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Equation of state and Raman-active $E_{2g}$ lattice phonon in phases I, II, and III of solid hydrogen and deuterium

We present results of lattice dynamics calculations of the $P-V$ equation of state and the pressure dependence of the Raman-active $E_{2g}$ lattice phonon for $p-$H$_2$ and $o-$D$_2$ in a wide pressure range up to $\sim$2 Mbar using our recently developed semi-empirical many-body potential, and density-functional theory. Comparison with existing body of experimental and theoretical results showed that the employed many-body potential is a reliable basis for high-precision calculations for phases I, II, and III of solid hydrogens.