For a closer look at *4-atom* pi conjugated systems, we will use the structure of **1,3-butadiene**.

**Concept:** Drawing MO Diagram for Dienes

Hey guys. In this video we're going to learn how to draw the molecular orbital diagrams for, four atom pi conjugated systems. So, guys four atom pi conjugated systems are usually in the form of diene. So, two double bonds next to each other and just you know a diene can also be more generalized to be called a polyene. So, I'm going to be referring anything that's conjugated by it with four or more atomic orbitals as being some form of polyene because it's usually the way that it works, okay? And we know that polyenes can resonate, okay? But, we're going to do here is we're going to learn how to draw the molecular orbitals for a diene a 4 atom conjugated system using the rules of molecular orbitals that I already showed you guys before. So, nothing's going to change, this is just an application, okay? So, let's go ahead and do this example, okay? So, it says, predict the LCAO model of 1-3 butadiene, identify the HOMO and LUMO orbitals, very cool. So, let's go ahead and just start off with the basics here, which is that we have four atomic orbitals and we have 4 electrons in those orbitals because we have two pi bonds, that make sense, right? And we know that according to aufbau principle that means that two electrons are going to sit in psi one and two electrons are going to sit in psi 2, okay? What we might not remember, is how to actually draw the molecular orbitals. So, let's go ahead and do that now. So let's, what would be the next thing that we do if all of our orbitals are already drawn for us, we just have to draw in the faces, what's the next thing to do, let's go ahead and shade the first orbitals, so the first orbital should not change, I should do this, this and this, cool? Awesome. So, that's our first step the next step. So, let's go to the last orbital and start flipping it because you know that has to flip every time. So, this one has to go up and then down and then up again, cool? Awesome and now we need to increase our nodes, okay? So, now let's increase our nodes. So, we have, we are starting off with 0 nodes here, then it needs to be one, two and three, so the way we're going to do this is try to add these nodes in the most symmetrical way possible so that means that, I'm going to put one node in the middle here, a node here, a node here for two and then finally for three is just a node in between every single orbital, cool. And that means that now I'm ready to shade the other orbitals in, and what that means is that I would get one face change here, right? Because, that's just the only node then I would get two face changes for this one. So, I get the first face change in the second face change and then the last one I would get just get all of them are changing, very cool. Awesome. So, now we know what our, basically what our molecular orbitals look like, we know how many electrons there are and now we just have to indicate which ones are the HOMO and LUMO orbitals, okay? And what we would have first of all, what I have for this section here is just how many pi electrons we have in each one. So, then this one would be up two pi electrons two pi electrons 0 pi electrons and 0 pi electrons, okay? Now, you don't want to do this every time but since we're new it looking at HOMO and LUMO I just want to make it very clear, which of these have electrons which of these don't and we know that according to the ordering it would only be up the psi 2, right? So, that means that my HOMO orbital or the highest occupied one must be psi two and that means that my limo orbital must be psi three because that is the lowest energy that doesn't have any electrons in it, once again, these are collectively known as your frontier orbitals, you may not know what they do yet but it's important that you're able to identify them, cool? So, that's it for this video, in the next video I want to talk about a specific type of notation that's used for dienes.

**Concept:** Alternative MO Notation for Dienes

So guys, it turns out that specifically for four atom conjugated systems, for dienes a lot of textbooks and some professors will actually describe molecular orbitals as the sum of pi orbitals. So, we'll think about it as, you know, you have four molecular, your molecular orbitals with four orbitals and those orbitals are actually the sum of different combinations of two orbitals, okay? This is only true for four orbital systems in case you see it I want you to know first of all that is not very important. So, this type of notation doesn't supersede what I already taught you, you already know how to do four orbital systems or four atomic orbital systems but I just wanted to go ahead and do an example with you so that in case you see it you know what you're looking at, so this is the way that it works. So, basically you know how usually we start with our dark lobes facing down on our first orbitals, that's just the way that I like to do it, so that is usually, if that's your starting point then that would be called your positive pi because just the way that you started, okay? If you were to then control an antibonding orbital from there. Remember, that the first one has to stay the same but the second one is to flip, right? So, that would be called the positive pi stock because it's like you start with a positive pi but then you made it antibonding okay? Well, just as correct as a starting point would be the negative pi, negative pi just means that you flipped it the other way, that's totally fine, some people want to use the negative pi as their starting point all the time, I just like to put the dark lobe down but if you're using this one, this would be called negative pi and then if you wanted to make the antibonding version of it, the antibonding would be negative pi star, got it so far? Now, we know that according, this is just basically looking at two different ethene molecules, we know that, what would happen is that inside one you would have two electrons here and two electrons here, okay? So, that's that's kind of like what I'm showing you so far. Now, when it comes to your size, let's go up and look again at this, what we want to do is figure out how can we describe these four molecular orbitals in terms of sum of two pi molecular orbitals, okay? So, for example. Notice that for psi one, I have four lobes all facing down, right? So, that means that if I wanted to use this type of notation, what would be the right summation of these orbitals to make that thing? and I'm going to draw it for you right now and hopefully you'll understand better, I will just draw it right here so we have a little bit of room psi one should be equal to what? it should be equal to positive pi plus, I should put it in brackets, positive pi, positive pi plus positive pi, why? Because the way that I drew it had both lobes at the bottom and it was just two of those so it was a positive pi plus another one of those. So, they're next to each other that would be psi one, cool? Let's go ahead and do psi two now, what is psi two going to be? Well, let's go ahead and look at it again for reference. So, psi two, it looks like the first two didn't change but the second one did. So, then what would this one would be if we looked at it, if you look at all the different possibilities, it's actually going to be positive pi again plus negative pi, right? Because in this case what we're adding, the second one that we're adding is the opposite configuration or the opposite face, okay? And the opposite phase of my bonding orbital would be this one, so that means that what psi two is actually, if you're adding a positive pi plus a negative pi, cool? Let's keep going psi three. So, psi three. Notice that it appears to be too, well, it appears to be two antibondings, right? Because notice that the first one has the faces different, the second one also has the faces different, note that the first one is starting off with the lobe down, the first lobe down, the second one is starting off with the first lobe up. So, let's see what it would be that means that it would be positive pi star, right? Because, that's the first one, plus negative pi star, right? Because, if you add those together don't you get psi three? it's just basically adding the top one there and the top one there and you would get psi 3 and then finally psi 4 would be what? it would be that everything's changing, it actually looks like it's the same thing twice, right? It's your antibonding one twice. So, what that means is that it would just be psi star plus psi star, why I kept saying psi, I'm at pi, positive, yeah I should have put a positive around it, so it would be positive, positive, positive, positive pi star, does this make sense, cool? So, you'd be saying, Johnny why are you showing me this? like why is this important? The truth of the matter is it's not important at all, this just, this is just a specific type of notation that certain textbooks and certain professors like to use to represent a four atom conjugated system, sometimes they might say discuss psi 3 in terms of pi and then you have to actually do this but for the purposes of actually understanding molecular orbital theory this doesn't provide any extra insight, it's just showing you all the different combinations of smaller molecular orbital that could be used to make a bigger one okay? Cool guys. So, I hope that this made sense, let's move on to the next video.