:45 are bonding are different. Let's look at the three sigma 676 00:48:45 --> 00:48:49 orbital for the carbon monoxide molecule. 677 00:48:49 --> 00:48:52 It would look like it does for N two. 678 00:48:52 --> 00:48:55 It is the same number of electrons. 679 00:48:55 --> 00:49:00 But look here. It is very asymmetric. 680 00:49:00 --> 00:49:04 And that has to do with the fact that carbon and oxygen have 681 00:49:04 --> 00:49:06 very different electronegativity. 682 00:49:06 --> 00:49:10 And so, this highest occupied molecular orbital for carbon 683 00:49:10 --> 00:49:13 monoxide, again, an eight orbital problem, 684 00:49:13 --> 00:49:16 and again, a ten electron system, is one where we have a 685 00:49:16 --> 00:49:21 larger coefficient on the lone pair piece that is on the carbon 686 00:49:21 --> 00:49:24 atom of the molecule. And I will start off with this 687 00:49:24 --> 00:49:30 next time, but that is one of two reasons why CO is a poison. 688 00:49:30 --> 49:33 Have a nice weekend.