Slater transition methods for core-level electron binding energies

Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a "full core hole" or "Delta-SCF" approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater's transition concept, in which the binding energy is estimated from the orbital energy level obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3-0.4 eV with respect to experiment for a data set of K-shell ionization energies, a level of accuracy that is competitive with much more expensive methods. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.3 eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn-Sham eigenvalues. It requires no more computational effort than Delta-SCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, and for which the Delta-SCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy