Fractional-Electron and Transition-Potential Methods for Core-Level Excitation Energies Using Density Functional Theory

Methods for computing x-ray absorption spectroscopy at the self-consistent field level are examined, based on a constrained core hole (possibly containing a fractional electron), and in some cases promoting an electron or a fraction of an electron into the virtual space. These methods are based on Slater's transition concept and its generalizations (including the transition-potential method), wherein core-to-valence excitation energies are determined using Kohn-Sham orbital energies. Variants of this idea are systematically tested, revealing a best-case accuracy of 0.3-0.4 eV with respect to experiment for K-edge excitation energies, although errors are much larger in many cases. For higher-lying near-edge transitions, even the best of these methods affords errors of ~2 eV. Absolute errors are reduced below 1 eV by introducing an empirical shift based on a charge-neutral transition-potential method, employing a single fitting parameter. Using conventional functionals such as SCAN, SCAN0, or B3LYP, this approach affords errors below 1 eV even for higher-lying transitions, via a procedure in which an entire excitation spectrum is obtained from a single fractional-electron calculation. Tedious state-by-state calculations are not required, and the cost is similar to a ground-state density functional theory. This approach may be especially useful for simulating transient spectroscopies or in complex systems where excited-state Kohn-Sham calculations are challenging.