Configuration energies in ligand field calculations

Dear Hélène,

two important questions indeed.

1) We follow the configuration energy definitions as for example used in the Zaanen Sawatzky Allen paper on band-gaps (fig 1.). If we define the onsite energy of the d-orbitals as ed and the onsite energy of the ligand orbitals as eL and add a Coulomb interaction $U$ to the electrons of the d-shell we have the configuration dependent energies:

$d^n L^{10} \to n \, ed + 10\, eL + \frac{( n)(n-1)}{2}\, U$

$d^{n+1} L^9 \to (n+1)\, ed + 9\, eL + \frac{(n+1)(n )}{2}\, U$

$d^{n+2} L^8 \to (n+2)\, ed + 8\, eL + \frac{(n+2)(n+1)}{2}\, U$

If you work this out and set the energy difference between the $d^n L^{10}$ and $d^{n+1} L^9$ configuration to be $\Delta$ you will find that the energy difference between the $d^{n+2} L^8$ and $d^{n+1} L^9$ configuration is $\Delta + U$

2) We normally do not calculate the absolute energy of a core level excitation. It is very hard to get this to be better than 1% accurate. This might sound good, but for a core level at 1 keV this is still of by 10 eV. That means we can choose a zero of energy. Any value you pick is possible and equally good. I standardly pick the $p^5 d^n$ configuration to be at zero. Nothing special other than convention and could have / can be done differently.