Molecular Orbitals

We were just talking about constructive and destructive interference. We said that when things constructively interfere, they're going to create unusual regions of shared electron density, that's just another way me saying, higher probability, called bonds. Remember that a bond is just an area where you wouldn't expect to find electrons.
Usually, you would say, there shouldn't be electrons here according to the math. If I did the math, there should not be electrons. But for some reason, these orbitals are interfering with each other constructively, so they're increasing the chance of finding electrons there. Does that make sense? Cool.
So it turns out that there's actually multiple ways to make these bonds or these shared regions of electron density. So let's talk about the simplest ways first which is the sigma bond, so as you see here I have sigma, sigma, sigma. First of all, you should know is that sigma is going to be synonymous with the word single. So whenever I say a single bond, I'm always referring to a sigma bond. What that means is that a sigma bond is a region of one region of overlap. There's only one place where these orbitals are coming together and they're making that bond happen.
It turns out that there's actually several ways to make this region of overlap, though. There's several ways to make a sigma bond. We could have an s orbital and an s orbital or we could have an s orbital and a p orbital or we could have a p orbital and a p orbital. The important part is that they all count as sigma bonds as long as there's only one region of overlap. So those are all the different types of sigma bonds I could make.
Now, another type of bond that I could make is one that has more than one region of overlap, that would be, for example, a pi bond. In fact, it would have two regions of overlap from two p orbitals coming together. As you can see there's a region at the top, there's a region at the bottom. Just so you know, pi bonds are found in double bonds. Now, I'm going to clarify this in a little bit, pi bond and double bond are not the same exact thing. What you should know is that a double bond has a pi bond in it. 

Now what I want to do is switch gears and talk about a type of notation that's very common in organic chemistry and it's a model that we use to really predict what molecular orbitals are going to look like. And it's called the Linear Combination of Atomic Orbitals, so if you ever see LCAO, that just means this little diagram that I have drawn right here.
So let's go ahead and just get right into it, figure out what's going on. So the first thing you need to do is learn how to read this. So there are two orbitals on the sides, here and here. These are your atomic orbitals, so write in AO, AO. Just so you know, these are the same types of orbitals that we were dealing with when we talked about atomic orbitals, so basically just orbitals that have two electrons in them. They don't interfere with each other. Those are just the orbitals with the atoms by themselves.
Now these orbitals in the middle have to do with interference. They have to do with how the atomic orbitals coming together. These are called molecular orbitals. So what molecular orbitals do is they predict where electrons are going to be in the entire molecule, not just for the atom. Does that make sense? So basically they predict the way the bond is going to behave.
So let's look at these three different possibilities of the way that atoms can interfere with each other, orbitals can interfere with each other.
Let's go ahead and start off with the simplest form of interference, which would be nonbonding. Now, I did not talk about nonbonding in the previous topic, so I want to ask you guys, what do you think nonbonding is? Well, just like it sounds, it means that they're not bonding. It means they're not interfering with each other. So you could almost think of it as I'm holding one hydrogen in one hand and one orbital in the other, one orbital in the other. They're not interfering with each other. Maybe they're too far apart or whatever, but they are just like freestanding.
So in that case, nonbonding, as you can see I just have like a comma here, that just means I have two orbitals that are not interacting. And the way that I would draw these is as atomic orbitals because they don't have any bond at all.
So let's go ahead and try and figure out what the atomic orbitals would look like. What I want you guys to do is just pretend that this is a hydrogen atom and what type of orbital does a hydrogen atom have? Do you guys remember?
Well, if you think about it, a hydrogen atom only has one electron, so that one electron should be in the 1s orbital so that's why as you notice, I have 1sa and 1sb. What that means is that this is the 1s orbital for the (a) hydrogen and this is the 1s orbital for the (b) hydrogen. Does that make sense? I hope that's not too confusing. Basically, what I'm doing is I'm just going to map out where the electron is going to be for this atomic orbital and where the electron is going to be for this one.
Now that I know which orbitals correspond to which atoms, you guys have to tell me how many electrons do I have in the nonbonding orbitals. How many electrons do I have in 1sa and in 1sb? Well, what's the atomic number of hydrogen? One. So how many electrons should I have? One. So what I'm going to do is I'm going to draw one electron here, one electron here. I'm done. That represents the one electron that's in this orbital here and the one electron that's in that orbital there. Does that make sense so far? I hope so. I know it's a little bit complicated. I'm trying to make it as easy as possible.
So those are my atomic orbitals. Now remember that I said, these orbitals in the middle, the molecular orbitals, have to do with how they're interfering, so let's talk about the easiest form of interfering first, which is bonding.
Remember that bonding would be a constructive interference. The way that you can – let me just write constructive. Go ahead and write down constructive. The constructive interference can be represented by just like a positive, I mean not a positive, a plus, meaning that one orbital is adding to another orbital and making the chances of finding an electron there better.
The way that you would denote that on my model is that I would have this electron jump down to this energy state and this electron just down to this energy state because they're being shared between both atoms. So what I'd have is that now one becomes an up spin and one becomes a down spin.
And the way that I've heard this as analogy before is that imagine that these are like two people that are financially unstable and they like can't pay their bills and they decide to move in together and like share costs. Imagine you're not cutting it and you're like, “Hey, let's just go ahead and room for a few months or whatever.” What that's going to do is it's going to make both of them more energetically favorable and I'm going to talk about that in a second.
When they constructively overlap like this, that's going to make what we call a sigma bond. Remember a sigma bond is a region of one overlap. The reason it's called sigma 1s is because that's the sigma bond created by 1s orbitals, two 1s orbitals. Cool. So hopefully that makes sense so far. That when they constructively interfere, you're going to wind up filling what's called the bonding orbital, which is this one right here.
Now let's see what happens when they destructively interfere. Let's say that these two people try and move in together, but they just hate each other's guts. Well, that would be an antibonding association, where you use a minus charge to show that they're actually going to form a node in the middle and there's going to be no overlap at all.
When that happens these two electrons are actually going to jump up to a higher energy state and fill the antibonding orbital. The antibonding orbital, just so you know, is denoted by this star. If you ever see that star, that means this is antibonding.
As you can see, these electrons are actually having to become – see the energy is going up. They're actually having to become more energetic to do that and that's bad. Remember that basically in all chemistry if you get more energetic, that's a bad thing because you have to work for it and molecules are lazy. They don't like to work.
Basically, that's the way we use this diagram. You could show that you could either do antibonding or it could do bonding, but in this case, we're just going to use the bonding orbital.
Now a question that you guys might have is, “Okay, Johnny, I understand what you're saying, but why would atoms ever do the antibonding if it's so energetically bad, why would they do it?” The answer is they don't want to. Antibonding orbitals are not favored. What would happen is that these two hydrogen atoms would come together and then they would realize that they're antibonding and then they would immediately split apart. Why? Because they're not energetically favorable. Maybe, later on, they'll meet their match and find someone else to bond with, but those two hydrogen atoms would not bond with each other. That's an antibonding interaction.
Now, what I want to do is connect this to another really important diagram that's found in your book. What it shows is that there's a relationship between how stable atoms are and how close they are together. So basically when two atoms are nonbonding, remember that that's the picture that I have here where they're nonbonding. This is the nonbonding line. When two atoms are nonbonding, they're kind of stable, but they're kind of not stable, especially when they're hydrogen atoms. Do you guys know why?
The reason why is because remember that each orbital can hold two electrons, but how many electrons does each orbital have right now? Only one. The 1sa has only one electron. The 1sb has only one electron, so those orbitals aren't completely filled, so they're not going to be very stable. Does that make sense so far?
If they can jump together and share electrons between each other, then what's going to happen is that they're going to form a bond. Remember that's the bonding diagram, where there's higher chances of finding electrons right there. That means that now they're going to have one molecular orbital that is completely filled. That's actually a really, really good thing because now it's completely filled, it's more stable.
One thing to keep in mind is look at the energy difference here. Now, I do not need you to memorize this, but just so you know, when we talk about energy and thermal dynamics in organic chemistry, we're going to talk in terms of kilojoules per mole. 436 kJ per mole is the energy that is saved by coming together. That's a huge amount of energy. So what that means is this is going to be very, very favorable interaction.
Actually, if you think of hydrogen in real life, it actually does this. When you breathe in hydrogen – there's lots of hydrogen in the air – you're not breathing in just regular hydrogen, you're breathing in H2.Why? Because the hydrogen saves a ton of energy by bonding together and filling its molecular orbital. Does that make more sense now? It's like a real-world application. This is very favorable reaction.
One more thing I want to point out is that I have this number 1.33Å, what is that? A with a little dot over it. It actually looks like this in case you can't see it. Oops. It looks like this. Is an angstrom. Do you guys remember what an angstrom is? It's a tiny, tiny unit of measurement that we use to measure atomic-scale things. For example, you would not want to measure your room in angstroms. It would be a very, very big number. What an angstrom is it's 1 x 10-10 meters. So basically it's a very, very tiny amount.
The distance between these nuclei is 1.33 angstroms in this specific single bond. So just keep that in mind that a sigma bond is about 1.33. That changes a little bit, but in this case, that's what it is.
Now, what I want to do is I want to move on to talking about pi bonds and how they can do the same thing, or p orbitals. So p orbitals can also from nonbonding, antibonding, bonding. Now I don't want to go through this as much in depth because we already did it and because this one's more complicated. There's some sigma bonds that I kind of ignored.
But what I do want to show is that once again, I would have one electron from my 2px, I could have one electron from my other 2px over here. Let's just say this is one and two, so this is one and two. And what I would get is these atomic orbitals that aren't very stable just by themselves. What they want to do is they want to combine constructively. So if they combine constructively, which is like this, shown by the colors being the same on both sides, then what's going to happen is that these electrons will jump down to a lower energy state and they'll form a molecular orbital that is more stable. Now notice that the name of this molecular orbital is different. The name is called a pi bond because of the fact that the pi bond has to do with two regions of overlap that are constructive, not just one.
In the same way, antibonding orbitals could form and that would be star pi. That would not be as stable, so it would not form. It would split apart and then it would form a bonding orbital later. Cool.

There's two differences here with this energy diagram they've drawn here, OK? Well one is that notice that the bond length is different, OK? So, it turns out that for a Pi bond is the bond length going to be shorter or is it going to be longer? It turns out that it's going to be shorter and that's going to be important later so I want you guys to know that a single bond is going to be longer and a Pi bond is going to be shorter, OK? Another thing to keep in mind is that check it out these numbers have changed, OK? So, if I were to ask you about you know this interaction, if I would say which one is more stable, OK? A Single pond where you really have one region of overlap or a double bond where I have two regions of overlap which we're going to say is overall more stable and it turns out that obviously the double bond is overall more stable because it actually saves even more energy than the one on top it saves 599 instead of 436, OK? So, the double bone is going to basically save more energy by becoming a double bond but now there's just one more thing to point out which is this it turns out as I'm going to explain in the next topic that a double bond is not just made out of Pi orbital it's actually made out of.... IÕm sorry a PI bond, a double bond is made out of a Pi and a sigma bond, OK? So, it turns out that a double bond has a Pi bond and a Sigma bond in it so now you have something else I have another question for you guys we said that the energy gained from the sigma bond was 436 and now I'm saying that the energy gained from a sigma and a PI because this is a Double bond is 599, OK? So, if I were to ask you which of the two types of bonds is more stable the Pi bond or the Sigma bond? The answer would be that the Sigma bond is actually a lot more stable, why? Because the Sigma bond is 436 Kilojoules out of 599, OK? So, think about it like this, 599 is the combination of both the energy gained from the sigma and of the PI, OK? So, if I were to subtract 599 and 436 from that what you would get is that only 163 Kilojoules are being saved by the PI bond and then 436 is being saved by the Sigma bond so this kind of brings up something that is a little bit tricky but that you guys need to know for those conceptual questions if a professor asked which was a stronger a double bond or single bond? You say double because the double is the Sigma and the Pi but if the professor asks you which one is stronger a Sigma bond or a PI bond? Then please say the Sigma bond because the Sigma bond is the one that contributes more to the overall strength of the double bond, does that make more sense now? I hope it does and I know it was a little bit confusing but just leave me a question to anything I'd love to help you understand more, OK? So, let's move on to the next topic.