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 electronic thermal excitation 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 for 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.
