  The self-interaction-corrected local-spin-density approximation is used to
describe the electronic structure of dioxides, REO$_2$, and sesquioxides,
RE$_2$O$_3$, 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 groundstate
configuration is found to be the most favourable. 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 CeO$_2$, PrO$_2$, and TbO$_2$ exist in nature. Tetravalent NdO$_2$ is
predicted to exist as a metastable phase - unstable towards the formation of
hexagonal Nd$_2$O$_3$.

Strongly Correlated Electrons