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