[Ephraim]

Hey all! I had a quick question about inter electron repulsion and the energy of excited states. (For example, Tanabe Sugano diagrams).

I understand for a d2 metal that you can get three d-d transitions.

You get two from bumping one electron from the ground state (in a metal octahedral complex). Due to electron electron repulsion, you get two "sets" of equal energy states:

Set one being z^2: 1 e-, xz: 1e-  || z^2 1 e-, yz 1 e-  || and x^2-y^2  1 e- , xy  1 e-.   And set two being:  z^2 1e-,  x^2-y^2 1e-  ||  x^2-y^2 1e-, xz 1e-  ||  x^2-y^2 1e-, and yz 1e-.

I understand that set one is higher in energy than set two.

My problem comes with the d4 case low spin case. We have taken a very qualitative approach to this in which we look at the spatial relationship between the two orbitals and how close the electrons are. Looking at the Tanabe Sugano diagram, I can see clearly that there should be two transitions. One of these transitions should correspond to the state where two electrons are bumped up.  But only one should come from the case where one electron is bumped an energy level.

I've examined the orbitals in this case and I can see what I appear to be two states of different energy.

One of them has the t2g orbitals with one electron each and one electron being in the z^2 eg* orbital, while the other one has the t2g orbitals with one electron each and one electron being in the x^2-y^2 orbital.

As far as I can tell, the one with the lone electron in the z^2 orbital should be of higher energy, as it has two negative interactions. One with the electron in the xz and the other with the electron in the yz. This is obviously not the case--> according to the tanabe sugano diagram these two cases are generate.

My question is why are these degenerate? To me there should be two clearly different energy levels.

Thank you!