Bethe-Salpeter Equation calculations of transition metal L$_{2,3}$ edge x-ray spectra including multiplet effects*

Calculations of x-ray spectra at transition metal L$_{2,3}$ edges often present theoretical difficulties due to strong core-hole multiplet effects. Here we discuss an {\it ab initio} method for treating these effects following the Bethe-Salpeter Equation (BSE) approach of Shirley.\footnote{E. L. Shirley, J. Electron Spectrosc. Relat. Phenom. {\bf 144}, 1187 (2005).} The method builds in spin-orbit interactions, intra-atomic Coulomb integrals, core-hole screening, and band-structure effects, and thus accounts for multiplet effects without the need for phenomenological ligand-field parameters. The method has been implemented in the core-level BSE code OCEAN,\footnote{J. Vinson, E. L. Shirley, J. J. Rehr, and J. J. Kas, arXiv:1010.0025} which uses as input wavefunctions from planewave, pseudopotential DFT calculations and PAW transition matrix elements. Examples are presented for several transition metal systems and compared with experiment.