Progress and challenges in the theory and interpretation of X-ray spectra.

There has been dramatic progress over the past decade both in theory and in ab initio calculations of X-ray absorption fine structure (XAFS). Rapid progress is now being made in understanding X-ray absorption near-edge structure (XANES). This presentation reviews the developments in this field by many groups leading up to the current state of the art. These developments have led to several ab initio codes, such as FEFF, which yield results comparable to experimental results for XAFS, and permit an interpretation of the spectra in terms of geometrical and electronic properties of a material. The review begins with a summary of the key theoretical developments that are essential for achieving a quantitative agreement with experiment for XAFS. The same high-order multiple-scattering (MS) theory of XAFS can also give an approximate treatment of XANES, but this approach can fail close to an edge, where full MS calculations are often necessary. However, a fully quantitative treatment of XANES remains challenging, largely as a result of a number of many-body effects, e.g. the approximate treatment of the core-hole, multiplet effects, the photoelectron self energy and inelastic losses. Finally, natural extensions of the theory to other spectroscopies, such as anomalous X-ray scattering, DAFS (diffraction anomalous fine structure) and XMCD (X-ray magnetic circular dichroism) are briefly discussed. These developments are illustrated with a number of applications.