  The electronic structure and thermodynamical properties of uranium
trihydrides ($\alpha$-UH$_{3}$ and $\beta$-UH$_{3}$) have been studied using
first-principles density functional theory. We find that inclusion of strong
electronic correlation is crucial in successfully depicting the electronic
structure and thermodynamic phase stability of uranium hydrides. After turning
on the Hubbard parameter, the uranium 5f states are divided into well-resolved
multiplets and their metallicity is weakened by downward shift in energy, which
prominently changes the hydrogen bond and its vibration frequencies in the
system. Without Coulomb repulsion, the experimentally observed
$\alpha\mathtt{\rightarrow}\beta$ phase transition cannot be reproduced,
whereas, by inclusion of the on-site correlation, we successfully predict a
transition temperature value of about 332 K, which is close to the experimental
result.
