  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.
