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The self-interaction-corrected local-spin-density (SIC-LSD) approximation is used to describe the electronic structure of dioxides REO₂ and sesquioxides RE₂O₃ for the rare earths, RE=Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, and Ho. The valencies of the rare earth ions are determined from total energy minimization. We find Ce, Pr, Tb in their dioxides to have the tetravalent configuration, while for all the sesquioxides the trivalent ground-state configuration is found to be the most favorable. The calculated lattice constants for these valency configurations are in good agreement with experiment. Total energy considerations are exploited to show the link between oxidation and f-electron delocalization, and explain why, among the dioxides, only the CeO₂, PrO₂, and TbO₂ exist in nature. Tetravalent NdO₂ is predicted to exist as a metastable phase---unstable toward the formation of hexagonal Nd₂O₃.
Petit et al. (2005) studied this question.