Real-Space Multiple-Scattering X-ray Absorption Spectroscopy Calculations of $d$- and $f$-state Materials using a Hubbard Model

We present calculations of the electronic structure and x-ray spectra of materials with correlated $d$- and $f$-electron states treated with the Hubbard model in a real-space multiple scattering (RSMS) formalism, and using a rotationally invariant local density approximation (LDA+$U$). Values of the Hubbard parameter $U$ are calculated ab initio using the constrained random-phase approximation (cRPA). The real-space Green's function approach with Hubbard model corrections is an efficient way to describe localized electron states in strongly correlated systems, and their effect on core-level x-ray spectra. The method is shown to give the correct density of states and x-ray absorption spectra for Transition Metal- and Lanthanide-oxides such as Ce2O3 and NiO, where the traditional RSMS calculations fail.