  A recent inelastic x-ray scattering study [Manley et al., Phys. Rev. B 85,
132301 (2012)] reveals that the phonon dispersion curves of PuO2 is
considerably consistent with our previous density functional +$U$ results
[Zhang et al., Phys. Rev. B 82, 144110 (2010)]. Here in the present work, using
the same computational methods, we further obtain the phonon dispersion curves
for \alpha-Pu2O3. We find that the Pu-O bonding is weaker in \alpha-Pu2O3 than
in fluorite PuO2, and subsequently a frequency gap appears between the
vibrations of oxygen and plutonium atoms. Based on the phonon dispersion curves
and Helmholtz free energies of PuO2 and \alpha-Pu2O3, we systematically
calculate the reaction energies for the transformations between Pu, PuO2, and
\alpha-Pu2O3. It is revealed that the thermodynamic equilibrium of the system
is dependent on temperature as well as on the chemical environment. High
temperature and insufficient oxygen environment are in favor of the formation
of \alpha-Pu2O3.
