Our dataset provide thermodynamic and elastic properties of phase H at various temperatures and pressures, including equation of states (Fig2_EOS.xlsx), thermodynamic properties (Fig3_Thermodynamics.xlsx), elastic properties(Fig45_Elasticity_orth/mon.xlsx), anisotropies (Fig69_Anisotropy_mon/orth.xlsx), and wave velocities along cold geotherm (Fig78_geoV.xlsx).