  The in-depth understanding of hydrogen permeation through plutonium-oxide
overlayers is the prerequisite to evaluate the complex hydriding induction
period of Pu. In this work, the incorporation, diffusion and dissolution of
hydrogen in $\alpha$-Pu$_{2}$O$_{3}$ are investigated by the first-principles
calculations and $\textit{ab initio}$ thermodynamic method based on DFT+U and
DFT-D3 schemes. Our study reveals that the hydrogen incorporation is
endothermic and the separated H atoms prefer to recombine as H$_{2}$ molecules
rather than reacting with $\alpha$-Pu$_{2}$O$_{3}$. The H and H$_{2}$ diffusion
are both feasible, generally, H will recombine first as H$_{2}$ and then
migrate. Both pressure P$_{H2}$ and temperature can promote the hydrogen
dissolution in $\alpha$-Pu$_{2}$O$_{3}$. The single H$_{2}$ molecule
incorporation and (H+H$_{2}$) mixed dissolution will successively appear when
increasing P$_{H2}$. Compared to PuO$_{2}$, this work indicates that Pu
sesquioxide is hardly reduced by hydrogen, but the porous
$\alpha$-Pu$_{2}$O$_{3}$ facilitates hydrogen transport in Pu oxide layers. We
presents the microscopic picture of hydrogen behaviors in the defect-free
$\alpha$-Pu$_{2}$O$_{3}$, which could shed some light on the study of the
hydriding induction period of Pu.
