{\em Ab Initio} Modeling of Transition-Metal Impurities in MgO

Fe- and Ni-doped MgO are promising materials for the catalytic conversion of methane and CO$_2$. However, theoretical studies of these materials are scarce. The self-interaction error (SIE) in approximate DFT leads to an incorrect description of the electron localization and hybridization between $d$ states of Ni or Fe and the oxide electronic bands. Replacing a fraction $\alpha$ of the (semi-)local exchange by the exact exchange reduces the SIE, but $\alpha$ remains a parameter depending on the target property. We explore the dependence of the formation energies of Ni$_{\rm Mg}$ and Fe$_{\rm Mg}$ substitutional defects in MgO on $\alpha$ in the Heyd-Scuseria-Ernzerhof hybrid functional (HSE), and compare the results to CCSD(T) embedded-cluster calculations. For Ni$_{\rm Mg}$ defects HSE($\alpha$ = 0.3) reproduces CCSD(T) formation energies and CO adsorption energies on Ni$_{\rm Mg}$. However, $\alpha $ = 0.48 is needed in the case of Fe$_{\rm Mg}$. For both Ni$_{\rm Mg}$ and Fe$_{\rm Mg}$, $\alpha$ = 0.44-0.50 satisifies best the exact DFT condition that the HOMO does not depend on occupation. Contrary to PBE and HSE06, HSE($\alpha $ $\approx$ 0.5) reproduces the experimentally observed $O_{h} \rightarrow D_{4h}$ (oblate) Jahn-Teller distortion for Fe$_{\rm Mg}$.