Benchmarking Density Functional Theory Functionals for Polarons in Oxides: Properties of CeO2

Abstract

We examine methods for studying polarons in metal oxides with density functional theory (DFT), using the example of cerium dioxide and the functionals, local density approximation + U (LDA+U), generalized gradient approximation + U (GGA+U) in the Perdew–Burke–Ernzerhof parametrization (PBE+U), as well as the hybrid functionals B3LYP, Heyd−Scuseria−Ernzerhof (HSE)03, HSE06, and PBE0. We contrast the four polaron energies commonly reported in different parts of the literature: formation energy, localization/relaxation energy, density-of-states level, and polaron-hopping activation barrier. Qualitatively, all these functionals predict “small” (Holstein) polarons on the scale of a single lattice site, although LDA+U and GGA+U are more effective than the hybrids at localizing the Ce 4f electrons. The improvements over pure LDA/GGA appear because of changes in the filled Ce 4f states when using LDA/GGA+U but due to changes in the empty Ce 4f states when using the hybrids. DFT is shown to have sufficient correla...