Classical and quantum ordering of protons in cold solid hydrogen under megabar pressures

Abstract

A combination of state-of-the-art theoretical methods has been used to obtain an atomiclevel picture of classical and quantum ordering of protons in cold high-pressure solid hydrogen. We focus mostly on phases II and III of hydrogen, exploring the effects of quantum nuclear motion on certain features of these phases (through a number of ab initio path integral molecular dynamics (PIMD) simulations at particular points on the phase diagram).We also examine the importance of van der Waals forces in this system by performing calculations using the optB88-vdW density functional, which accounts for non-local correlations.Our calculations reveal that the transition between phases I and II is strongly quantum in nature, resulting from a competition between anisotropic inter-molecular interactions that restrict molecular rotation and thermal plus quantum fluctuations of the nuclear positions that facilitate it. The transition from phase II to III is more classical because quantum nuclear motion plays only a secondary role and the transition is determined primarily by the underlying potential energy surface. A structure of P 2 1 /c symmetry with 24 atoms in the primitive unit cell is found to be stable when anharmonic quantum nuclear vibrational motion is included at finite temperatures using the PIMD method. This structure gives a good account of the infra-red (IR) and Raman vibron frequencies of phase II. We find additional support for a C2/c structure as a strong candidate for phase III, since it remains transparent up to 300 GPa, even when quantum nuclear effects are included. Finally, we find that accounting for van der Waals forces improves the agreement between experiment and theory for the parts of the phase diagram considered, when compared to previous work which employed the widely-used Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional.arXiv:1302.0062v1 [cond-mat.mtrl-sci]

Path-integral simulation of solids

“…Classical and quantum ordering of protons in cold high-pressure solid H 2 have been recently investigated by Li et al 155 , at several points on the phase diagram, using ab initio PIMD simulations. These calculations revealed that the transition between phases I and II is strongly quantum in nature, which results from a competition between thermal plus quantum fluctuations that enhance molecular rotation, and anisotropic intermolecular interactions that hinder it.…”

Raman measurements of phase transitions in dense solid hydrogen and deuterium to 325 GPa

“…There are apparent discrepancies among experiments for the transition pressures and reported evidence for spectral changes that are not understood or are controversial, particularly weak spectral changes near 270 GPa, which tentatively were identified as evidence of a possible new solid phase (6) and the loss of the Raman vibron and the claim of strong metallization (3). Despite the broad agreement between theory and experiment that phase IV has a mixed-layer structure, the detailed structure is not known, and numerous related lower symmetry forms are possible but difficult to predict because of small free energy differences and other challenges of the simulations (9,13,14,16,17,(19)(20)(21)(22)(23). These theoretical studies also predict other phases in the P-T range that currently is accessible.…”

“…Important information about these transitions has been provided by recent theoretical calculations (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21). Notably, the type of structure constrained by vibrational spectroscopy for phase IV was among the structures predicted by theory before the experiments (10).…”

“…These subsequent calculations predict that the structure consists of graphene-structured, honeycomb sheets and molecular interlayers. The molecular layers exhibit higherfrequency vibrons from the stronger molecular bonding, and the graphene sheets are predicted to have less strong bonding, therefore corresponding to the lower-frequency vibron in the vibrational spectra (10,(12)(13)(14)(15)(16)(17)(18). As for the question of metallization, the infrared transparency at photon energies down to 0.1 eV (5) rule out a transition to a fully metallic phase; however, phase IV might be a very poor metal, with absorption below 0.1 eV (20,21), perhaps above a particular range of P-T conditions.…”

Identification of high-pressure phases III and IV in hydrogen: Simulating Raman spectra using molecular dynamics

“…[18][19][20] Although these calculations typically ignore quantum effects on the protons, they still provide a useful indication of the likely structures. Very recent papers 22,23 applying path integral MD to high-pressure hydrogen show no qualitative behavioral change to the phase diagram: the main effect is that tunneling allows molecular rotations to occur at slightly lower temperatures than in classical MD, lowering the phase lines. Most importantly for the present work, the vibrational frequencies of the molecules are largely unchanged by the path integral dynamics.…”