Chemistry: Ligand Field Theory

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We've been exploring the origin of color in transition metal complexes. We started our discussion by considering two solutions of cobalt three. One is a hexafluora cobalt solution, and the other is a hexamino cobalt solution. They have very different colors even though the metals are the same and the oxidation states are the same.
We said that the difference could be explained by differing frequencies of photons that are absorbed. And that the reason the frequencies of the photons were different was because the spacing between the d orbitals was different for these guys. In other words, what we said was, in this case, the hexafluora cobalt solution appeared green to us because a red photon was absorbed. And that red photon was absorbed due to an electron being kicked up from a lower energy d orbital to a higher energy d orbital. And if you compare that frequency to the frequency of the photon needed to cause the same transition in the cobalt hexamine solution, that a higher photon energy was needed. So when a blue photon is absorbed, which is the case here, the complimentary color appears to us. So again the orange color indicates a higher energy photon absorbed.
We further went on to say that the difference in energy, the amount of splitting of those d orbitals, had its origin in the ligands of these complexes interacting to differing degrees with the d orbitals themselves. We said that some d orbitals point directly at the ligands, and others don't. And particularly, the x^2-y^2 and the z^2 orbitals point right at the ligand axes. And due to a repulsion of electrons in the d orbitals and the ligands, we got this split.
But now all ligands cause an equal amount of splitting. There is clearly a big difference between ammonia and fluoride. And we look then at something called the spectrochemical series, an ordering of different potential ligands for metals ranging from what are referred to as weak field ligands, ligands that caused a very small split in a relative sense in the d orbitals. And strong field ligands, ligands which caused a very strong split, a very large split in the d orbital energies of the metal, and then those things in the middle, the kind of intermediate field, if you will, ligands. And we attributed this general trend to differences in electronegativity. We said that over here you find things that are relatively electron deficient, electronegative in other words. And they would hold their electrons in tighter causing less repulsion than of those electrons with the electrons in the d orbitals. On the other hand over here, these are atoms that are comparatively less electronegative, and so they don't hold their electrons as tightly. And those electrons are more free if you will to repel with the d orbital electrons causing a greater split in the d orbital energies then. And again these guys are somewhere in between.
Well being a very smart, inquisitive chemistry student, I know that this explanation just didn't satisfy you, that ultimately you said, "Now wait a minute." I've got hydroxide, and I know hydroxide is a pretty strong base. It's not holding its electrons in as tightly due to that negative charge here, as water would be for instance. And also look over here. CO is not basic at all. Its electrons are held in pretty tight to the carbon. What the heck is it doing way out here as a very strong ligand. There are clearly some things about this series that just don't make sense if all we consider is electronegativity or charge of the ligand, and nothing else. What could be possibly going on?
Well okay, you asked for it. You're going to get the explanation. The explanation lies in looking at a molecular orbital treatment of the coordination complex. Now this is often referred to as ligand field theory. And we're just going to touch on the surface of it. My goal here is to just give you a little bit of a flavor for what it is and why the spectrochemical series is more complex than just simply an ordering of electronegativity differences.
Let's start out by reminding ourselves a little bit about molecular orbital theory. Remember that in the molecule HF, for instance, we talk about--and by the way, if this is not familiar to you, you'll probably want to go back and review our tutorials on molecular orbital theory. But when we looked at the molecule hydrofluoric acid, the 1s orbital from hydrogen interacted with the 2p orbital fluoride. And they made a pair of molecular orbitals, a bonding orbital and an antibonding orbital. The bonding orbital was a little lower in energy than the 2p orbital of the fluorine. And the antibonding orbital was a little higher in energy than the 1s orbital of the hydrogen. Now we said that the greater the difference in energy between these orbitals, the less they'll interact with each other. The closer they are together in energy, the greater the interaction will be. Remember that. It's going to be important. In the same way, and this we could almost think about it as an acid-base interaction. You could almost think about that as a fluoride donating its electrons to an H^+. And we could draw a molecular orbital for that.
And we can do the exact same thing with transition metals and ligands. In the same sense of fluoride interacting with hydrogen, we could imagine a fluoride or a lone pair from ammonia interacting with one of the d orbitals of the transition metal, forming, again, a bonding orbital and an antibonding orbital. So we have, again, this relationship that the closer in energy that these are, the greater that interaction is going to be. If these guys get sufficiently far away in energy, there's going to be no significant interaction. But again, notice what happens. The ligand orbital gets lowered in energy, stabilizing it. And this metal orbital gets pushed up in energy. Well that is the origin of what we have just been talking about, the type of interaction of ligands and metals causing the split in d orbitals.
Now brace yourself. This is what the molecular orbital diagram looks like. And before you turn off your computer, just bear with me a moment. I'm going to show you the important piece of this molecular orbital diagram. I've got my ligand orbitals. I've got my metal orbitals. I get a whole bunch of new molecular orbitals, most of which we're not going to care about. These correspond essentially to the ligands all being brought to lower energy. Fine, okay. Ligands are stabilized by an acid-base interaction with a metal, end of story. This is what I'm interested in. My metal orbitals have been split now, because two of them interacted with the ligands to make a bonding and an antibonding combination. And it's these two orbitals here that are now slightly antibonding. Now they used to be d orbitals. So notice the effect is they push up the energy of two of those d orbitals in an octahedral framework. The other three are not affected by these ligands. They're nonbonding orbitals. They don't interact because they don't point in the right direction. We say that they don't have the right symmetry to interact with the ligand orbitals. So this is where we get the splitting of the d orbitals from. Remember this is just a different model to explain, so far, what is the exact same thing that we've talked about before. The d orbitals split not because of these ligands just kind of hanging out near the metal causing repulsion, but because they're making bonds with some of the d orbitals, but not the others. So we get a split between the d orbitals that don't bond, and the d orbitals that do bond.
So that difference in energy is what we've been calling delta, the same delta that we called when we talked about crystal field theory. Now that tells us an equally good explanation for the spectrochemical series as crystal field theory. Now let's just quickly go back to our series. I want to remind you that the closer these are in energy, the greater they'll interact, in other words, the bigger the split is going to be. Remember that. So if I have a ligand that's really electronegative, it's lower in energy, it won't interact with the d orbitals as much, and we expect the splitting to be smaller. The exact same consequence we had with crystal field theory. But that doesn't explain the exceptions that we saw with crystal field theory.
To understand that we have to then take this to one higher level, and that is to introduce pi interactions. Now by the same token that an orbital can interact with another orbital by pointing at it, remember that when we have two p orbitals, they can interact in a parallel sense. They can come together parallel like that and form a pi bond. Well in that same way, a metal orbital, a d orbital, can come together with a p orbital to make a pi bond, not only a pi bond, but also as we know a pi antibond. Remember you always get the bonding and the antibonding combination. So we've got two orbitals that were created from these two atomic orbitals. And that's happening in addition to the type of bonding we've been talking about, the sigma bonds.
So altogether then, we have the sigma interaction, meaning a ligand simply donates electrons from one of its orbitals into one of the metal orbitals. And that makes a bonding orbital, and then the antibonding orbital. Okay, that's the major interaction in those coordination complexes right there. Everything we've been talking about before, this is it. This is an acid-base interaction. Here's the base. Here's the acid, Lewis acid-base interaction, nothing new here.
But then there's also a pi interaction possible. The ligand could have a pair of electrons in a p orbital. This usually is going to show up as a second lone pair in addition to the one that's donating like this. So chloride, fluoride can do this. Hydroxide can do this, where that orbital interacts with the pi orbital and donates additional electron density into the metal.
But then you can even have a third kind of interaction with the pi orbitals where a metal, that has a lot of electrons in it, an electron rich metal, with a filled d orbital. That can put electron density into an empty orbital that's on the ligand. Usually this is an antibonding orbital that's not filled on the ligand, a pi star orbital typically, like is in carbon monoxide. So if you're forgetting where that comes from, you might again want to review that. Carbon monoxide or dinitrogen have a pi star orbital that's empty. And the metal can put its electron density back into that orbital.
So this is all getting very complicated, I know. So I want to now step back and say the consequence of this. When we have donation... Now we're going to go again, get ready because here is the final--I promise I won't give you anything uglier than this. And actually this simplifies a lot. This is what we've seen before. That's the splitting in the d orbitals due to just sigma bonds, just a simple Lewis acid-base interaction of ligand and metal. But if we have pi donation, like is found in hydroxide, the pi orbital that does that, whether it's a p orbital or a pi orbital, interacts with these d orbitals, the one's that weren't interacting at all with anything, just these atomic orbitals. And that pushes the energies of these orbitals up. And that makes that spacing smaller. So when you have a pi-donor ligand, it reduces the spacing between the metals. That's why hydroxide is such a low field ligand. It's not because it's a weak sigma donor, but it's because it's a good pi donor also. So it pushes these orbitals up, making that separation smaller.
Now the reverse of that is something like carbon monoxide, which is a pi acceptor. It's like an acid, except that it uses a pi star orbital to accept electron density, rather than an empty sigma orbital. So it takes electron density, but that means it interacts with these guys, which are the pi symmetry orbitals. But because it's higher in energy than them, it pushes them down. And that means that it makes this separation larger. So pi-acceptor ligands make the splitting between the d orbitals, in other words what we call delta, larger. Pi-donor ligands make it smaller.
And then finally if we go back to our spectrochemical series, all of the pieces start to fall together. Everything we said before is basically true about electronegativity, but notice the exceptions are now explained. Over here at the very far end, strong field ligands like carbon monoxide, that's because they're pi acceptors. They're interacting with the d orbitals causing a bigger split in the d orbitals. On this side again, hydroxide is a weak field ligand, because it's acting as a pi donor. It's donating electron density to the metal. So that's why it's not showing up over here some place.
So we can make sense out of the entire spectrochemical series, for the most part, with crystal field theory. Again, crystal field theory does a nice job of pretty much explaining what's going on. It's a very crude model though, and it has its limitations because it's such a crude model. But what's appealing about it is that it is simple, and so we can explain a lot with it. But then when we take that to the next level, and we look at ligand field theory, we can explain the few exceptions that showed up with just using crystal field theory. Again, it's simply acknowledging that bonds are being formed between the ligand and the metal. And that there is more interaction at play than just the sigma donation, just the orbitals pointing at each other. That there's this pi interaction also at work in orbitals, just like the pi interaction that we saw earlier with a molecule like dinitrogen, for instance.
Transition Elements
Bonding in Coordination Compounds
Ligand Field Theory Page [2 of 3]