Used in the following papers: First-Principles Determination of Elastic Anisotropy and Wave Velocities of MgO at Lower Mantle Conditions, B.B. Karki, R.M. Wentzcovitch, S. de Gironcoli, and S. Baroni, Science 286, 1705 (1999). High pressure lattice dynamics and thermoelasticity of MgO, B.B. Karki, R.M. Wentzcovitch, S. de Gironcoli, and S. Baroni, Phys. Rev. B 61, 8793 (2000). Ab initio lattice dynamics of MgSiO_3 perovskite at high pressure, B.B. Karki, R.M. Wentzcovitch, S. de Gironcoli, and S. Baroni, Phys. Rev. B 62, 14750 (2000). First principles thermoelasticity of MgSiO$_3$-perovskite: consequences for the inferred properties of the lower mantle, B.B. Karki, R.M. Wentzcovitch, S. de Gironcoli, and S. Baroni, Geophys. Res. Lett. 28, 2699 (2001).