  We present a study of the structural phase transition, mechanical and
thermodynamic properties of UO$_{2}$ by means of the local density
approximation (LDA)$+U$ approach. A phase transition pressure of 40 GPa, which
agrees well with the experimental value of 42 GPa, is obtained from theory at 0
K. Pressure-induced enhancements of elastic constants, elastic moduli, elastic
wave velosities, and Debye temperature of the fluorite phase are observed.
Phonon spectrums of both the ground state fluorite structure and high pressure
cotunnite structure calculated by the supercell approach show that the
cotunnite structure is dynamically unstable under ambient pressure. Based on
the imaginary mode along the $\Gamma$$-$$X$ direction and soft phonon mode
along the $\Gamma$$-$$Z$ direction, a transition path from cotunnite to
fluorite has been identified. We calculate the lattice vibrational energy in
the quasiharmonic approximation using both first-principles phonon density of
state and the Debye model. Calculated temperature dependence of lattice
parameter, entropy, and specific heat agree well with experimental observations
in the low temperature domain. The difference of Gibbs free energy between the
two phases of UO$_{2}$ has predicted a boundary in the pressure-temperature
phase diagram. The solid-liquid boundary is approximated by an empirical
equation using our calculated elastic constants.
