Theory and calculations of X-ray spectra: XAS, XES, XRS, and NRIXS

There has been dramatic progress in recent years both in calculations and in the interpretation of various X-ray spectroscopies, ranging from X-ray absorption and emission to elastic and non-resonant inelastic X-ray scattering. Here we review a number of recent developments focusing primarily on the ab initio real-space Green's function (RSGF) approach, which is applicable to arbitrary aperiodic materials. The RSGF approach is essentially a quasi-particle approximation which takes into account final state effects including many-body, core-hole effects, lifetime, and Debye–Waller factors. While generally adequate for deep core spectra, corrections due to local screening fields can be important, even far above an absorption edge. Such corrections require a theory beyond the independent-electron approximation, and can be calculated using a combination of the time-dependent density functional theory (TDDFT) and the Bethe–Salpeter equation. The combined approach makes possible efficient calculations of optical constants from the UV to X-ray energies.