Ab initio based ligand field approach to determine electronic multiplet properties

A method is developed to calculate the ligand field (LF) parameters and the multiplet spectra of local magnetic centers with open $d$ and $f$ shells in solids in a parameter-free way. This method proceeds from density functional theory and employs Wannier projections of nonmagnetic band structures onto local $d$ or $f$ orbitals. Energies of multiplets and optical, as well as x-ray spectra are determined by exact numerical diagonalization of a local Hamiltonian describing Coulomb, LF, and spin-orbit interactions. The method is tested for several $3d$ and $5f$ compounds for which the LF parameters and multiplet spectra are experimentally well known. In this way, we obtain good agreement with the experiments for ${\mathrm{La}}_{2}{\mathrm{NiO}}_{4}, {\mathrm{CaCuO}}_{2}, {\mathrm{Li}}_{2}{\mathrm{CuO}}_{2}$, ZnO:Co, and ${\mathrm{UO}}_{2}$.