Leah here from leah4sci.com and in this video we're going to look at molecular orbital theory for sigma and pi bonds. If you look up what is molecular orbital theory, you'll find some complicated math and physics explanation of quantum wave functions that overlap and all really nice except that in organic chemistry, we're looking to understand the simple takeaway. Rather than the complicated over your head don't need to know this information and that's what I want to look at today So let's back up and talk about atomic orbitals Atomic orbitals as you may remember tells us where an electron is located or specifically in the type of orbital that an electron is located around an atom and if you go back to my Orgo basic video series you'll see how we have the sp3, sp2, sp and even p orbitals that house different electrons.
If you need a refresher, visit the link below or go to my website leah4sci.com slash orgobasics. For example, in the molecule CH4, we have a carbon atom bound to 4 hydrogen atoms. The carbon is sp3 hybridized and each of the hydrogen atoms have an s orbital only, so no hybridization.
The bond between carbon and hydrogen is an overlap between the sp3 hybrid orbital of carbon and the s orbital of hydrogen. But when that bond forms, we're no longer looking at the individual atomic orbital because now these two orbitals have fused together to make a molecular orbital to show that the atoms are bound together. The difference between atomic and molecular orbitals Is that the atomic orbital refers to just the atom where the molecular orbital now shows us the electrons on the entire molecule.
The energy between an atomic and molecular orbital is very different and depends on the specific situation. So let's take a look at a simple molecule, H2 gas. This is made up of two hydrogen atoms that each have a lone electron.
If we plot this on an energy diagram. Then each of the hydrogen atoms has its energy somewhere in the middle. They're not happy but they're not unhappy. This is how they are and they're okay with it. This one electron refers to the atomic orbital for each hydrogen sitting in the 1s orbital.
When they come together to form a bond, we no longer have the atomic orbitals because now the electrons are sitting in a new molecular orbital. Another way to visualize this. is the two hydrogen atoms, we have the one atomic orbital, the second atomic orbital, now they're overlapping and you get one giant molecular orbital.
When the two atoms come together to form that molecular orbital, what's happening is they get combined mathematically using the LCAO, the linear combination of atomic orbitals. No, no, no, this is too much mathematical mumbo jumbo. that we don't care about.
What we do care about, the takeaway is that we get two different options. The first is constructive interference or should we say low energy bonding molecular orbital and the second is destructive interference or should I say higher energy antibonding molecular orbital. You'll often see an asterisk at the antibonding molecular orbital.
So where does this go in the energy diagram? We have the low energy bonding molecular orbital and we have the high energy antibonding molecular orbital where the bonding is a sigma bond and the antibonding is a sigma star. Remember that we only had two electrons and that means we have the option of putting them into the low energy bonding molecular orbital where they're happy or bumping them up to the antibonding. but they're not going to occupy both molecular orbitals at the same time. So how does this make sense?
I like to think of the electrons as people in or out of a relationship. We start with the atomic orbital where we have a single electron. Here we have a single person and another single person.
They don't know each other, they're just living life and happy enough and then one day, they meet and fall in love. Together they are so happy and so stable even more stable than their single days Giving them the lowest possible energy because remember happy stable Unreactive and if energy represents anger and temper there's not a lot going on there But as with most couples every now and then they get into a fight. They're still in a relationship. They're still together But right now they're so mad at each other, they have opposing views, differing opinions, there's yelling and screaming and very very high energy that together in a fight, they're much higher energy, meaning much less stable than their single days. As a reminder, the two electrons are sitting in the bonding molecular orbital.
If they get excited by something upsetting, these electrons can temporarily come up to the anti-bonding. But if that source of extra energy goes away, they prefer to sit here in the comfortable, happy, stable bonding molecular orbital. This temporary rift between them, this fight is called the anti-bonding node, that thing that separates them even though they're technically together. Turning our stick figures back into hydrogen, we have almost a single bubble where the two electrons exist together in the bonding molecular orbital and this right here for the the anti-bonding molecular orbital where there's a clear node between them showing that the atoms while still together are definitely not holding on to each other as well.
This is a topic I used to struggle with and my TA told me, oh don't worry, this is just mathematical physics beyond what you need to understand, which made sense that I didn't need to understand it but I was so confused. So even though I'm telling you the same thing, don't worry about the math and the physics behind all of this. I still want you to have a simple enough take away of what the heck is going on here. So if you're with me so far, make sure to give this video a thumbs up and let me know your biggest take away in the comments below and then let's move on to pi bonds.
Molecular orbitals for pi bonds start out very similar to sigma but can get complicated. So let's take a step back. A pi bond or a double bond doesn't refer to two bonds.
It's actually the second bond in a double bond. For example if we look at the molecule Ethene or Ethylene which is CH2CH2, the simple drawing for this is a carbon double bound to another carbon atom and each carbon has two additional hydrogen atoms sigma bound on the side. The double bond between them has two lines that don't differentiate so it makes it look like it's two of the same when in actuality. We have one sigma bond and one pi bond. Remember that a sigma bond like we saw with the hydrogen atoms is a simple overlap and don't forget the carbon to hydrogen bonds are also all sigma.
The bond would be shown with the sp2 hybrid from carbon overlapping with the s non-hybrid from hydrogen to form a sigma bond. But since our interest is the pi bond, let's simplify this as follows. We have carbon single bound to carbon and almost imagine that this is drawn just tilted off the plane of the page so that for each carbon we have one hydrogen coming forward out of the page and one hydrogen going back into the page.
That lets us put our eye right here and look straight on to see about the pi bond. The pi bond is made with a non-hybridized p orbital that individually sits just above and below the plane of the molecule, in our case the plane of the page. When those p orbitals come together and overlap, the pi bond is formed.
Now, let's bring them a bit closer together. What this shows us is the electrons are free to go up and down, around and around between the two atoms with a node in the middle. So they're sitting either at the top half or bottom half of that pi bond.
The energy diagram for this will look exactly the same as the energy diagram for hydrogen. We start out with some in between neutral energy for the 2p orbital, each of which has a single electron. That 2p orbital comes from the hybridization of carbon which as you remember is 1s2, 2s2, 2p2, when the 2s and 2p electrons hybridize. We get 3, 2sp2.
So let me tell you what the numbers mean. We have 3, 1, 2, 3 sp2 hybrids in row 2. That's what all the numbers mean. So we can take away that too. And then on the side, we also have that single p but because it's coming from the second row, it's coming from a 2p, that's what this 2p stands for.
When the electrons come together, we get a pi bonding molecular orbital but if they get excited, they jump up into the pi star antibonding molecular orbital which we can imagine something like this. As you can see, it looks very much like our initial ethylene molecule but with a very obvious node in between them because right now the carbons in this relationship are not getting along very well. If you're following up to this point but you're trying to think how to make sense of this in the grand scheme of molecules and reactions, here is how I like to think of it. We have our ethylene molecule CH2CH2.
which if we draw it out, we have a pi bond between the two carbon atoms. I like to think of the bonding molecular orbital as a pi bond. But remember in resonance structures, one type of unstable resonance is to take the two electrons and collapse it onto one of the atoms. Show the double-headed arrow and this new less stable contributing structure. We still have the sigma bond between them but now we have one lone pair on the carbon on the right, that means it's got extra electrons and a negative charge.
The carbon on the left lost the pi bond, got nothing in return, is now deficient and therefore gets a positive formal charge. Remember, this is not the mathematical and physics explanation of bonding and anti-bonding but instead this is how I like to think of it. In bonding, they're together, they're happy.
In anti-bonding, they're separated. There's that burden of charge. One is negative, one is positive.
They don't like that burden. That's what makes them so unstable. As soon as you take away that extra energy, the electrons are able to come back, able to resonate back to that comfortable structure, back to the happy, low energy bonding molecular orbital. And to be honest, once I started thinking of it this way.
That's when the topic finally clicked. But this is just one pi bond with two electrons. What about a more complex system with four, six or more electrons and lots of resonance involved? Remembering that not all of the molecular orbitals will be occupied brings us to the concept of highest occupied molecular orbital or HOMO.
and lowest unoccupied molecular orbitals or LUMO. And this is exactly what we'll discuss in the next video which you can find on my website by clicking the link below or going to leah4sci.com slash m-o theory. The link again, leah4sci.com slash m-o theory.