But just a recap, you have the idea of a molecular orbital is that you have two atomic orbitals. So here the simplest case is hydrogen, so you have the 1s orbitals. And they combine to give you, you kinda push them together if you like, to give you two molecular orbits. And the idea behind all of these is that they, I hope you now realize that electrons don't reside in boxes. Sometimes, student, in school especially, have this idea that orbitals are little boxes and electron are little contacts that reside in them. These are just mathematical descriptions. And they're waves, that's why I put this plus sign here. And these come from the solution of the equation for the hydrogen atom. So this is three dimensional, this is spherical shaped for an s orbital, is a three dimensional representation of the wave. Function that comes after the shown equation. So they've got nothing to do with boxes. So like any wave, if you have a sine, a typical wave that you're familiar with, you have positive and negative parts and the same thing for these. That's why we put a plus or minus on these orbitals sometimes. So what they can do then, ways they can combine together. And we know that if you get constructive interference you'll get increased amplitude for the wave and therefore in these two one has orbitals come together. And you get construct the interference. And the combined amplitude is greater. So that's what's called a bonding molecular order. And when they come together for the sigma, for the one S, we call that a sigma. A sigma orbital. But you can also add these together. So right here you're adding plus plus, but you can also say plus minus. So you put a minus one here, and then you get this antibonding. As the two waves destructively interfere here in the middle. You have the plus and the negative parts together. So they cancel out and you get an empty one in combination. So this one is more stable, the bonding. Because it's got an electron behavior the two nuclei they're positive charged. And here you've got electron density here. And that's a stable situation. And that electron density can spread out. So it's a stable situation here. You have no electron density in the middle between the two nuclei. So that's an unstable a situation, two positive charges and none of the electrons then shield them from each other, and also there is a much more confined space to like for the electron density. So that's the basic principles of Molecular Orbital Theory. You have an antibonding combination, and here I just elaborate on this for your For your notes. So then, this is just an energy level diagram. The way you usually write this is you have an energy level diagram, here you have you two atomic orbitals on each side, and then you have a lower energy bonding molecular orbital and you have a higher energy antibonding molecule. And then if you want to say this is a hydrogen, you'd have one electron on each of the hydrogens, and then you'd fill them up just like you learned in school. You'd fill up at each atomic orbital, you put two electrons in, and the two electrons have to be of opposite spin. And each orbital can only accommodate two electrons. Okay, so here I've just summarized it for you, again for your notes, [COUGH] what I've been talking about, so you get close enough, you get the atomic orbitals, they reshape the molecular orbitals. And then you have some key points here, so the number of molecular orbitals is going to be equal to the number of atomic orbitals so if you have all together six atomic orbitals you're gonna get six molecular orbitals. And then you have the bonding which is a lower energy one and the antibonding which is the higher energy you want. And the reason why it's higher energy and lower energy, we've just gone through electrons enter the lowest orbital first, and then the maximum number of electrons is two, and this is due to the Pauli Exclusion Principle. And then sometimes, if you have equal energy orbitals, say you had, What we call degenerate orbitals, so here's our energy like this. Now, the electrons, as you learn in school for P orbitals, they fill these each up separately. That's a lower energy situation than pairing up in the same orbital. So when you say you had three degenerate orbitals like that. Then if you had another electron, they fill up. The others one would fill up and pair up like that. And then they'd have to go up to the next level. [COUGH] Right, so there what we talked about is anti-bonding orbitals, but what we need to understands that in certain molecules as well, you have what are called non-bonding orbitals. And these are orbitals that are usually the same as in there. So you have two atoms coming together staying the simplest pace, and yo have an orbital on one and there's no counterpart to bond with on the other one. So it doesn't build that from anti-bonding orbital or a bonding orbital. It just stays non-bonding. So it's an orbital that isn't involved in bonding. It's just as the same as it would be pretty much first approximation, as it would be in the atomic system. So then we have the p atomic orbitals. So we've looked at the signal 1s at this stage, but you also have the p orbitals. So and you go to the second shell, you have the two, the P orbitals. And here we have how they're combined. Now there's two different types of combinations. You can get the sigma overlap, which is the same as we got for the s-s overlap already. And that's when the two orbitals point at each other. And by definition, that's usually for the pset. So we can imagine, this is a carbon atom here, and that's a carbon atom there, and then we define our axis system. Say that that's the Zed axis. So you have this [COUGH] excuse me, the P orbitals have positive and negative phases. So they could combine, so you can combine a situation so you switch this one over from the way it's written. You have the positive here, so now you get a positive positive overlap. Again, they're waves, so it's constructive interference, so you get a build up of electron density between the nuclei. And that's a bonding situation. If you think it over like it's drawn here, you have positive and negative so you get interference destructive. Interference between the two waves and therefore you get no electron density between them. So this situation here is a stable situation compared with separated orbitals and this is a destabilized situation. This is a bonding, sigma orbital, and this is an anti-bonding sigma star. And of course you all know that you got, in addition to the p-z, you got the p-x orbitals, and you got the p-y orbitals. They undergo a different type of bonding. They undergo what we call pie bonding. Because these now, instead of head-on, this head-on collision that's happening here between the p-z orbitals, you have side by side interactions. So again, you can imagine a situation where you get the two phases together. So you've got a plus, plus together. Then you'd get a nice bonding situation on the bottom there. And likewise the two negative lobes overlap, and you get constructive interference. But if you flick this orbital over, say you flick this one over, so you now have positive side up here, and a negative side down here. Then you have positive against negative, and that's destructive interference. So now, you have again an absence of electron density in them. And we classify them as pi, and [COUGH] the definition of pi comes from the symmetry of these orbitals, which involves symmetry theory, which you don't need to worry about. But usually, sigma orbitals have electron density along the internuclear access if you like, that's the definition of sigma. And you can see for the pi orbitals here, they've got no electron density. Even the bonding ones have got no electron density along that internuclear axis. So this is a sigma and this is a pi. And as for the px and of course the py is, perpendicular, to that. It's, if you like, coming out, at the projector from us. And you get exactly the same type of interactions. You get, so you can get, constructive overlap here. Giving you a bonding orbital, and you can get destructive, giving you an antibond. Okay, so again, if you notice, this is pretty much covered here, and then you'll have a sigma bond and a bond formed by the p orbitals overlapping side by side. That's a pi bond. And then we have what are called non-bonding orbitals as well in certain molecules.