On the calculation of crystal field parameters using Wannier functions

TL;DR

This paper presents a method to calculate crystal field parameters using Wannier functions, separating ligand and Coulomb contributions, and applies it to various transition metal oxides to analyze their electronic structure.

Contribution

The paper introduces a novel Wannier function-based approach to distinguish ligand field effects from Coulomb contributions in crystal field calculations.

Findings

Ligand field contributions can be separated from Coulomb effects using Wannier functions.

The method reveals trends in crystal field splitting in distorted perovskites.

Application to CsAuCl3 shows ligand contributions can reverse expected energy levels.

Abstract

We discuss the calculation of crystal field splittings using Wannier functions and show how the ligand field contributions can be separated from the bare Coulomb contribution to the crystal field by constructing sets of Wannier functions incorporating different levels of hybridization. We demonstrate this method using SrVO$_3$ 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 "electro-static" contribution to the crystal field and the simple point charge model. Finally, we apply our method to the charge disproportionated 5$d$ electron system CsAuCl$_3$. We show that 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 $e_g$ states of the nominally Au$^{3+}$ cation are energetically lower than the corresponding $t_{2g}$ states.