The electronic structure and properties of PuO$_{2}$ and Pu$_{2}$O$_{3}$ have been studied from first principles by the all-electron projector-augmented-wave (PAW) method. The local density approximation (LDA)+$U$ and the generalized gradient approximation (GGA)+$U$ formalism have been used to account for the strong on-site Coulomb repulsion among the localized Pu $5f$ electrons. We discuss how the properties of PuO$_{2}$ and Pu$_{2}$O$_{3}$ are affected by the choice of $U$ as well as the choice of exchange-correlation potential. Also, oxidation reaction of Pu$_{2}$O$_{3}$, leading to formation of PuO$_{2}$, and its dependence on $U$ and exchange-correlation potential have been studied. Our results show that by choosing an appropriate $U$ it is promising to correctly and consistently describe structural, electronic, and thermodynamic properties of PuO$_{2}$ and Pu$_{2}$O$_{3}$, which enables it possible the modeling of redox process involving Pu-based materials.
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