  The mechanical properties, electronic structure and phonon dispersion of
ground state ThO$_{2}$ as well as the structure behavior up to 240 GPa are
studied by using first-principles density-functional theory. Our calculated
elastic constants indicate that both the ground state fluorite structure and
high pressure cotunnite structure of ThO$_{2}$ are mechanically stable. The
bulk modulus, shear modulus, and Young's modulus of cotunnite ThO$_{2}$ are all
smaller by approximately 25% compared with those of fluorite ThO$_{2}$. The
Poisson's ratios of both structures are approximately equal to 0.3 and the
hardness of fluorite ThO$_{2}$ is 27.33 GPa. The electronic structure and
bonding nature of fluorite ThO$_{2}$ are fully analyzed, which show that the
Th-O bond displays a mixed ionic/covalent character. The valence of Th and O
ions in fluorite ThO$_{2}$ can be represented as Th$^{3.834+}$ and
O$^{0.452-}$. The phase transition from the fluorite to cotunnite structure is
calculated to be at the pressure of 26.5 GPa, consistent with recent
experimental measurement by Idiri \emph{et al}. \cite{Idiri}. For the cotunnite
phase it is further predicted that an isostructural transition takes place in
the pressure region of 80 to 130 GPa.
