  We report a comprehensive density functional theory (DFT) + $U$ study of the
energetics of charged and neutral oxygen defects in both PuO$_{2}$ and
$\alpha$-Pu$_{2}$O$_{3}$, and present a quantitative determination of the
equilibrium compositions of reduced PuO$_{2}$ (PuO$_{2-x}$) as functions of
environmental temperature and partial pressure of oxygen, which shows fairly
agreement with corresponding high-temperature experiments. Under ambient
conditions, the endothermic reduction of PuO$_{2}$ to $\alpha$-Pu$_{2}$O$_{3} $
is found to be facilitated by accompanying volume expansion of PuO$_{2-x}$ and
the possible migration of O-vacancy, whereas further reduction of $\alpha
$-Pu$_{2}$O$_{3}$ is predicted to be much more difficult. In contrast to the
endothermic oxidation of PuO$_{2}$,\ the oxidation of $\alpha$-Pu$_{2} $O$_{3}$
is a stable exothermic process.

Materials Science