 Okay, so the class is going to be taped for the rest of the quarter, I think. Shant back there is in charge of the video. If you do not want the back of your head videoed for any reason, then move to the back of the class. So, you know, as I mentioned in discussion section yesterday, I totally honor you for going up in front of the class and presenting problems. So you can imagine how terrified I am to have myself on video that will probably eventually be on YouTube. Okay, so I want to start off by continuing where we left off. We're starting on our next lecture on molecular orbitals. And remember lecture one, that was more than a one-hour lecture. We talked about the fundamental idea behind arrow pushing, that it represents the interaction of filled orbitals with unfilled orbitals. And I gave you seven rules for mechanistic arrow pushing that we are going to agree to follow as a class when we do problem sets, when we do exams, those are the times when you really have to pay attention to those rules. And so, because arrow pushing represents the interaction of filled orbitals with unfilled orbitals, we have to make sure we all are on the same page with orbitals. So today we're going to talk about orbitals. And I want to start off with a simple problem for you to solve. Let's just imagine that we have two particles that are both positively charged on the atomic scale. And to make things meaningful, let's make these two protons that are ready to form a bond. And we all understand what electrostatics does. We understand Coulomb's law. If you were an electron with a negative charge, what's the ideal position for you to occupy relative to these two-point positive charges? An electron has a negative charge. I think we have this idea. I have this notion that I want to put that negatively charged electron right there. With all of my being, I want to put that electron there. But if you do that, you have violated the Heisenberg uncertainty principle. You can't specify the location of an electron. You have to put that electron all over the place. And that's what results in bonding. So we have two simple outcomes to that. One is we need orbitals. We need some sort of mathematical description of the probability of finding an electron smeared all over the place around those two hydrogen atom nuclei. So there's a second problem here. Whenever we put electrons into orbitals, we put them in two at a time. We put in electron pairs. And because we're putting in electron pairs, we need some way to show that those electrons will avoid each other. And so as a result of that, we need phasing. We need to phase those orbitals to show that there's a way for the electrons to get out of the way. And so let's go ahead and draw the canonical types of orbitals that we will use in this class. And there's really only two types. I'm going to represent an S orbital like this as just simple little voles and they'll have phasing, either hashed phasing or unhashed phasing like this. We'll also use P orbitals. And we'll represent them with this kind of lame representation like this. They don't look exactly like that, but this is good enough. And they could have various orientations with the X or Y or Z axes. So these are P orbitals. And so note the importance of phasing. Here I've separated the two different S orbitals. You have to imagine them on top of each other with that different phasing. Okay, so phasing allows us to think about the idea of having two electrons around the same place in space but avoiding each other. And so we need that. Okay, so we're going to talk about three types of orbitals today. And it's supposed to be reviewed for you. Supposedly these are ideas that you've already seen before. And so the intention is to review. So first we're going to review atomic orbitals. This is the stuff that you know is SPD and F orbitals relative to the structure of atoms. Then we're going to talk about combining those things into hybrid atomic orbitals. That's SP2, SP3, SP, stuff like that. So you should be familiar with that. And then finally we're going to talk about combining those things to make molecular orbitals. Okay, so let's go ahead and start off with atomic orbitals. Well hopefully we can add some new insight. Hopefully you can take these ideas that I'm sure you heard at some point in time. But when you take those ideas and you reapply them to reactions you already know, then hopefully you'll be able to do some more stuff with that. Okay, so let's go ahead and start off with atomic orbitals. So there's four types of canonical atomic orbitals that we use in chemistry commonly. There are potentially other shapes and other formulations but these are the ones that you should be familiar with from freshman chemistry and from sophomore organic chemistry. From general chemistry and organic chemistry. And that's SPD and F. Now fortunately we can rationalize everything in this class with just S and P orbitals. Now there will be examples of organometallic chemistry, transition metal chemistry where we will need to put in DNF orbitals but we will be able to explain everything in this class just by focusing on S and P orbitals. In a way that makes our life incredibly simple but what you'll learn is just handling these two types of orbitals and the way they interact is going to be immensely complex and yet immensely powerful. Okay, so we're just going to focus on S and P orbitals in this class. And I have one super important statement to make. And that is that P orbitals are higher in energy than S orbitals. I think every one of you knows this already. But what you don't know is just how powerful that is. And so let me go ahead and start off by graphically representing the fact that P orbitals are higher in energy than S orbitals. And I'm going to start by using a construct that we're going to use many times in this class called a molecular orbital or an orbital energy diagram. I'm going to have some mystical orbital axis here and I'll call that E. Sometimes I'll write E with a subscript like MO for molecular orbitals. Or maybe I'll just write here orbital and I'm going to show you some atomic orbitals. So let's graphically represent the fact that P orbitals are higher in energy than S orbitals. And I want to focus on P orbitals on a carbon atom because this is organic chemistry. We care most about carbon. Usually everything that I talk about is going to be carbon or else nitrogen, oxygen. And then sometimes things from slightly lower levels. So this is a P orbital energy. There's three types of P orbitals. They're orthogonal to each other. If I draw the shapes out for those orbitals. And I'm going to draw a little subscript here on that P to tell me that I'm talking about a P orbital on carbon. You'll see why that's important that I specify that in just a moment. So let me go ahead and try to represent those P orbitals. This would be a P orbital aligned with the Y axis. And there's two other orthogonal types of P orbitals that can coexist in space on a carbon atom. These are the other types of atomic orbitals. There would be one on the X axis. And I'm showing one of two arbitrary phasing combinations here. And then finally there's one sticking straight out at you that would look something like this. And I'll try to draw the hashed part going in the back of the plane of the board. Okay, so those are P orbitals. The important point is that these are way higher in energy than an S orbital on carbon. And I'll put a subscript there. Vastly higher in energy. If you were an electron in a P orbital, you'd be much more energetic and likely to attack things than an electron in an S orbital. That's the importance of energy. And that's what you care about. You care about which electrons are likely to attack other things. It's the most energetic ones. Conversely, if I were a pair of electrons and wanted to put myself somewhere, I would want to go into the S orbital because it's lower in energy. Electrons always want to go into orbitals that are lower in energy. That makes sense. They're more stable. That's a more stable place for them. So, let's draw a little comparison there here just to let me make some room here. And I'll draw two different cations. Let's think about these two cations momentarily and try to imagine which of these two cations is more reactive. I just gave you enough information to answer this question. You probably have an idea for which of these types of cations is more reactive or maybe you don't. But I just told you in essence how to answer this question. So, I've got two different cations and the way to answer this question is we finish this up by drawing the fact that there's an empty p orbital on carbon centered on carbon here. And here there's an empty p orbital located on nitrogen. Let me draw it in. It's empty. It would love to have a pair of electrons there. And what we need to do is think about the effect of electronegativity on the energy of atomic orbitals. And all orbitals associated with that nitrogen atom. So, the effect of electronegativity is that all of these energy levels will drop. If I were an electron, I would much rather be on one of the p orbitals on nitrogen than on one of the p orbitals on carbon. The effect of electronegativity is that these p orbitals will be lower in energy. The effect of electronegativity on the s orbitals that they will be lower in energy on nitrogen. And that makes sense. Let me sketch out the periodic table for you just in miniature form. As we march across the periodic table from boron to carbon to nitrogen to oxygen to fluorine, things become more electronegative because there are more protons in the nucleus. There is one more proton in the nucleus of carbon. There's yet one more proton in the nucleus of nitrogen. There's one more proton in the nucleus of oxygen. Those protons have a positive charge. And if you were an electron, you would enjoy those positive charges more. So this makes total sense that as we go to more and more electronegative atoms, that we should expect all the orbital energies to decrease if they are involved with that nitrogen atom. So that's a powerful idea. So you can guess from this that this empty p orbital is more reactive, more electrophilic than the empty p orbital that I drew on that carbocation. Just based on electronegativity and we represent that with that orbital energy diagram. So a very powerful idea to extend. Okay, so let's talk about hybrid atomic orbitals. We're done talking about just plain simple atomic orbitals, SP, DNF. And let's talk about what happens as we mix together different atomic orbitals. Okay, so I'm going to give you a rule for mixing orbitals, for thinking about the way the orbitals mix together. It's best to think of them as mixing two at a time. And the rule is pretty simple. If you mix two orbitals, you get two orbitals out. I take two orbitals and I mix them together. And there's two different ways that they can combine together. And this is a result of that phasing idea. There's two different phasing combinations for every orbital. When you mix them together, there's two possible ways that they can interact based on phasing. So let me start off by drawing out just an atomic orbital energy diagram. Once again, I'm basically repeating what I showed you before and I've got this sort of arbitrary axis. It used to really bother me when I was a graduate student. I was like, why don't they draw units on there? The units are actually in electron volts. If you'd like, you can convert those into K-cal's per mole but it won't do you any good. The only thing energies in K-cal's per mole are good for are converting into number ratios, 10 to 1, 30 to 1, 0 to something. That's the only thing K-cal energies are good for. And we're never going to do that with orbitals. We're never going to divide into ratios. This orbital is 99% more populated than the other one. So don't worry about the fact that there's no energies on this axis. Again, they're measured in electron volts typically and you don't need to worry about that. So I'm going to start off by drawing out the orbitals. This could be on a second row atom and it could be carbon, nitrogen, oxygen. It doesn't matter and those are the orbitals that matter are the 2s orbitals and the 2p orbitals. There's a 1s orbital that's way down below the level of the floor. That's never going to be involved in bonding. Don't worry about that. So I'm going to start to soon abbreviate like I did over here. It was just writing p and s. But you just have to remember that's the 2s and the 2p orbitals that are important for second row atoms like carbon, boron, nitrogen, oxygen. So if I represent these orbitals, let me once again draw out these canonical orbital shapes and the phasing is arbitrary here. So one is aligned with the x-axis. We would call that the p sub x orbital, sorry, y-axis. One is aligned with the z-axis coming straight out of the board. That would be the p sub z orbital, et cetera. And the s orbital, we would draw sort of this sphere. Actually, the 2s orbital has this egg yolk inner core that has the opposite phasing. But I never represent that inner core. I just draw a circle and that's good enough for us. There's two arbitrary phasing combinations to that. What I want to do is I want to think about the fact that in order to get ready for bonding, we can think about this in a different way. We can take exactly that same carbon atom if this is carbon and we can think about a different set of four orbitals by mixing orbitals together. And we're going to call this hybridization. When we mix orbitals on just a single atom, we're not forming bonds. I'm just talking about a single carbon atom. I have a different way of thinking about this carbon atom, for example. And what I can do is I can think about just invent little games like what would happen if I mixed this 2s orbital with this 2p orbital. If I take a low energy orbital like the 2s orbital and I mix it with a high energy orbital like the 2p orbital, on average, I ought to get two orbitals out because I mixed two orbitals and they ought to be somewhere right in between. And that's exactly the picture that we get. So let's imagine that I take this orbital here, the py orbital and I mix that together with the, let me call it the px orbital, that looks like an x-axis. If I take the px orbital and I mix that with the 2s orbital, what I should expect is these other two orbitals will stay at the same energy. I'm not talking about mixing those. But I should get two new orbitals out and they should be halfway in between the high energy and the low energy. So I'll try to draw my new orbital energy lines here. And here's my two hybrid atomic orbitals. It's just a different way to think about this carbon atom. I'm not changing the carbon atom in any way. And so what I get out of this are two non-bonding orbitals. I mean, if I draw them that way, two new orbitals that are ready to form bonds. And the hybridization of those orbitals is not s, it's not p, it's 50% s and 50% p. And we represent that with this sp sort of symbolism here. So a carbon atom normally has four electrons ready for bonding. So now I would have one electron in each of these orbitals and one electron in each of these p orbitals ready for bonding. And so you know this to be the hybridization, I hope, for something like an alkyne. Those two bonds sticking out at the sides are the result of these hybridized orbitals, these sp hybridized orbitals. And then of course you have room for pi bonds. Let me try to draw these in sort of a bluish color. And then we have room for pi bonds if we wanted to form an alkyne like this, that's what the p orbitals would do. We'll talk about that deconstruction in just a second. The point is that we can take the atomic orbitals and we can think about hybridizing them with each other. So let's go ahead and look at another hybridization combination. There's other ways that we can hybridize these and I hope you're familiar with these. So let's suppose I take one of these orbitals and I mix it with those others, I'll be left with one of the p orbitals but I still have three other orbitals left. And now these orbitals, if I mix two of these p orbitals with one of the s orbitals, I'll have three more orbitals. And now with that extra p orbital mixed in the energy, the average energy ought to go up. And these are sp2 hybridized orbitals. I can draw these with a little non-bonding symbolism there. We'll talk more about that in just a bit. And hopefully you know that whenever you have trigonal carbon, these are the orbitals that are forming those bonds. They have this hybridization associated with them that's sp2. Finally, I'm going to try to move to the other board here. I'll draw the last possible hybridization combination. And I shouldn't say last possible. These are kind of extremes but if we understand these extremes then we can understand things that are in between. And then finally, the last possible combination is to take these three orbitals and mix them with this last p orbital to add even more p character. And so this is supposed to be on the same axis. And hopefully you know that this is sp3 hybridized. Three parts p character, one part s character. That's the recipe. And I'll use a little non-bonding orbital combination. So those would look something like this. And this is supposed to be a tetrahedral carbon atom with four sp3 hybridized orbitals ready for bonding. What's the really important point here? The really important point is that whenever you see orbitals that are higher in energy, they're more nucleophilic. If I were an electron in a higher energy orbital, I would be more nucleophilic. If you're adding to an empty orbital and it's lower in energy, you're more electrophilic. Hybridization tells you about chemical reactivity. It tells you about where to start your arrows. When you do arrow pushing, it tells you where to end your arrows. So last important point, let me keep this on board so it's at the same level, has to do with the strict correlation between hybridization and geometry. Atom geometry correlates with hybridization. And it's, maybe correlates isn't strong enough for it equates with hybridization. So if I were to take a nitrogen atom, if I were super small, and I could reduce myself to the atomic level, and I could grab onto these bonds on ammonia or on amine and stretch them upward so that this were a planar molecule, what would happen is the hybridization would have to change in response to that geometry. If I placed this amine functional group into some molecule that constrained it so it had to be planar, that lone pair would become screaming hot in terms of nucleophilicity because by changing the geometry, I would be changing from an SP3 hybridized orbital to one that's purely P hybridized. And I just told you what the difference is between something that's SP3 versus something that's P. SP3 orbitals are lower in energy than P orbitals. Let me try to draw all these on a single diagram so that you can see what's going on. So if I have an S orbital down here and a P orbital up here, SP3 orbitals are lower in energy and P orbitals are higher in energy. SP orbitals are midway in between and SP2 orbitals are up here, and you may look at this diagram, this pathetic diagram and say, oh, but that energy difference is so small. The energy difference between a pair of SP3 hybridized electrons over there and a pair of P hybridized electrons is massive. The difference is massive in terms of nucleophilicity. And I'll put some quantitative numbers on that in just a little bit, but you need to appreciate this difference in reactivity just by changing the geometry. It's not sufficient to say that that's a lone pair on nitrogen. We have to go beyond that to hybridization. Okay, so hybridization is super important. Understanding the hybridization of every atom and every molecule is essential. Okay, this is a command for you. It's a command that you must do this. Every time you see a molecule, I want you to deconstruct that into atomic orbitals. And I'm going to start with a very simple example so we can see how that works. I'll take hydrocyanic acid. And let's try to think about the atomic orbitals about a picture of bonding that's based on hybrid atomic orbitals. How do I think about what kinds of hybrid atomic orbitals would make a bond between nitrogen and carbon, a sigma bond or a pi bond? So the way I think about that is let me just draw the three atoms here without the bonds. And let's try to draw some hybrid atomic orbitals associated with that. Okay, what's the hybridization of the carbon atom here? It's sp hybridized. And you know that because this is a linear molecule. I told you that geometry correlates with hybridization. If it's linear, that means there's two p orbitals that never mixed in. So I'll try to draw one p orbital that's on the y-axis and another one coming out at us. This is supposed to be aligned with the z-axis coming out of the board, but I'm not very good at drawing that. What's the hybridization of the nitrogen atom? It's sp also. And so again, I'll try to draw one of the p orbitals coming out of the board. And I'm going to label this p orbital on carbon, p orbital on carbon. I'll put a little subscript c there just so that I don't forget that that's a p orbital on a carbon atom. And as we just said, a p orbital on a carbon atom is not the same as a p orbital on a nitrogen atom. P orbitals on nitrogen atoms are lower in energy. And that's how you get those pi bonds. Two of the three bonds here are pi bonds that result from the mixing of those p orbitals. Okay, last, we're going to draw the hybrid atomic orbitals. And I'll change this line here to blue just so I can more easily see it. And I'll remember that there's an sp t orbital, sp 2 orbitals sticking out this side. And I'll hybridize it in this way. And there's a tiny lobe on the back end. And then for the nitrogen atom, there's another sp t orbital that's sticking out. And these two are combining together to make that carbon-nitrogen sigma bond. And there's a little orbital on the back end sticking out. Okay, I've got three orbitals now. Let me go ahead and label these. This is my sp 2 hybrid atomic orbital. I'll call this sp 2. And I'll say that it's on carbon. And then this one here, I'll put a little label line sp 2 on nitrogen. And those two hybrid atomic orbitals get together to make a sigma bond, the blue sigma bond in my Lewis structure. Okay, there's a lone pair in an orbital that's sticking out here. Let me draw that. And that's sticking in another sp 2 orbital with its lobe on the back end. And I can phase it this way if I want. Let me not phase that part. And I'll call that another sp 2 orbital on nitrogen. And I need to do the same sp. Thank you, everybody who got upset by that. These are sp hybridized. That's what we said before. Sorry, I'm getting p orbital happy here. So these are sp hybridized. We said carbon is sp hybridized. Nitrogen is sp hybridized. So these are sp orbitals on nitrogen. I need to do the same thing for that carbon atom. And draw another bond going back here. So let me draw another sp orbital on carbon sticking out on the back end. And then finally, that makes a bond with hydrogen. Hydrogen only has a 1s orbital to contribute. We don't need to worry at all. There is no way to do hybridization with a hydrogen atom. It's only got one orbital. It can't hybridize with its own atomic orbitals. And it's the combination of this 1s orbital and sp orbital that makes the bond. Now, why am I so intensely interested in the hybridization of these individual atoms? Why am I so intensely interested in the hybridization of this bond? Why am I so intensely interested in the hybridization of this lone pair? What I'm trying to do is I'm trying to gauge how much p character there is in that bond and in that lone pair. And you should be asking yourself this every single time. This is the fundamental question that you need to ask for every single structure you draw, for every single bond, for every single lone pair. How much p character? Let me just remind you of why I'm always asking myself how much p character there is. It's because p orbitals are high in energy and the more p character you have, the more nucleophilic you are. I am always asking myself how much p character there is in every single bond and every single lone pair because I care how nucleophilic this bond is. I care how nucleophilic that lone pair is relative to other molecules. Now, let's put some numbers on this. I keep telling you it's important to think about p character. Let's put some numbers on how important it is to think about p character. So, the fundamental idea is that the more p character, the more reactive. I'm going to start off by looking at nitrogen lone pairs because it's easy to rank the reactivity based on pKa or acidity. So, I'm going to draw a little table here. And in my table, I want to compare lone pairs on nitrogen. So, if I had some alkylamine with a carbon bonded to an NH2 group, there's a lone pair on there. If I have some sort of an emine with a lone pair on nitrogen that has two other bonds to it, that's not the same. And if finally I compare that to that hydrocyanic acid or to an organic nitrile, I would end up with something that looks like this. So, here's three different nitrogen lone pairs. They're all lone pairs. They're all on nitrogen, but they're different. So, I want to start off by ranking the hybridization. What's the hybridization of this lone pair on the top nitrogen? It's sp3. How about the second one? The emine or pyridine or emidazole. And then finally I get down to the nitrile and we already said that that's sp hybridized. Now, what's the percentage of p-character in this top case, sp3? 75% p-character. Sp2, what's the percentage of p-character about? It's about two-thirds or 67% and then finally the sp, 50%. These are paltry differences, 75 cents, 66 cents. What's the difference there, right? How big of a difference could that make? Maybe you already know something about the relative basicity of these. I can go to a pKa table and look up the converse of basicity, acidity. What you find out is, I'll assign this a relative value of one, that an sp3 hybridized nitrogen lone pair is 100,000 times more basic than an sp2 hybridized nitrogen lone pair. You know, if you put $1 in front of me and $100,000, I would have no problem seeing the difference between the two piles of money. It would be totally trivial and yet, why is it so hard to see the difference between these two? The difference is just as great, 100,000 times in reactivity. So, when I come over to this other board here, let me raise this up and pick a new board, draw out these two molecules. Which of these is more nucleophilic? Answer should be instantaneous. This one is more nucleophilic. It is about 100,000 times more nucleophilic than pyridine. Lone pair on nitrogen, but they're not all the same. And that's because this is sp3 hybridized and this is sp2 hybridized. Those lone pairs are totally different. Now, if I come down to an sp hybridized, okay, this is like a difference of what? I'm not good at math. 8% versus 17%. How big of a difference could that make? How many zeros did I, does it matter how many zeros I drew really? It's 15 zeros or 10 to the minus 15. There's a huge difference in reactivity. This is the effect of p-character. What looks to you like small differences in p-character translate into phenomenal differences in orbital energies. And this is why, if you from the very beginning of sophomore organic chemistry were not paying attention to p-character, I don't know how you made sense of the subject. They probably told you this at the beginning of the book and at the beginning of the first quarter and then they forgot to emphasize how important this is. So I'm going to ask you to pay attention to hybridization from now until the end of your career as organic chemists. Let's make sure we understand these differences. Which of these oxygens is more, I guess what I'm asking is basic. Which of these oxygen atoms would you expect to be more basic? I've got a ketone and an ether. Yeah, the ether oxygen. They both have two lone pairs but these lone pairs are sp2 hybridized and the lone pair sticking off of this oxygen are sp3 hybridized. Now the important point is we look at a pKa table and the difference is not 10 to the fifth this time. It's not always 10 to the fifth. Here it's only a thousand times more basic. But again, when you're pushing arrows, if you know that one lone pair is a thousand times more reactive than another, that kind of settles the issue. It doesn't have to be 100,000 times. Even a thousand times more reactive is useful to you in terms of thinking about reactivity. This is incredibly powerful stuff. But let me put one sort of fly in the ointment here, one word of caution in applying this very simple idea that hybridization is important and that p character correlates with basicity and nucleophilicity. More p character means more nucleophilic and more basic. I've got two oxygen atoms here. I've got a carbonyl oxygen on top and a carboxyl oxygen on the bottom. Top and bottom. Which oxygen atom is more basic? We mentioned this yesterday in discussion section. The top atom is more basic. I don't know of a single example ever in the field of recorded organic chemistry where the bottom oxygen atom acts as a nucleophile or as a proton acceptor. Now why is that? The only way to understand that is by truly understanding the structure and geometry of this molecule. In order to understand the geometry and the hybridization, we need to remember that there's resonance. And resonance is going to influence our picture because it tells us about the hybridization. The true structure of this molecule really has partial double bond character between this carboxyl oxygen and the carbonyl oxygen. Once we draw a resonance structure for this, we realize that these lone pairs up here are not really sp2. And this lone pair that I've got drawn at the bottom is not sp3. You can't think about the hybridization of these atoms until you've drawn the resonance structure. You have to incorporate resonance before you assign the hybridization to something. So really, this is more like sp3 in this extreme resonance structure and this is more like sp2. And if you draw the charges, it's even less likely you would ever, ever in your life make the mistake of trying to protonate this oxygen atom on the bottom. Who would do that? Nobody. Nobody would make that mistake. So you have to think about resonance before you try to assign hybridization. And as soon as you draw the resonance structure, it's absolutely clear that this is the more reactive set of electrons on the top oxygen. There's no cases where the carboxyl oxygen on the bottom is more reactive. Okay, so we've talked about atomic orbitals. We've talked about hybrid atomic orbitals. We've talked about the supreme importance of p-character. p-character, p-orbitals are higher in energy. More p-character means more nucleophilic. Let's go ahead and talk about mixing hybrid orbitals in order to generate molecular orbitals. Tent was that this is supposed to be review. I'm stunned. I went back and I looked at the sophomore organic chemistry texts that I teach out of and all this stuff is in there. But somehow it just gets lost and dropped. All of these important concepts get lost once you get to the chapters beyond chapter one. Okay, so let's go ahead and build up this picture of starting with a carbon atom that has atomic orbitals on it. So let me go ahead and depict the atomic orbitals on carbon. There's a 2s orbital that's shaped something like this. And I'm not going to worry about the phasing. There's this egg yolk-shaped part of the orbital that's in the center. I'm not even going to draw that because it will make the picture too confusing. Inside here I'm going to draw the picture of a 2x orbital, or sorry, a px orbital. There's a p orbital. I'm kind of overlaying it on top. It looks a little bit confusing. The actual overall shape of a p orbital is, it fits inside a sphere. So ChemDraw draws these orbital shapes that are so badly distorted you'd never know what a real p orbital looks like. So we take two atomic orbitals. Let's suppose we had a carbon atom and we wanted to get that ready for bonding. What we think about is the mixing of the p orbital here with the s orbital here, 2s orbital and a 2p orbital. And we think about the idea that that can hybridize. So we've just been through this, but now I'm not drawing out the energy diagrams. I'm just drawing pictorially the way I think about this. Yeah, an s orbital and a p orbital can get together to make two different sp type orbitals. So here's one of the two sp orbitals. I'm going to draw this particular one with that phasing combination. And I can imagine this interacting with another atom to make a bond. So this is my hybrid orbital here. And I'll draw that interacting with a hydrogen atom. And I'll make sure the phasing combination matters. If I want to represent the formation of a bond, I have to make sure that the phasing, the arbitrary phasing, either hashed or unhashed matches the phasing of this orbital. If they don't match, then it's an anti-bond. It's the opposite of a bond. And when I mix these two orbitals together, when I mix this 1s orbital on hydrogen with this hybridized sp orbital on carbon, sorry, sp orbital on carbon, I get a new bond. And that's a sigma bond. And it has a shape that looks something like this. Let me try to get this right. And if I wanted to give you extra information, I often put subscripts on my orbitals to give you extra information. That's not just a sigma bond. It's a sigma bond between a carbon and a hydrogen atom. And that's different from a sigma bond on a nitrogen and a hydrogen atom. Orbitals on nitrogen are lower in energy and less nucleophilic. CH bonds are higher in energy and more nucleophilic. So this is a molecular orbital. And you should already be familiar with this nomenclature. Double and triple bonds, we call pi bonds, single bonds, we call sigma bonds. You should be familiar with that kind of idea. So I want to return to this the way we started our class. We started our class by talking about arrow pushing. And the idea that we're going to use arrow pushing to help describe one part of a powerful equation for thinking about reactivity. So remember I started off by telling you that any time two things get closer and closer together, if we wanted to think about the interaction between those, the energy we get, either forming a bond or sterically bumping into each other, we have this equation that we use to think about the energetic consequences. We said that this equation obligates us, whenever we have two things interacting with each other, obligates us to add together all the charges. So if I had some sort of an amine interacting with some sort of an electrophilic organic compound like bromomethane, as these get closer and closer together, if I want to calculate how good or bad it is for these things to get closer and closer, I have to think about the charges between the proton and the bromine, the proton and the carbon, the proton and the H. I have to think about the charges on the nitrogen interacting with the proton. You have to add that up for every single atom in your system. If you want to get a full accounting for the overall charge effects as these things come closer together, we have to think about the non-bonding interactions, the steric interactions that don't form bonds, the bumping of this H into that H, the bumping of this nitrogen into that H. In addition to thinking about the formation of a new bond, we have to think about all those bumping interactions that aren't good. And we add all of them together as these get closer and closer together. And then finally, this is our arrow pushing. We agreed that lastly arrow pushing wasn't going to represent sterics, it wasn't going to represent charge, it was going to represent the interaction of this filled orbital, this sp3 hybridized orbital on nitrogen with some sort of an anti-bonding orbital that we usually don't draw with Lewis structures. Now I want to get down to the nitty gritty of this equation because I didn't tell you the form of this equation and now I'm going to have to give you an equation that may look sort of complex but it's not too complex. That's the equation. This is the equation that underlies arrow pushing. It says, what does this equation tell you? That if you want to think about how good your arrow pushing is, is that good arrow pushing or better, is that likely or unlikely? Was that a good idea for me to push arrows like this? You have to think about the interaction spatially of the orbitals. Are they getting close or they're overlapping in space? How good is that degree of overlap? And then secondly, you have to think about the difference in energy between the orbitals. Is this high in energy and is this empty orbital low in energy and it is the difference between the filled orbital energy and the empty orbital energy that determines how much energy you get as these get closer and closer. So let's take a look at that and I want to start off by using something called a molecular orbital interaction diagram. It's a device that you should have been introduced to back in freshman chemistry and then you never used it again. It was like why did we learn that? I have no idea why we learned these molecular orbital interaction diagrams. So let me just start off by reviewing pictorially the molecular orbitals in a molecule. If I were to draw an energy diagram showing the molecular orbitals of ammonia, for example, what would it look like? At the level of resolution that I think. And again, don't worry about the energy on the energy axis. The big point I want to make is you got all these molecular orbitals associated with any molecule. And when you look at the electron occupation, it looks something like this. There's filled orbitals that have two electrons in each and then above that there's empty orbitals. And they're not all mixed together. And always these empty orbitals and I'll call them molecular orbitals, MOs, the empty orbitals are always higher in energy than the filled orbitals. It's just a fundamental fact. If I measure the energy difference between filled and empty, it's there's always some sort of an energy difference associated with them. Okay, so we're going to learn about how to think about the interaction of one molecule here that has energy levels with another molecule that has its own molecular orbitals that are different and how to think about the differences in energy in those orbitals. And instead of thinking about an actual chemical reaction, what I want to do is I want to draw a picture of some sort of a species and I want to ask you what do you think is the geometry of this species? It's a carbocation. Or is it a carbocation? What does this look like? I think that's stabilized and I think you can tell that it's stabilized. But how do you think about the stabilization? Is this like an allyl cation that has this sort of a lillic resonance? It's so that would mean the positive charge is distributed on both of these carbon atoms. But the alternative way of thinking about this is maybe the lone pairs donate into that. And maybe it really looks like this linear molecule that might be best represented like this. And what kinds of tools do you have at your disposal to answer a question like that? They are exactly the same tools that you use to think about this reaction between two molecules. And the difference is here we're talking about two kinds of nucleophiles, a pi bond versus a lone pair that are attached to the same nitrogen atom. It's just the same story. Here I'm talking about a nucleophile on two different molecules. And here I'm talking about two different nucleophiles that are on the same atom. So I'm going to start off by drawing a molecular orbital interaction diagram that will immediately answer that question. And here's what a molecular orbital interaction diagram says. I've got some nucleophile with a filled orbital. I've got some electrophile with an empty orbital. So I'm going to start off by representing the case where the lone pair on nitrogen is interacting or sorry the pi bond on nitrogen, the double bond is interacting so that bond between carbon and nitrogen, the pi bond, if it's donating into the carbocation I need to draw that as my nucleophilic filled orbital. Then on the other atom, the carbon atom, I've got some empty orbital, this empty p orbital, the carbocation orbital on the carbon atom. And I have to think about the interaction of these two orbitals. When I mix two orbitals together, when I donate the electrons from that carbon-nitrogen pi bond into the carbocation, when this donates into that I have to get two new orbitals out. Here's the orbitals in my product. When I mix two orbitals, I get two orbitals out. When I mix a filled orbital with an empty orbital, when I donate these electrons in, I'm going to get two orbitals back out. So here's what the orbitals would look like in my product. One is going to be lower in energy and one is going to be higher in energy. And if I try to diagram, I'm going to try to draw this sort of edge on so you can see what I'm talking about. I'm going to have some empty orbital here on the carbon atom. That's an empty orbital on p carbon. And then there's this pi bond and I'm, I don't know how good of a job I can do to represent this pi bond here, but I'll try to smear some electron density and make that my pi bond. This is the pi bond between the other carbon-nitrogen. So what happens when those two orbitals overlap? What happens when this pi bond between carbon and nitrogen donates into the carbocation there? I'll get two new orbitals out and this one is going to have pi symmetry, the new orbital that I get out. And this is if they're in the correct phasing combination where the top is hashed and the top is hashed, but there's also an anti-phasing combination to the way those two can combine. And when I mix the other phasing combination, I'll get an anti-bonding orbital. We represent that with a star that's just as destabilized as the new bonding combination was stabilized. So I'll generate some new pi bond if I think about that interaction. Now let me contrast that and I'm going to try to quickly draw this diagram because we're running out of time here. Let me contrast that with an alternative scenario and that's the lone pair interacting. And I'm going to try to draw my diagram at the same axis, I didn't label it over here. And I'm trying to try to make sure I draw my p orbital at exactly the same energy because that's not different. The carbocation is the same. But instead of thinking about the pi bond interacting with that orbital, I'm going to think about the lone pair on nitrogen interacting. And what I immediately need to do is think about the idea that non-bonding lone pairs on nitrogen, sp2 hybridized non-bonding lone pairs of nitrogen are higher in energy than pi orbitals. And this is something that we will talk about shortly. I'll tell you how we know that shortly in our next lecture. And if this is higher in energy, I'm going to try to draw a line across here just to show you that I'm trying to draw this non-bonding lone pair on nitrogen being higher in energy. If this is higher in energy, then the difference between these two is smaller. And if the difference between those two is smaller, I've lost my equation here, that equation that I showed you, if the difference in energy is smaller, the overall interaction energy is bigger. In other words, you want more nucleophilic things that are higher in energy. And if these are closer in energy and the energy difference is smaller, the overall interaction energy drop is bigger. You get more interaction energy out when these two are smaller. So this is delta E between our MOs. And I get more interaction energy out, E sub interaction. I get more interaction energy out than when these are far apart. And you kind of knew that. What I'm telling you here is, well, this is less nucleophilic. Of course, it's harder to donate into that empty orbital. This is more nucleophilic. Of course, it's better to donate into that empty orbital. You get more overall bonding energy out. What that tells you is the answer is it's the nitrogen lone pair that you'd want to donate into that cation. This should be a better representation of that structure because nitrogen lone pairs are more nucleophilic. Okay, sorry I went over on my time. We'll get back together on Friday. And I'll tell you about how did I know that this nitrogen non-bonding lone pair would be more nucleophilic than a pi bond? Yeah.