Molecular collective dynamics in solid para-hydrogen and ortho-deuterium: The Parrinello–Rahman-type path integral centroid molecular dynamics approach

The single-particle and collective dynamics of hydrogen/deuterium molecules in solid hcp para-hydrogen $(p-H2)$ and ortho-deuterium $(o-D2)$ has been investigated by using the path integral centroid molecular dynamics (CMD) simulations at zero-pressure and 5.4 and 5.0 K, respectively. For this purpose, we have newly unified the standard CMD method with the Parrinello–Rahman–Nosé–Hoover-chain-type isothermal–isobaric technique. The phonon density of states have been obtained and the dynamic structure factors have been calculated to observe the phonon dispersion relations of both crystals. For solid $p-H2,$ the high energy edge of the phonon energies of solid $p-H2$ is >13 meV, and the calculated phonon energies are significantly higher than those observed in Nielsen’s previous neutron scattering experiments in the energy region >9 meV. The relationship between the present results and the data reported so far is discussed to resolve the outstanding controversy regarding the phonon energies in solid $p-H2.$ On the other hand, the excitation energies for solid $o-D2$ are in fairly good agreement with those of the neutron experiments. The calculated isothermal compressibility of solid $p-H2$ is found to be very close to the experimental result.