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.
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