When are Multiplets important?

Applying one-electron codes** to transition metal oxides one finds excellent agreement for the metal and oxygen K edges, whereas the other edges, in particular the metal L_2,3 edges, are very poorly described. 

The reason for this discrepancy is not that the density-of-states is calculated wrongly, but that one does not observe the density of states in such x-ray absorption processes. 

This is caused by the strong overlap of the core wave function with the valence wave functions. 

In the final state of an x-ray absorption process one finds a partly filled core state, for example a 2p⁵ configuration. In case one studies a system with a partly filled 3d-band, for example NiO, the final state will have an incompletely filled 3d-band. For NiO this can be approximated as a 3d⁹ configuration. 

The 2p-hole and the 3d-hole have radial wave functions that overlap significantly. This wave function overlap is an atomic effect that can be very large. It creates final states that are found after the vector coupling of the 2p and 3d wave functions. 

This effect is well known in atomic physics and actually plays a crucial role in the calculation of atomic spectra. 

Experimentally it has been shown that while the direct core hole potential is largely screened, these so-called multiplet effects are hardly screened in the solid state. This implies that the atomic multiplet effects are of the same order of magnitude in atoms and in solids.

(** 'one-electron' applies to a one-electron core excitation, not to the treatment of the valence electrons)

If have a question concerning the programs and/or you would like a spectrum to be calculated please contact me by email at f.m.f.degroot@chem.uu.nl.