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A combination of state-of-the-art theoretical methods has been used to obtainan atomic-level picture of classical and quantum ordering of protons in coldhigh-pressure solid hydro-gen. We focus mostly on phases II and III ofhydrogen, exploring the effects of quantum nuclear motion on certain featuresof these phases (through a number of ab initio path-integral molecular dynamics(PIMD) simulations at particular points on the phase diagram). We also examinethe importance of van der Waals forces in this system by performingcalculations using the optB88-vdW density functional, which accounts fornon-local correlations. Our calculations reveal that the transition betweenphases I and II is strongly quantum in nature, resulting from a competitionbetween anisotropic inter-molecular interactions that restrict molecularrotation and thermal plus quantum fluctuations of the nuclear positions thatfacilitate it. The transition from phase II to III is more classical becausequantum nuclear motion plays only a secondary role and the transition isdetermined primarily by the underlying potential energy surface. A structure ofP21c symmetry with 24 atoms in the primitive unit cell is found to be stablewhen anharmonic quantum nuclear vibrational motion is included at finitetemperatures using the PIMD method. This structure gives a good account of theinfra-red (IR) and Raman vibron frequencies of phase II. We find ad-ditionalsupport for C2/c structure as a strong candidate for phase III, since itremains transparent up to 300 GPa, even when quantum nuclear effects areincluded. Finally, we find that accounting for van der Waals forces improvesthe agreement between experiment and theory for the parts of the phase diagramconsidered, when compared to previous work which employed the widely-usedPerdew-Burke-Ernzerhof (PBE) exchange-correlation functional.

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