Orbital Diagram: 6-atoms- 1,3,5-hexatriene

In this video we're going to learn how to draw the molecular orbital diagrams of six atom conjugated systems, usually hexatriene, let's go ahead and get started. So, as we know well conjugated polyenes are famous for their ability to resonate and we can explain that resonance using molecular orbitals, so the primary purpose of this page is to apply the rules of building my molecular orbitals to a six atom system, it does get more complicated, we are going to have to think a little bit more about this but we're doing it together. So, it's all going to be, okay. So, let's talk about the things that we do know, which is that there are six atomic orbitals, six pi electrons and six molecular orbitals, alright? And I've gone ahead and as always filled in the first one for you so that we know what we're dealing with, it's also the easiest one and then we're responsible for the rest, okay? So, what do you think is the best place to start here, let's go ahead and fill in the first orbital and the last orbital for all of these. So, I'm going to fill in first, first, first, first and first, then I'm going to start flipping the last one flip, flip, flip, flip and flip, cool? And, if you guys don't mind, I'm even going to do one more little cheat, which is I'm going to fill in psi six already, because we already know that the psi six is always just going to be every single orbital facing different direction. So, we can already fill that, just kind of like by definition, we're used to this by now, cool? So, that means that all we really need to worry about is these four in the middle for these first psi to through five, okay? Let's also just remind ourselves how many nodes we're supposed to have. So, it's supposed to start at 0 and then 1, 2, 3, 4 and 5, we can also fill in the nodes for five, we know that it's just going to be between every single orbital, cool? The hard part is the others okay, cool. So, let's start off with psi 2, I don't think this one's going to be too challenging, let's look at this together, we need to put in one node, what do you think is the best place, let me know when I'm getting closer, yeah right here, right? So, this is it, let's put in our node and that's it, that's totally symmetrical, that's all we want to do, okay? Let's go to 2, what do you think we should do for 2? its psi three but for two nodes, it's actually not that hard, this was pretty straightforward, it's just going to be here and here, right? So, just 2, 2, 2 that makes sense, that's not really that difficult, okay? Now, we get to psi four and psi four and five are tricky enough, so that I think that it is appropriate for me to actually use an obscure rule that was in my molecular orbital rules and remember that that rule said that if in doubt if you don't know where to put your nodes, what do you do? you draw fake orbitals at position 0 and position n plus one and then you try to draw a sine wave, I haven't done this yet, we've just been using kind of common sense and symmetry so far but at this point, this is the thing about three, you guys might be putting it in a lot of different places like, for example, someone might say that it should be here, here and here, I don't know, like maybe they want to go down the nodes or maybe someone thinks that they should go here, here and here, which doesn't look bad, this is probably not a good pick, I would not pick that one, but for example, it might be difficult to determine is that appropriate, right? So, let's go ahead versus the other one.

So, let's go ahead and draw those orbitals and draw a sine wave and see what we get. So, what that means is by that rule, what I would do is I would actually draw fake atom over here and a fake atom over here and I would throw these fake basically fake, a sine wave coming from the first one and a second one, but I want to just add an orbital just that you guys know what I'm doing in terms of that, this is just a pattern that we're going to learn, okay? These orbitals don't exist, it's just helping me to figure out where to put the nodes okay? Well, once you draw that and once you start to think, use that as a guideline, what you start to realize is that if I were to draw a wave that were basically going back and forth, right? Let's say that I were to do this, I'm terrible, let's say we were to do it this way, where it's going through the orbitals, okay? That kind of works but notice that what I have is that the peaks and the valleys of the sine wave aren't very symmetrical, like what I have is that they're more compressed in this side and they're longer over here, okay? So, this isn't the best way that I could do it, a better way would be to do it here through the middle then here and through the middle like this, if you do it this way, what you notice is that, and I mean it's hard cuz I'm drawing this really ugly, but it's actually a much better wave like in terms of the symmetry of the wave, if this part at the end was connected this part at the beginning all of these ups and downs would look much more symmetrical, okay? So, what I'm trying to do is I'm trying to use this as a kind of a guide to say that if you were to put your node here and here, that wouldn't make the best sine wave overall, the better sine wave would be, if you were to put it here and here, okay? That's, what I'm trying to show you guys. So, just you guys know, this is the answer, just another word of caution in case, in just like in case you end up getting confused later, for an even-numbered molecular orbital you can never through an orbital you only pass through orbitals on odd member molecular orbitals. So, the answer of going through these orbitals was never really a great option anyway, okay? I'm just letting you know. Now, that we've already drawn the sinewave, okay? Cool. So, that was that, we already have our nodes in place. Now, we just have to go to psi five, let's do the same thing, let's draw our fake atoms and our fake orbitals and now we realize is that we need four nodes, we need four nodes, which by the way, that means that every single real orbital is going to get a node except for one, okay? Let's think about it this way. Notice that five nodes means that every single lobe is switch, switch switch, switch, switch, right? Notice that for a for four nodes or psi five, we're going to have four nodes that can't pass through any lobes and two of them, two of them can't have a node between them but the rest should, so how do we do that? Well guys, what makes the most sense is if any two of them have to be together without a node, it should be the ones in the middle because those are the only ones that you have a chance of making a sine wave with, if you keep them together and that means that there should be another node here and another node here, okay? Now, if we were to use our sine wave method, what we would see? if the sine wave method does make sense because what I would have is this then this then this and that, go back here, sorry guys, my pen is, well, my handwriting is sucking, cool. Awesome. So, what we get is a pretty good flow it's not perfect because there's an asymmetry here, but it's pretty good, if you were to do something different you would get an uglier wave. So, for example, if you were to, I mean there really isn't even another way to do this, that would be symmetrical but if you were to like, let's say move it over, you know like, that's the whole point, I'm trying to use this as an illustration for how you can't have a symmetry. So, if we were to try to like move this over so that it did this and this, right? Well, what you would then get is something really weird that looks like this, boom, boom, boom, boom like that and then you have a bunch of little ones together and then big ones on the sides. So, we want to do is we want to draw our nodes in a way that preserves basically a sine wave look as much as possible and once again, what that would be is keep the two ones in the middle and then the two on the psi. So, then it would give you something like this, okay? and that one, I drew it ugly again, but you can see that it's better than the other options okay, cool? So, now we have our nodes in place and now we just need to actually draw the orbitals in. So, here what we would have is one phase change and one phase change, cool? For two we would have this, this, this, this, for three we would have this, this, this, this and then for four nodes, I'm going in order of nodes, it would be this, this, this, this and this and at this point we can erase our fake orbitals because we don't need them anymore, I just want to point out guys that this explanation that I gave you is the non-technical way to try to tell you, give you instructions on how to do molecular orbitals, there's actually is math behind why this is correct and the other versions are wrong but that math is so complicated that I don't want to overcomplicate things, you shouldn't have that much math in orgo, I'm trying to give you a very basic version of how you can arrive to this without doing like insane quantum calculations, okay? And I want to make another point, which is that I'm probably going to comment on this video saying, hey Johnny, I did it another way and why isn't this right? Why isn't this other way right? And what I would just tell you guys is because it's not going to make as nice of a sine function as the ones that I showed you it's not going to be as even or symmetrical, any other combinations are going to have a little bit more, a little bit more asymmetry, okay? So, that's why this would be the most favored, actually the technical reason has to do in math, which we're not going to get to but this is a nice like kind of shortcut to get the right faces in case that you are asked to do this okay, cool? So, we have

all our faces in place and now, just to fill in our MO's and that's easy, it's just going to be psi one, psi two and psi three, would we expect this to be a stable molecule? yeah because notice that all of the electrons can conjugate into bonding orbitals. So, these are all bonding. So, that's going to increase the level of stability, these are all antibonding, these don't have electrons, thankfully they should get stars because they are going to decrease the stability of the molecule and there are no nonbonding orbitals here because the fact that there's nothing at the halfway. Finally, we have to determine our HOMO and LUMO orbitals. So, we know that, I'm just going to use yellow to say that yellow is our HOMO, and then I'm going to use green to say that green is my LUMO. So, psi 3 is my HOMO own and psi 4 is my LUMO. Thanks for joining me guys, I hope that this helped and let's move on to the next video.