Systematic computation of crystal-field multiplets for x-ray core spectroscopies

We present an approach to computing multiplets for core spectroscopies, whereby the crystal field is constructed explicitly from the positions and charges of surrounding atoms. The simplicity of the input allows the consideration of crystal fields of any symmetry and in particular facilitates the study of spectroscopic effects arising from low-symmetry environments. The interplay between polarization directions and the crystal field can also be conveniently investigated. The determination of the multiplets proceeds from a Dirac density functional atomic calculation, followed by the exact diagonalization of the Coulomb, spin-orbit, and crystal-field interactions for the electrons in the open shells. The eigenstates are then used to simulate x-ray absorption spectroscopy and resonant inelastic x-ray scattering spectra. In examples ranging from high-symmetry down to low-symmetry environment, comparisons with experiments are done with unadjusted model parameters as well as with semiempirically optimized ones. Furthermore, predictions for the RIXS of low-temperature MnO and for Dy in a molecular complex are proposed.