Taming multiple valency with density functionals: A case study of defective ceria

Modeling multiple-valence compounds using density-functional theory has long been considered a formidable task due to the role that strong electronic correlations play in these systems. We show that, in the case of defective ceria, the main effect of these correlations is to produce a multitude of metastable low-energy states among which the one displaying the correct valence of cerium is the most stable. This ground state may be difficult to access in practice and it has in fact so far escaped a proper identification. The introduction of a Hubbard-$U$ term in the energy functional stabilizes the physical ground state and makes it easily accessible to routine calculations. When this contribution is defined in terms of maximally localized Wannier functions, the calculated energies and structural properties are independent of the value of the parameter $U$.