  We present the ab-initio thermoelastic properties of body-centered cubic
molybdenum under extreme conditions obtained within the quasi-harmonic
approximation including both the vibrational and the electronic thermal
excitations contributions to the free energy. The quasi-harmonic temperature
dependent elastic constants are calculated and compared with existing
experiments and with the quasi-static approximation. We find that the
quasi-harmonic approximation allows a much better interpretation of the
experimental data confirming the trend found previously in other metals. Using
the Voigt-Reuss-Hill average we predict the compressional and shear sound
velocities of polycrystalline molybdenum as a function of pressure for several
temperatures which might be accessible in experiments.
