Molecular Orbitals: Videos & Practice Problems

Constructive and destructive interference in molecular orbitals leads to bonding and antibonding interactions. A sigma bond, representing a single bond, forms from one region of overlap between orbitals, while a pi bond, found in double bonds, involves two regions of overlap. The stability of bonds increases with the number of overlapping regions, with sigma bonds being stronger than pi bonds. The energy gained from forming these bonds is significant, with sigma bonds saving 436 kJ/mol and double bonds saving 599 kJ/mol, highlighting the importance of electron sharing in molecular stability.

What’s the difference between sigma and pi bonds?

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 of me saying higher probability called bonds. 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 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. As you see here, I have sigma, sigma, sigma. First of all, what 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 are several ways to make a single 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. And that would be, for example, a pi bond. In fact, it would have 2 regions of overlap from 2 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. So 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. All right? Cool.

What’s the difference between atomic and molecular orbitals?

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. 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. The first thing you need to do is learn how to read this. There are 2 orbitals on the sides, here and here. These are your atomic orbitals. 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. Basically, just orbitals that have 2 electrons in them. They don't interfere with each other; those are just the orbitals by themselves 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 are coming together. These are called molecular orbitals. 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? Basically, they predict the way the bond is going to behave.

All right. So let's look at these three different possibilities of the way that atoms could interfere with each other, orbitals could interfere with each other. So let's go ahead and start 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, 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. This means I have 2 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 to 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've noticed, I have 1 and 1. 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.

So 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 each in 1s, a and in 1s, b. Well, what’s the atomic number of hydrogen? 1. So how many electrons should I have? 1. So what I’m going to do is I’m going to draw 1 electron here, 1 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.

Okay. So, remember that bonding would be a constructive interference. The way that you can constructive, go ahead and write down constructive. The constructive interference can be represented by just a positive, 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 jump down to 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. The way that I’ve heard this as an analogy before is that imagine that these are like 2 people that are financially unstable and they can’t pay their bills and then they decide to move in together and share costs. So 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. And the reason it’s called sigma-1s is because that’s the sigma bond created by 1s orbitals, 2 1s orbitals. All right. 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. So let’s say that these 2 people try to move in together, but they just hate each other's guts. 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 going to be no overlap at all. When that happens, these 2 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 the 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-[TRANSMISSION END]-

Sigma bond vs. pi bond, which is stronger?

There are two differences here with this energy diagram that I've drawn here. Well, one is that notice that the bond length is different. 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 sigma bond, I mean that a sigma bond, is going to be longer and a pi bond is going to be shorter.

Another thing to keep in mind is that check it out, these numbers have changed. So, If I were to ask you about this interaction, If I were to say, which one is more stable? A single bond where I only have one region of overlap or a double bond where I have two regions of overlap? The double bond is more stable because it actually saves even more energy than the one on top. It saves 5.99 instead of 436. So the double bond is going to basically save more energy by becoming a double bond.

But now there's just one more thing I need 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 a pi orbital. It's actually made out of a pi bond and a sigma bond. So, It turns out that a double bond has a pi bond and a sigma bond in it.

So now we 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 it's a double bond, is 599. 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 accounts for 436 kilojoules out of 5.99. So think about it like this, 5.99 is the combination of both the energy gained from the sigma and the pi bond.

So, If I were to subtract 599 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 asks which one is stronger, a double bond or a 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. I know it was a little bit confusing but just leave me a question. If anything, I'd love to help you understand it more.

Okay, so let's move on to the next topic.

Here’s what students ask on this topic:

What is the difference between sigma and pi bonds in molecular orbitals?

Sigma (σ) bonds and pi (π) bonds differ in their formation and properties. A sigma bond forms from the head-on overlap of atomic orbitals, creating a single region of electron density between the nuclei. This bond is found in single bonds and is characterized by its strong, stable nature. In contrast, a pi bond forms from the side-by-side overlap of p orbitals, resulting in two regions of electron density above and below the plane of the nuclei. Pi bonds are found in double and triple bonds, adding to the stability but are generally weaker than sigma bonds. The combination of sigma and pi bonds in double bonds increases overall stability.

How does constructive and destructive interference affect molecular orbitals?

Constructive and destructive interference significantly impact molecular orbitals. Constructive interference occurs when atomic orbitals combine in-phase, increasing the probability of finding electrons in the bonding region, leading to the formation of bonding molecular orbitals. This results in a lower energy state and greater stability. Destructive interference happens when atomic orbitals combine out-of-phase, creating a node where electron probability is zero, forming antibonding molecular orbitals. These orbitals are higher in energy and less stable. The balance between these interactions determines the overall stability and bonding characteristics of the molecule.

What is the Linear Combination of Atomic Orbitals (LCAO) method?

The Linear Combination of Atomic Orbitals (LCAO) method is a model used to predict molecular orbitals by combining atomic orbitals. In this approach, atomic orbitals from individual atoms are mathematically combined to form molecular orbitals that describe the electron distribution in a molecule. The resulting molecular orbitals can be bonding, antibonding, or nonbonding, depending on the constructive or destructive interference of the atomic orbitals. LCAO helps in understanding the bonding, stability, and electronic structure of molecules, making it a fundamental concept in molecular orbital theory.

Why are sigma bonds stronger than pi bonds?

Sigma bonds are stronger than pi bonds due to the nature of their orbital overlap. Sigma bonds result from the head-on overlap of atomic orbitals, creating a single, robust region of electron density directly between the nuclei. This direct overlap leads to a stronger, more stable bond. In contrast, pi bonds arise from the side-by-side overlap of p orbitals, resulting in two regions of electron density above and below the plane of the nuclei. This type of overlap is less effective, making pi bonds weaker and less stable compared to sigma bonds.

What is the significance of bonding and antibonding molecular orbitals?

Bonding and antibonding molecular orbitals play crucial roles in determining the stability and properties of molecules. Bonding molecular orbitals result from constructive interference, where atomic orbitals combine in-phase, leading to a lower energy state and increased electron density between the nuclei. This enhances molecular stability. Antibonding molecular orbitals, formed by destructive interference, have higher energy and a node where electron density is zero, making them less stable. The presence and occupation of these orbitals influence the bond strength, length, and overall stability of the molecule.