When atomic orbitals interfere constructively with each other, they increase the chances of finding electrons between nuclei, forming what we call a bond.
Types of Bonds
A sigma (σ)-bond is formed by one region of constructive overlap between orbitals (regardless of the type of orbital used).
A pi (π)-bond is formed by two regions of constructive overlap between orbitals (p-orbitals).
What’s the difference between sigma and pi bonds?
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we were just talking about constructive and destructive interference, right? And we said that when things constructively interfere, they're gonna create unusual regions of shared electron density. That's just another way of me saying higher probability. Okay, called bonds. Okay, so 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 orbital's 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 bonds. So, as you see here, I have Sigma Sigma sigma. Alright, first of all you should know is that Sigma is going to be synonymous with the words single. Okay, so whenever I say ah, single bond, I'm always referring to a Sigma Bond. What that means is that a single a single bond is a region of one region of overlap okay. There's only one place where these orbital's air coming together, and they're making that bond happen. All right. It turns out that there's actually several ways to make this region of overlap, though there's several ways to make a single bond. We could have an s orbital and an s orbital. Okay? Or we could have an s orbital and a P orbital, or we could have a P orbital and a P orbital. Okay, The important part is that they all count a signal bonds as long as there's only one region of overlap. All right, so those are all the different types of signal bonds I could make. Now, another type of bond that I could make is one that has more than one region of overlap. All right. And that would be, for example, a pi bon. In fact, it has. It would have to regions of overlap from two p. Orbital's coming together. Okay, As you can see, there's a region at the top. There's a region at the bottom. Okay? Just you know, pi bonds are found in double bonds. Okay, so now I'm going to clarify this in a little bit pie bond and dull bond are not the same exact thing. But you should know is that a double bond has a pipe on in it. All right, cool.
The LCAO Model:Predicting Molecular Orbitals
What’s the difference between atomic and molecular orbitals?
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Now what I wanna do is switch gears and talk about a type of notation that's very common in organic chemistry. And it's it's a model that we use to really predict what molecular orbital they're gonna look like. All right, and it's called the linear combination of Atomic Orbital. So if you ever see LCL, that just means this little diagram that I have drawn right here. Um, so let's go. 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 orbital's on the sides here and here. These air, your atomic orbital's so right in a Oh, a Oh, just so you know, these are the same types of orbital's that we were dealing with when we talked about atomic Orbital's so basically just orbital's that have two electrons in them. They don't interfere with each other, those just the orbital's by themselves, with the atoms by themselves. Now these orbital's in the middle have to do with interference. They have to do with How are the atomic orbital's coming together? These air, called molecular orbital's okay So what molecular orbital's do is? They predict where electrons They're gonna 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. Alright. So let's look at these three different possibilities of the way that Adams could interfere with each other. Orbital's could interfere with each other, so let's go ahead and start off with simplest form of interference, which would be non bonding. Okay, now, I did not talk about non bonding in the previous topic. So I want to ask you guys, what do you think non bonding 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, one orbital on the other, one orbital in the other. They're not interfering with each other. Maybe they're too far apart. Whatever. But they're just like freestanding. Okay, so in that case, non bonding As you can see, I just have, like a common here. This means I have to, or rules that are not interacting and the way that I would draw. These is as atomic orbital because they don't have any bond at all. So let's go ahead and try to figure out what the atomic orbital's would look like. Okay, What I want you guys to do is just pretend that this is a hydrogen atom. Okay? And what type of orbital does the hype hydrogen atoms 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 one s orbital. That's why, as you've noticed, I have one s A and one SB. What that means is that this is the one s orbital for the A hydrogen. And this is the oneness orbital for the B hydrogen. Does that make sense? I hope that's not too confusing. So 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. So now that I know which orbital's correspond to which Adams you guys tell me, how many electrons do I have in the non bonding orbital's? How many electrons do I have in each in one s and in one SB. Well, what's the atomic number of hydrogen One? So how many electrons should I have? One. So, what I'm gonna do is I'm gonna 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 trying to make it as easy as possible. So those are my atomic orbital's. Now remember that I said Thies, Orbital's in the middle. Have the molecular orbital's have to do with how they're interfering. So let's talk about the easiest form of interfering first, which is bonding. Okay, so remember that bonding would be a constructive interference the way that you can, Um, can I just make a constructive go ahead and write down constructive. The constructive interference can be represented by just like a positive that I mean, not positive a plus, meaning that one orbital is adding toe another orbital and making the chances of finding electron. They're better. Okay. And 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 jumped onto this energy state because now they're being shared between both atoms. So what I would 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 two people that are, like, financially unstable and they can't pay their bills, and then they decided to move in together and like, share costs. All right, so imagine, like, you're not cutting it, and you're like, Hey, let's just go ahead and, like, you know, room for a few months, Whatever. All right. So what that's going to do is it's gonna make both of them more energetically favorable. I'm gonna talk about that in a second. When they constructively overlap like this, that's going to make what we call a signal bond. Okay, I remember a signal bond is a region of one overlap, and the reason it's called Sigma one s is because that's the signal bond created by one s orbital's 21 s orbital's. Alright, cool. So Hopefully, that makes them so far that when they constructively interfere, you're gonna wind up filling what's called the bonding orbital, which is this one right here. Okay, Now let's see what happens when they destructively interfere. So let's say that these two people try to move in together, but they just hate each other's guts. All right, well, that would be an anti bonding association where you use a minus charge to show that they're actually going to form a node in the middle. And there's gonna be no overlap at all, Okay? And when that happens, these two electrons actually gonna jump upto a higher energy state and fill the anti bonding orbital. Okay, the anti bonding orbital, just, you know, is denoted by the star. If you ever see that star, that means this is anti bonding, all right. And as you can see, these electrons are actually having to become See, the energy is going up right there, actually having to become mawr energetic to do that. And that's bad. Remember that. Basically in all chemistry, if you get more energetic, that's a bad thing, okay? Because you have toe, you have to work for it. and molecules are lazy. They don't like toe work. All right, so basically, that's the way we use this diagram. You could show that they could either do anti bonding or could do bonding, but in this case, we're just going to use the bonding orbital. Now a question that guys might have is okay, Johnny, I understand what you're saying. But why would Adams ever do the anti bonding? If it's so bad if it's so energetically bad, why would they do it? And the answer is, they don't want Thio. Anti bonding Orbital's are not favored. So what happened is that these two hydrogen atoms would come together, and then they would realize that their anti bonding and they would immediately split apart. Why? Because they're not energetically favorable. Maybe later on they'll meet their match and like find someone else to bond with. But those two hydrogen atoms would not bond with each other. All right, that's an anti bonding interaction. Now what I want to do is connect this to another really important diagram that's found in your book, and what it shows is that there's a relationship between how stable of atoms are and how close, they are together. So basically, when two atoms are non bonding, remember that That's the That's the picture that I have here, where they're non bonding. And this is the non bonding line. Okay, when two atoms air non bonding, they're kind of stable, but they're kind of not stable, especially when they're when they're hydra jobs. 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 one s A has only one electron. The one SB has only one electron. So those orbital's 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 gonna happen is that they're gonna form a bond. This is remember, that's the bonding diagram where there's higher chances of finding electrons right there. And that means that now they're gonna 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, um, in thermal dynamics in organic chemistry, we're gonna talk in terms of killing joules per mole. 436 kg per mole. Is the energy you gain, or will the energy that is saved by coming together? That's a huge amount of energy. What that means is this is going to be very, very favorable interaction, okay? And actually, if you think of hydrogen riel 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 h two. Why? Because the hydrogen saves a ton of energy by bonding together in filling its molecular orbital. Does that make more sense now? It's like a real world application. Okay, there's a very favorable reaction. One more thing I want to point out is that I have this number 1. a 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 remember what an angstrom is? It's a tiny, tiny unit of measurement that we use to measure atomic scale things. So, for example, you would not want to measure your room in Angstrom. It would be a very, very big number. Okay? And when Angstrom is, it's one times 10 to the negative. 10. Okay, meters Meters. Okay, so basically, it's a very, very tiny amount. The distance between these nuclei is 1.33 banks drums in this specific single bond. Okay, so just keep that in mind that a signal bond is about 1.33 That changes a little bit, but in this case, that's where it is now. What I want to do is I want to move on to talk about pie bonds and how they could do the same thing. So, or P? Orbital's soapy orbital's can also form non bonding, anti bonding bonding. Now, I don't want to go through this as much in depth because we already did it because this one's more complicated. There's Cem Sigma Bonds that I kind of ignored. But what I do want to show is that once again, I would have one electron for my two p x. I could have one electron for my for my other two. P x. Over here. This is Let's just say that this is one and two. So this is one and two, All right. And what I would get is thes orbital's that aren't atomic orbital's 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, show him by the colors, being the same on both sides. Okay, then what's gonna happen is that these electrons will jump down to a lower energy state, okay? 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 pie bond. Okay, because the fact that the Pi Bon has to do with two regions of overlap that air constructive not just one okay, In the same way anti bonding orbital's could form and that would be star pie that would not be a stable so it would not form. It would split apart and then would form a bonding orbital later. Okay, cool
The hexagon-thingy in the middle is the LCAO (Linear Combination of Atomic Orbitals):
The side orbitals are your atomic orbitals (like you are used to drawing)
The top and bottom orbitals represent atomic orbital overlap (molecular orbitals).
When atomic orbitals constructively interfere, they create bonding molecular orbitals that are more stable than the original atomic orbitals.
Bond Lengths and Strengths
Sigma bond vs. pi bond, which is stronger?
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There's two differences here with this energy diagram that I've drawn here. Okay, well, one is that notice that the bomb length is different. Okay, so it turns out that for a pie bond, is the bond length gonna be shorter or is it gonna be longer? It turns out that it's gonna be shorter, and that's gonna be important later. So I want you guys to know that a signal bond, I mean that a single bond is gonna be longer and a pi bon is gonna be shorter. Okay, Another thing to keep in mind is that Check it out. These numbers have changed. Okay, So if I were to ask you about you know, this interaction if I were to say which one is more stable? Okay, a single bond where I only have one region of overlap or a double bond where I have to regions of overlap. Which one would you 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 5 99 instead of 4. 36. Okay, so the double bond is going to is going to basically save more energy by becoming a doula pawn. But now there's just one more thing I need to point out, which is this. It turns out, as I'm gonna explain in the next topic, that a double bond is not just made out of pie orbital. It's actually made out of I'm sorry. A pie bond. A double bond is made out of a pie and a signal bond. Okay, so it turns out that a double bond has a pie bond and a signal bond in it. So now I have something else. Thio. I have another question for you guys. We said that the energy gained from the signal bond was 36. And now I'm saying that the energy gained from a Sigma and Pi because there's a double bond is 5 99. Okay, So if I want to ask you which of the two types of bonds okay is more stable, the pie bond or the signal bond? The answer would be that the Sigma Bond is actually a lot more stable. Why? Because the signal bond is 436 killer jewels out of 5 99. Okay, so think about it. Like this. 5 99 is the combination of both the energy gained from the Sigma and of the pie. Okay, so if I were to subtract 5 99 and 4. 36 from that, what you would get is that on Lee, 163 kg jewels are being saved by the pie bond, and then 4 36 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 this conceptual questions. If a professor asks which one is stronger a double bonder single single bond, you say double because the double is the sigma and the pie. But if the professor asks you which one is stronger a signal bond or a pie bond, then please say the Sigma Bond because the signal bond is the one that contributes more to the overall strength of the bond. Does that make more sense now? I hope it does. I know it was a little bit confusing, but just leave me a question. If anything, I'd love toe. I'd love to help you understand it more. Okay, so let's move on to the next topic.
Hey! Turn that frown upside-down. I know this section sucks. The rest of this chapter should be cake compared to this.