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

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 correlation to predict both adiabatic and (approximate) diabatic hopping barriers. Overall, LDA+U = 6 eV provides the best description in comparison to the experiment, followed by GGA+U = 5 eV. The hybrids are worse, tending to overestimate the gap and significantly underestimate the polaron-hopping barriers