

Chemistry: Molecular Orbital Theory



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  • Type: Video Tutorial
  • Length: 12:41
  • Media: Video/mp4
  • Use: Watch Online & Download
  • Access Period: Unrestricted
  • Download: MP4 (iPod compatible)
  • Size: 136 MB
  • Posted: 07/14/2009

This lesson is part of the following series:

Chemistry: Full Course (303 lessons, $198.00)
Chemistry: Molecular Geometry and Bonding Theory (11 lessons, $18.81)
Chemistry: Valence Bond & Molecular Orbital Theory (7 lessons, $12.87)





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You know, we've been doing pretty well, just assuming that atoms come together and form bonds. The electrons stay in the atomic orbitals. Well you know what? We've been just lying to you. You might ask, "All right, if you're lying to us, what's going on?" Why would we lie to you? We've been lying to you because we've been using models. The models are not exactly correct. Why should we be talking to you about these models, then? Because they're good enough. What they do is they allow us to predict useful things by making approximations. That's what a model is good for. A model simplifies nature to the point that we can make useful predictions; that we can understand the observations that we make. It's okay that it's not the exact truth as long as we acknowledge that, as long as we know what the limitations of the model are.
What is the truth then? The truth is that electrons actually are in molecular orbitals, not in atomic orbitals. In other words, there in a completely new set of orbitals now that are unique to the molecule, not unique to the atom. Why don't we talk about molecular orbitals? Well, because they are so complicated that it just gets very difficult to discuss them. That's exactly what we're going to do right now--look at molecular orbitals.
Before you turn me off, bear with me. If I can get you to understand the notion of what a molecular orbital is and how it comes about, then we can go a long way with our earlier models, our Lewis electron dot structures and our VSEPR and our hybridization theory. In fact, we can do most things with those models as long as we keep in mind what we're assuming and what is not, in fact, quite true. Then we'll know when we need to go to the molecular orbital level and when we can get by explaining things just on an atomic orbital level.
What is this notion of a molecular orbital? Let's go to a simple picture here of what's happening in a chemical bond. In a chemical bond, we talk about 2 nuclei getting close enough together to share electrons. There's nothing wrong with that idea. That is, indeed, our understanding of what happens in a chemical bond. The fundamental principle here is that it's a better deal for electrons to be between two nuclei than for them each to have only one nucleus apart from themselves. Each get the benefit of experiencing two positive charges rather than just one. It seems like a good deal. What we need to understand is, mathematically, how does this come about?
What is the nature of the orbital? In other words, what is the state of these electrons? Where are we likely to find them? To understand that we need to start back with atomic orbitals. Remember, we actually talked about the probability density of a 1s orbital, a long time ago. What we saw was that it had its greatest probability near the nucleus. You may recall, just to clarify here, we did talk, when we were talking just about atoms, about a radial probability function. That was useful because we were talking just about an atom, which was a sphere.
Now we're going to be talking about a molecule, which won't be spherical. We won't be looking any more at radial probability distributions, but simply where are likely to find the electron along a particular axis. That axis is just going to be the axis that connects my two atoms together. My interpretation of this is that I have a large chance of finding the electron density in this atom here and in this atom here--simple enough. All I've done is bring two atoms closer together. Now, here's the trick. We're going to combine this atomic orbital mathematically, with this one. What it's going to do for us is, in the middle here, we're going to add those two wave functions together. When we add them together, we get a bigger value for the wave function and that means that when we square it, we get a higher probability of finding the electron in the middle. Let's actually do that and see what that looks like. Okay, what we're doing is, in green now, I'm just showing you the mathematical sum of this wave function and this wave function. The red ones, again, are atomic wave functions. I just add them together and I get this green one, which is just a sum of atomic wave functions. Then I square it and that answers the question, "What's my probability of finding the electron?" What I get as a result is an orbital that looks like this, with a large amount of probability right in the middle. This is a great deal for the electron. The electron then, or two electrons in this orbital, would get to spend time in between those two nuclei. We started at the beginning saying that that is exactly what they want to do. The important thing about making a bonding molecular orbital is that there is a lot of electron density in the middle, right in between those two atoms.
Now, there's no such thing as a free lunch. The other side of this is that we need to create another orbital in addition to this one in order to have the same number of spaces to put electrons. If you think about it, if I bring a 1s orbital and another 1s orbital, I've got enough room for 4 electrons, 2 electrons in each of those orbitals. This orbital will take two electrons, but I need to find another orbital where I can put two more electrons if I'm going to have the same amount of space. I mathematically could combine them this way by adding them. The other solution turns out, mathematically, to be subtracting them. If I do that, let's see what happens. Here's the 1s orbital again just like before. Now I'm showing in blue the negative of this atom's atomic orbital. This is a 1s orbital also, but I've just mathematically made the opposite. We say that we add these in the opposite phase. Again, think that if these have wave properties, we're adding the wave properties destructively. They destructively interfere in the middle. If I want to add this to this, you can see what is going to happen. Somewhere in the middle here they're going to cancel each other out.
Let's think about the significance of that. By them canceling each other out (in green I'm drawing just the sum of those two, but this time, we go through 0 right here. If I square that term, remember that I have to square that function in order to find out where the electrons are, what I find is something really important. I find that right in the middle of the molecule, right where the electrons want to be the most, there is a node. It is fundamentally forbidden for the electrons to be where they want to be in this orbital. They must spend most of their time on the outside looking into where they want to be. They are out here. Those are the two nuclei again. The electron density is over here someplace. If we compared the energy of electrons in this state and this orbital compared to the energy of the electrons in their atoms that they came from, being in the atoms is a better deal. This is higher energy than the electrons would have been if they were in their own atoms.
Let's review what just happened. We brought the two atoms together. We got two new solutions to the Schrödinger equation. We got that the electrons could be added to give a bonding orbital, meaning an orbital where the electron density was in between two nuclei. Then we got another solution, a solution which said that the electrons in this state have to be on the outsides of the two nuclei. Well, why would a molecule ever form if this is true? This is not a good deal. This, we refer to, by the way, is an anti bonding orbital, whereas the other orbital that we looked at was a bonding orbital. You can see why it is anti bonding because the electron density is on the outside and these two protons see each other. The nuclei see each other. The nuclei see each other, they repel each other because they are the same charge. The effect of having electrons in this is to push the nuclei away from each other, so it's anti bonding.
Let's answer the crucial question: "Why would this ever happen?" I'm going to now draw an energy diagram. We'll put "energy" on the side here. We'll draw - so we know where we are, that's the energy of an atomic 1s orbital. Over here is the energy of an atomic 1s orbital - the other guy that we are going to bring together. I'm now going to write down here the energy levels of the bonding orbital. We said it was bonding, so it's lower energy. It's a better deal. We call this a sigma orbital. Don't worry about the name, but this is the bonding orbital. Remember that we also created an anti bonding orbital. It's up there. That's referred to, actually, as a sigma star orbital usually. That again is anti bonding.
Now here is the punch line. When I make the make the molecule dihydrogen, and I'm just going to write the molecule by the side here just to remind us. When I make the molecule dihydrogen I have a total of two electrons. Well great, those two electrons can go in this bonding orbital. Fantastic. We predicted that we'd form a bond. The two electrons--we know where they are. We know everything about this molecule in fact--where the electrons are. They spend a lot of time in the middle between the two nuclei. We know that that is much more stable than having the two atoms themselves.
What about the molecule He[2], the dihelium atom? Well, how many valence electrons do we have now? Two from each helium atom. We now have to find homes for four different electrons. Two can go here, but where is the next available space? Up here. Now we have to put two electrons in this anti bonding orbital...Well, wait a minute. There's a 2s orbital, or a 2p orbital somewhere higher in energy. Those are even further in energy. Electrons are not going to want to go there. So we put them in the sigma star orbital, and that causes a repulsion, and it breaks the bond that we had just formed down here. So there's no net gain for nature to make a bond, in the case of helium, simply because there's not enough places down here to put electrons. Nature is forced to put electrons in an anti bonding orbital and that de-stabilizes the bond. What happens is that the two atoms just stay apart. They never form a bond, and again, we know that that is true in the case of helium.
That's a long way to go to say, "Hey, look. Hydrogen has got a bond. Helium has no bond." We told you that. Why go through all of this trouble? The reason is that there are some molecules that we are going to be able to predict properties for that we could never have hoped to be able to predict properties for with our valence bond model. For instance, the molecule dioxygen turns out to be a paramagnet. What's that? That allows us to actually set up an attraction between it and a magnet. We can use that to actually separate oxygen from other gasses. There's no way that we can understand how that could possibly happen with our model that we have up until now. So our next step is to look a little deeper--not too much deeper--into molecular orbital theory and understand just how significant it is and the important lessons that it can teach us.
Molecular Geometry and Bonding Theory
Valence Bond Theory and Molecular Orbital Theory
Molecular Orbital Theory Page [1 of 3]

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