Equation of state and Raman-activeE2glattice phonon in phases I, II, and III of solid hydrogen and deuterium

Abstract

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...

Sound velocities in solid hydrogen under pressure

“…While effective pair potentials work reasonably well for EOS up to 40 GPa, they fail for the dynamical properties like Raman spectrum. Similarly to that we had for the EOS, at pressures lower than ~ 150 GPa the SE curves calculated for the many-body potential [25] agree with experiment better than DFT-LDA (local-density approximation) calculations [25] but at higher pressures the situation is reversed. The limiting pressures at which the SE approach still works are ~ 175 GPa while the DFT-LDA has a fine agreement with the experiment for H 2 from 150 GPa up to the highest considered pressures ~ 230 GPa [25].…”

“…25 in comparison with density-functional theory (DFT)-generalized gradient approximation (GGA) calculations [26] and the main experimental results from [3,5,[7][8][9][10]12,13,16]. It was shown that the semi-empirical (SE) calculations with the proposed many-body potential are in an excellent agreement with experiment in the pres-sure range 1-140 GPa (phases I and II).…”

“…These measurements show that hcp-based structures are stable in this pressure range. The comparison between theoretical and experimental pressure dependencies () P of the 2g E optical phonon Raman-active mode [25] have shown that the phonon Raman modes calculated using various empirical potentials are highly sensitive to details of the potential used, making it a hard test for any empirical potential (or for any other theoretical method, e.g., DFT). The frequencies calculated from the SG potential [15] deviate from experiment even for very low pressures.…”

“…As known, this problem arises because of neglecting of the three body and higher-order terms in the intermolecular potential [14,[18][19][20][21][22][23][24][25]. Our many-body potential includes not only pair forces, but triple forces as well.…”

Melting of cryocrystals at high pressures. Computer simulation

“…Interaction of hydrogen molecules was the subject of many studies (see e.g., monograph [8] and recent paper of Freiman et al [10]). Most of them have been based on semi-empirical isotropic potentials, which consider the anisotropy of intermolecular interaction as a small correction and ignore interplay between inter-and intramolecular coordinates.…”