Ab initioBethe-Salpeter calculations of the x-ray absorption spectra of transition metals at theL-shell edges

Abstract

We present ab initio Bethe-Salpeter equation (BSE) calculations of the ${L}_{2,3}$ edges of several insulating and metallic compounds containing Ca, V, Fe, Co, Ni, and Cu, spanning a range of 3$d$-electron occupations. Our approach includes the key ingredients of a unified treatment of both extended states and atomic multiplet effects, i.e., Bloch states, self-consistent crystal potentials, ground-state magnetism, $GW$ self-energy corrections, spin-orbit terms, and Coulomb interactions between the ${L}_{2}$ and ${L}_{3}$ levels. The method is implemented in the ocean package, which uses plane-wave pseudopotential wave functions as a basis, a projector-augmented-wave construction for the transition matrix elements, and a resolvent formalism for the BSE calculation. The results are in near quantitative agreement with experiment, including both fine structure at the edges and the nonstatistical ${L}_{3}$/${L}_{2}$ ratios observed for these systems. Approximations such as time-dependent density-functional theory are shown to be less accurate.