  We perform first-principles calculations of the structural, electronic,
mechanical, and thermodynamic properties of thorium hydrides (ThH$_{2}$ and
Th$_{4}$H$_{15}$) based on the density functional theory with generalized
gradient approximation. The equilibrium geometries, the total and partial
densities of states, charge density, elastic constants, elastic moduli,
Poisson's ratio, and phonon dispersion curves for these materials are
systematically investigated and analyzed in comparison with experiments and
previous calculations. These results show that our calculated equilibrium
structural parameters are well consistent with experiments. The Th$-$H bonds in
all thorium hydrides exhibit weak covalent character, but the ionic properties
for ThH$_{2}$ and Th$_{4}$H$_{15}$ are different due to their different
hydrogen concentration. It is found that while in ThH$_{2}$ about 1.5 electrons
transfer from each Th atom to H, in Th$_{4}$H$_{15}$ the charge transfer from
each Th atom is around 2.1 electrons. Our calculated phonon spectrum for the
stable body-centered tetragonal phase of ThH$_{2}$ accords well with
experiments. In addition we show that ThH$_{2}$ in the fluorite phase is
mechanically and dynamically unstable.
