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

Methods for computing X-ray absorption spectra basedon a constrainedcore hole (possibly containing a fractional electron) are examined.These methods are based on Slater's transition concept andits generalizations, wherein core-to-valence excitation energies aredetermined using Kohn-Sham orbital energies. Methods examinedhere avoid promoting electrons beyond the lowest unoccupied molecularorbital, facilitating robust convergence. Variants of these ideasare systematically tested, revealing a best-case accuracy of 0.3-0.4eV (with respect to experiment) for K-edge transition energies. Absoluteerrors are much larger for higher-lying near-edge transitions butcan be reduced below 1 eV by introducing an empirical shift basedon a charge-neutral transition-potential method, in conjunction withfunctionals such as SCAN, SCAN0, or B3LYP. This procedure affordsan entire excitation spectrum from a single fractional-electron calculation,at the cost of ground-state density functional theory and withoutthe need for state-by-state calculations. This shifted transition-potentialapproach may be especially useful for simulating transient spectroscopiesor in complex systems where excited-state Kohn-Sham calculationsare challenging.