We present results of lattice dynamics calculations of the P − V equation of state and the pressure dependence of the Raman-active E2g lattice phonon for p−H2 and o−D2 in a wide pressure range up to ∼2 Mbar using our recently developed semi-empirical many-body potential, and densityfunctional 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.PACS numbers: 64.30. Jk, 78.30.Am An accurate determination of the equation of state (EOS) of solid hydrogens has been an important research objective for decades. Systematic high-pressure studies were started in the seventies of the last century 1-3 (see reviews 4-6 and references therein). At present these x-ray and neutron studies span the pressure range up to ∼2 Mbar 7-15 and temperature range up to 1000 K. The highest compression reached in the EOS experiments is 10.4 for solid H 2 15 (7.6 for solid D 2 14 ), essentially higher than that for solid helium (8. 4) 16 . The EOS data provide a fundamental basis for examining intermolecular interactions, and for testing ab initio theories. A number of model intermolecular potentials 17,18 have been proposed based on the experimental EOS data. Another experimental technique which complements x-ray and neutron diffraction by providing direct information on intermolecular interactions and vibrational dynamics is Raman scattering. The hcp structure has a Raman-active optical mode (E 2g symmetry) in the phonon spectrum which corresponds to the out-of-phase shear motions in the two orthogonal directions in the ab plane. The frequency range of this Raman mode is extremely large, from 36 cm −1 at zero pressure 19-27 to 1100 cm −1 at 250 GPa. The Raman spectrum of solid molecular deuterium has been measured up to ∼200 GPa [19][20][21][22][23]28,29 . These measurements show that hcp-based structures are stable in this pressure range. The calculations of the E 2g Raman frequency ν(P ) using various empirical potentials 5,22,23 show that the result is highly sensitive to details of the potential used. Therefore, comparing the calculated and experimental ν(P ) is a hard test for any empirical potential (or for any other theoretical method, e.g. ab initio calculations). It is essential that these properties are sensitive to different characteristics of the intermolecular potential: while EOS is sensitive to the potential well depth, the Raman scattering experiment probes the second derivative of the potential at the minimum. In our recent paper 30 we have proposed new semi-empirical isotropic potentials for H 2 and D 2 . Unlike the previous potentials 12,17,18,31 they include not only pair forces, but triple forces as well. The goal of the present paper is to perform detailed calculations of the EOS and pressure dependence of Raman frequencies for H 2 and D 2 using our new potentials and to compare the results to available experimental data and theoretical results for...