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, and may be useful for complex systems where alternative approaches are either inconvenient or too expensive.