Electronic, bonding, and optical properties of ${\mathrm{CeO}}_2$ and ${\mathrm{Ce}}_2{\mathrm{O}}_3$ from first principles

First-principles electronic structure calculations of cerium oxide in two forms, ${\mathrm{CeO}}_2$ and ${\mathrm{Ce}}_2{\mathrm{O}}_3,$ are presented. The $4f$ state of Ce is treated as a part of the inner core in ${\mathrm{Ce}}_2{\mathrm{O}}_3$ and as a valence-band-like state in ${\mathrm{CeO}}_2.$ The calculated ground-state and magnetic properties of the Ce (III) oxide are shown to be in agreement with available experimental data as well as the calculated ground-state and optical properties of Ce (IV) dioxide. The nature of the bonding in cerium oxide is discussed on the basis of an analysis of the charge-density and electron localization function distributions and described as a polarized ionic bond in both oxides.