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

Abstract

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.

A centroid molecular dynamics study of liquid para-hydrogen and ortho-deuterium

“…͑20͒ is not mathematically rigorous, the CMD with classical operators approach has been shown to accurately describe the coherent dynamic structure factor for several systems which exhibit quantum behavior. 34,[39][40][41][42] For liquids in which the particles are not purely coherent scatterers, such as liquid hydrogen and deuterium, the incoherent dynamic structure factor is also experimentally observed,…”

Centroid molecular dynamics approach to the transport properties of liquid para-hydrogen over the wide temperature range

“…Recently, several approaches such as the analytic continuation approach, 7-16 the quantum mode coupling theory, [17][18][19][20][21] and the forward-backward semiclassical method [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40] have been developed for this purpose. The CMD has been widely used to reveal the dynamics of various quantum systems, liquid p-H 2 , 43-47 crystalline hydrogen, 48 and helium-4, 49 aqueous systems, [50][51][52][53] ion-doped hydrogen clusters, 54,55 hydrogen slabs, 56 and the unification with ab initio calculations. 21 Another approach for the quantum dynamics simulations is the path integral centroid molecular dynamics ͑CMD͒ proposed by Cao and Voth.…”

Communication: Dynamical and structural analyses of solid hydrogen under vapor pressure

“…[6][7][8][9] This typical quantum solid has actually attracted a number of theoretical and experimental researchers who adopted Raman scattering, 10,11 neutron scattering, [12][13][14] optical Kerr effects, 15 lattice dynamics calculations, 16,17 and path integral molecular dynamics (PIMD) simulations based on ab initio electronic potentials [6][7][8][9]18 or spherical SilveraGoldman (SG) model potentials. 19 Pressure-induced structural changes have been reported by a combination of synchrotron experiments and density functional theory (DFT)-based PIMD calculations. [6][7][8][9][10]20 The hexagonal close-packed (h.c.p.)…”

“…18,[21][22][23] The dispersion interaction is empirically included in the spherical SG model or in Lennard-Jones model potentials, 24 but its transferability to different phases is not obvious. 19 Additionally, these PIMD simulation methods are appropriate for ensemble averages but not for real-time dynamics of each molecule. [3][4][5] In these senses, solid H 2 under vapor pressure still remains open for further investigations.…”