Crystal field splitting in correlated systems with the negative charge-transfer gap

Special features of the crystal field splitting of $d-$levels in the transition metal compounds with the small or negative charge-transfer gap ${\mathrm{\Delta }}_{CT}$ are considered. We show that in this case the Coulomb term and the covalent contribution to the $t_{2g}-e_g$ splitting have different signs. In order to check the theoretical predictions we carried out the ab-initio band structure calculations for Cs${}_2$Au${}_2$Cl${}_6$, in which the charge-transfer gap is negative, so that the $d-$electrons predominantly occupy low-lying bonding states. For these states the $e_g$-levels lie below $t_{2g}$ ones, which demonstrates that at least in this case the influence of the $p-d$ covalency on the total value of the crystal field splitting is stronger than the Coulomb interaction (which would lead to the opposite level order). We also show that the states in conduction band are made predominantly of $p-$states of ligands (Cl), with small admixture of $d-$states of Au.