Separating different contributions to the crystal-field parameters using Wannier functions

We discuss the calculation of crystal-field splittings using Wannier functions and show how contributions to the crystal-field splitting that are due to hybridization with different ligand states can be separated from the bare Coulomb contribution by constructing sets of Wannier functions incorporating different levels of hybridization. We demonstrate this method using SrVO3 as a generic example of a transition metal oxide. We then calculate trends in the crystal-field splitting for two series of hypothetical tetragonally distorted perovskite oxides and discuss the relation between the calculated 'electrostatic' contribution to the crystal field and the simple point charge model. Finally, we apply our method to the charge disproportionated 5d electron system CsAuCl3. The proposed procedure elucidates the way in which the negative charge transfer energy in this material leads to a reversal of the p-d ligand contribution to the crystal-field splitting such that the eg states of the nominally Au(3+) cation are energetically lower than the corresponding t2g states.