sp² hybridized orbitals and pi bonds

In the last video, I touched on the idea of a sigma bond. And that was a bond-- well, let me draw two nucleuses and let me just draw one of the orbitals. Let's say this is an sp3 hybridized orbital, and that's on this atom and this is kind of this big lobe right there. And then this guy has an sp3 hybridized orbital as well. That's the small lobe, and then that's the big lobe like that. A sigma bond is one where there's an overlap kind of in the direction in which the lobes are pointed. And you might say, well, how can there be any other type of bond than that? Well, the other type of bond, so this right here-- let me make this clear. This right here is a sigma bond. And you say, well, what other kind of bond could there be where my two orbitals overlap kind of in the direction that they're pointing? And the other type of bond you could have, you can imagine if you have two p orbitals. So let me draw the nucleus of two atoms, and I'll just draw one of each of their p orbitals. So let's say that that's the nucleus and I'll just draw their p orbitals. So a p orbital is just that dumbbell shape. Let me draw them a little bit closer together. So a p orbital is that dumbbell shape. So let me draw this guy's-- one of his p orbitals. I want to draw it a little bit bigger than that, and you'll see why a second. So one of his p orbitals right there. It comes out like that. And then this guy over here also has a p orbital that is parallel to this p orbital, so it goes like that. Let me draw that other one a little bit straighter. It goes-- I want it to overlap more, so it goes like that. I think you get the idea. So here, our two p orbitals are parallel to each other. This, you can imagine, these are sp3 hybridized orbitals. They're pointing at each other. Here, they're parallel. p orbitals are parallel to each other, and you see that they overlap on this kind of top lobe here and in this bottom lobe here. And this is a pi bond. Let me make this clear. And this is one pi bond. So you could call it a pi, literally, with the Greek letter pi: pi bond. Sometimes you'll see this just written as pi bond. And it's called a pi bond because it's the Greek letter for essentially p, and we're dealing with p orbitals overlapping. Now sigma bonds, which are what form when you have a single bond, these are stronger than pi bonds; pi bonds come into play once you start forming double or triple bonds on top of a sigma bond. To kind of get a better visualization of how that might work, let's think about ethene. So it's molecular structure looks like this. So you have C double-bonded to C, and then each of those guys have two hydrogens. So let me draw what it would look like, or our best visual, or our best ability to kind of conceptualize what the orbitals around the carbon might look like. So first I'll draw the sp2 hybridized orbitals. So let me just make it very clear what's going on here. So when we were dealing with methane, which is literally just a carbon bonded to four hydrogens, and if I actually wanted to draw it in a way that it kind of looks a little three-dimensional with a tetrahedral structure, it might look like this. This hydrogen is pointing out a little bit. This hydrogen is kind of in the plane of the page, and then maybe that hydrogen is behind it, and then you have one hydrogen popping up. That's methane. And we saw that these were all sp3 hybridized orbitals around the carbon, and then they each formed sigma bonds with each of the hydrogens. We saw that in the last video. And when we drew its electron configuration, in order for this to happen, carbon's electron configuration when bonding in methane needed to look like this. It needed to look like 1s2. And then instead of having 2s2 and then 2p2, what you essentially have is-- let me try it this way, actually, even better. Let me write this better. In 1s, you had two electrons, and then instead of two s's, you had two electrons and on each of the p's, you had one, the s's and the p's all got mixed up and you had a 2sp3 hybridized orbital, another 2sp3 hybridized orbital, another 2sp3 hybridized orbital, and then another one, sp3. Normally, when carbon's sitting by itself, you would expect a 2s here, and then you'd have a 2p in the x-direction, a 2p in the y-direction, and then a 2p in the z-direction. But we saw in the last video, they all get mixed up and they all have a 25% s-character, and a 75% p-character when carbon bonds in methane and the electrons kind of separate out in that situation. When you're dealing with the carbons in ethene, remember, eth- is for two carbons and ene-, because we're dealing with an alkene. We have a double bond here. In this situation, the carbon's electron configuration when they bond in ethene looks more like this. So you have your 1s, and the 1s orbital is still completely full. It has two electrons in it. But then in your 2 shell, I'll just write-- let me do this in a different color. So in our 2 shell, I'll show you what I mean in a second. I'm not writing the s or p's so far on purpose, but we're going to have four electrons just like we had before. We're still forming four bonds. We're going to have these four unpaired electrons. We're still forming one, two, three, four bonds with each of the carbons, so they're going to be separated out. But in this situation, instead of all of them being a mixture, kind of one part s, three parts p, the s mixes with two of the p orbitals. So what you have is 2sp2 orbital. So you can imagine that the s orbital mixes with two of the p orbitals. So now it's one part s, two parts p. And then one of the p orbitals kind of stays by itself. And we need this p orbital to stay by itself because it is going to be what's responsible for the pi bond. And we're going to see that the pi bond does something very interesting to the molecule. It kind of makes it unrotatable around a bond axis. And you'll see what I mean in a second. So let me see if I can, in three dimensions, draw each of these carbons. So you have-- let me do it a different color. You have this carbon right there. So let's say that's the nucleus. I'll put a C there so you know which carbon we're dealing with. And then I'll draw-- you could assume that the 1s orbital, it's really small right around the carbon. And then you have these hybridized orbitals, The 2sp2 orbitals, and they're all going to be planar, kind of forming a triangle, or I guess maybe a peace sign on some level, but I'll try to draw it in three dimensions here. So you have one, this is kind of coming out a little bit. Then you have one that's going in a little bit. And then you have-- and they have another lobe a little bit on the other side, but I'm not going to draw them. It'll complicate it. They still have characteristics of p, so they'll have two lobes, but one is bigger than the other. And then you have one that's maybe going in this side. So you can imagine that this is kind of a Mercedes sign if you drew a circle around it, on its side. So that's this carbon right here. And, of course, it has its hydrogens. So you have this hydrogen there. And so this hydrogen might be sitting right here. It just has one electron in its 1s orbital. You have this hydrogen up here. It's sitting right over there. And now let's draw this carbon. This carbon will be sitting-- I'm drawing it pretty close together. This carbon will be sitting right there. He has his 1s orbital. They have the exact same electron configuration. He has his 1s orbital right around him, and then he has the exact same configuration. Either of these guys, we've so far only-- or in this first guy, I've only drawn these first three. I haven't drawn this unhybridized p orbital yet. So I'll do that in a second. But let me draw his bonds. So first of all, he has this, or you could imagine, that bond right there, which would be an sp2 hybridized bond. Let me do that in the same color. So he has this bond right here, which would be an sp2 hybridized bond, just like that. And notice, this is a sigma bond. They overlap in kind of the direction that they're pointing in. That's the best I could think about it. And then he's got these two hydrogens, so one-- he's got this guy in the back, and then there's one in the front. I'll draw it a little bigger so it's kind of pointing out at us, right? And then we have this hydrogen is sitting right over here. And these are also sigma bonds, just to be very clear about things. This is an s orbital overlapping with an sp2 orbital, but they're kind of overlapping in the direction that they're pointed, or kind of along the direction of each other, of the two atoms. This is a sigma bond, sigma bond, and then we have this hydrogen in the back, which is also going to form a sigma bond. So everything I've drawn so far is a sigma bond, so that, that. Maybe I don't want to make this picture too-- so I can just put sigma bond there, sigma bond there, sigma bond there, sigma, sigma. So far I've drawn this bond, this bond, this bond, this bond, and this bond, all of those sigma bonds. So, what happens to this last p orbital for each of these guys? Well, that's going to be kind of sticking out of the plane of the Mercedes sign, is the best way I can describe it. And let me see if I can do that in a color that I haven't done yet. Oh, maybe this purple color. So you can imagine a pure p orbital. So a pure p orbital, I'm going to need to draw it even bigger than that, actually. A pure p orbital, it normally wouldn't be that big relative to things, but I have to make them overlap. So it's a pure p orbital that's kind of going in, maybe you can imagine, the z-axis, that the other orbitals are kind of a Mercedes sign in the x, y plane. And now you have the z-axis going straight up and down, and those bottom two have to overlap so let me draw them bigger. So it looks like that and it looks like that. And they're going straight up and down. And notice, they are now overlapping. So this bond right here is this bond. I could've drawn them in either way, but it's that second bond. And so what's happening now to the structure? So let me make it very clear. This right here, that is a pi bond, and this right here is also-- it's the same pi bond. It's this guy right here. It's the second bond in the double bond. But what's happening here? Well, first of all, by itself it would be a weaker bond, but because we already have a sigma bond that's making these molecules come closer together, this pi bond will make them come even closer together. So this distance right here is closer than if we were to just have a single sigma bond there. Now, on top of that, the really interesting thing is, if we just had a sigma bond here, both of these molecules could kind of rotate around the bond axis. They would be able to rotate around the bond axis if you just had one sigma bond there. But since we have these pi bonds that are parallel to each other and they're kind of overlapping and they're kind of locked in to that configuration, you can no longer rotate. If one of these molecules rotates, the other one's going to rotate with it because these two guys are locked together. So what this pi bond does in the situation is it makes this carbon-carbon double bond-- it means that the double bonds are going to be rigid, that you can't have one molecule kind of flipping, swapping these two hydrogens, without the other one having to flip with it. So you wouldn't be able to kind of swap configurations of the hydrogens relative to the other side. That's what it causes. So, hopefully, that gives you a good understanding of the difference between sigma and pi bond. And if you're curious, when you're dealing with-- just to kind of make it clear, if we were dealing with ethyne, this is an example of ethene, but ethyne looks like this. You have a triple bond. And so you have each side pointing to one hydrogen. In this case, one of these, so the first bonds, you can imagine, so these bonds are all sigma bonds. They're actually sp hybridized. Your 2s orbital only mixes with one of the p's, so these are sp hybrid orbitals forming sigma bonds, so all of these right here. And then both of these-- let me do this in different color. Both of these are pi bonds. And if you had to imagine it, could imagine another pi bond kind of coming out of the page and another one here coming out of the page and into the page, out and into the page, and they, too, are overlapping, and you just have one hydrogen pointing out in each direction. Maybe I'll make another video on that. So, hopefully, you--