# Lecture 2: Jahn-Teller distortion

...explains the occurrence of the shoulder by introducing the concept of Jahn-Teller distortion. Energy level diagrams for tetragonal elongation and compression of an octahedron are derived. The size and type of distortion are discussed as a function of electronic configuration.

So what about question 2, the origin of that shoulder in the UV-visible spectrum of [Ti(OH2)6]3+?

Perhaps the easiest way to deal with this is to think about a different system for a while. Let's consider a d4 high spin complex (something like [Cr(OH2)6]2+ might be a good example). When we start filling up our crystal field splitting diagram, we can put one electron into each of the three t2g orbitals, and then the fourth one will be placed in one of the two eg orbitals. We have a choice whether to put it into the dz2 (shown on the left below) or into the dx2-y2, like on the right. The question is, does it matter?

At first sight the answer is no. Actually though the answer is, yes, it does matter. Suppose we put the electron into the dz2 orbital. This is the one that lies along the z axis. So the two ligands which also lie along the z axis are going to be repelled by that electron, and this is going to push them out a bit, whereas the ligands in the xy plane (those that have approached along the x and y axes) will not feel so much repulsion, so they will be able to move in a bit. This means we will end up with a slightly distorted octahedral structure with the bonds to two of the ligands longer than the bonds to the other four. This is what's called a tetragonal elongation.

It also has an effect on the orbital energies. Because the two z ligands have moved out a bit, this lowers the energy of the (occupied) dz2 orbital. And because the x and y ligands have come in a bit, this will raise the energy of the dx2-y2 orbital. (This is a bit like what happened when we made a square planar complex from an octahedral one by gradually pulling off the z ligands... go here if you need a reminder). So we get a extra small splitting of the eg level superimposed on our crystal field splitting diagram. This is beneficial because our occupied d-orbital, the dz2, is now at a lower energy level than it would have been in the undistorted octahedron.

In fact these geometric changes also have an effect on the t2g level: those orbitals which have a z component (the dxz and dyz) will move to slightly lower energy, and the one that lies in the xy plane (the dxy, believe it or not) will move to slightly higher energy. This won't make any difference to the overall energy though because they're all singly occupied anyway.

I've exaggerated the size of the additional small splittings, δ1 and δ2, on that diagram. They are nowhere near as big as the main Δo splitting, and they won't affect whether a complex is high spin or low spin.

Suppose instead we put our electron into the dx2-y2 orbital instead? Go to the next page.

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