Polarization corrections to core levels

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Abstract
Theoretical predictions for ionization energies of inner core electrons generally come out much more accurately by taking the difference between the total energies of two self-consistent Hartree-Fock calculations than by using Koopmans' theorem. For the outer core electrons, on the other hand, little or no improvement over Koopmans' theorem is obtained from a `ΔSCF method'. We show here that the difference between the results from the ΔSCF method and from Koopmans' theorem can be expressed in terms of a polarization potential. A simple physical argument can then be made as well as a comparison with second-order perturbation theory, which both show why the ΔSCF method should give good results for inner core levels but not necessarily for outer core levels. The formulation in terms of a polarization potential allows a systematic discussion and an easy calculation of chemical shifts in core levels. We find that the core electrons serve as probes on the charge density and the polarizability of the valence electron system. As numerical examples, results are given for ions, atoms and metals of sodium and potassium. The limitations and possible extensions of the theory are discussed.