Ab initio Bethe-Salpeter calculations of the x-ray absorption spectra of transition metals at the L-shell edges

We present ab initio Bethe-Salpeter equation (BSE) calculations of the L-2,L-3 edges of several insulating and metallic compounds containing Ca, V, Fe, Co, Ni, and Cu, spanning a range of 3d-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.