<i>Ab initio</i>curved-wave x-ray-absorption fine structure

Abstract

The most important elements of ab initio calculations of x-ray-absorption fine structure (XAFS) are studied. To obtain accurate results without ad hoc adjustable parameters, we find it essential to include (i) curved-wave effects, (ii) a complex, energy-dependent self-energy, (iii) an approximate molecular potential, and (iv) a fixed energy reference for the photoelectron wave number. Based on these findings, an automated code has been developed for ab initio calculations of single-scattering XAFS, in which curved-wave effects are treated exactly in terms of effective backscattering amplitudes, inelastic losses and self-energy shifts are incorporated with use of a Hedin-Lundqvist self-energy, an automated relativistic overlapping-atom muffin-tin potential is used, and the energy threshold is estimated from electron-gas theory. The efficiency of the code is made possible by analytic expressions for the Hedin-Lundqvist self-energy. This code replaces existing tables of XAFS phases and scattering amplitudes and yields reliable theoretical XAFS standards for arbitrary pairs of atoms throughout the Periodic Table (Z\ensuremath{\le}94). These results are comparable to those from self-consistent calculations and are valid to within about 20 eV of the absorption edge. Comparisons with experiment are presented for Cu, Ge, Pt, ${\mathrm{Br}}_{2}$, and ${\mathrm{GeCl}}_{4}$. The calculated XAFS amplitudes are found to be accurate to within 15%; XAFS phases are accurate to within 0.2 rad; and nearest-neighbor distances are typically accurate to within 0.02 \AA{}.