Strong Isotope Effect in Phase II of Dense Solid Hydrogen and Deuterium

Abstract

Quantum nuclear zero-point motions in solid H2 and D2 under pressure are investigated at 80 K up to 160 GPa by first-principles path-integral molecular dynamics calculations. Molecular orientations are well-defined in phase II of D2, while solid H2 exhibits large and very asymmetric angular quantum fluctuations in this phase, with possible rotation in the (bc) plane, making it difficult to associate a well-identified single classical structure. The mechanism for the transition to phase III is also described. Existing structural data support this microscopic interpretation.Keywords: hydrogen, deuterium, path-integral, quantum fluctuation, broken-symmetry phase Over the past 20 years, pressure-induced structural changes have been studied for most elements up to the 300 GPa range by a combination of synchrotron diamond anvil cell experiments and ab initio calculations. Although hydrogen has probably been the most extensively studied element under pressure, its crystalline structures above 10 GPa are still largely unknown. Experimental structural determination is hampered by hydrogen's weak x-ray scattering cross-section, and the use of neutron diffraction is equally, if not more, difficult. Theoretically, the difficulties stem from the fact that nuclear zero-point motions and exchange contributions can have important effects. Novel quantum many-body states of matter should be expected, such as the recently predicted superconducting/superfluid metallic state [1]. Understanding the phase diagram of hydrogen is thus an open challenge in modern condensed matter physics.The phase diagrams of solid hydrogen and deuterium have been extensively studied by Raman and infra-red vibrational spectroscopies. Phase boundaries have been determined for three phases [2][3][4]. The transition from phase I to II appears to be related to a quantum ordering of the molecules, whereas that from II to III is more likely a classical ordering [5]. A strong difference in pressure has been measured between the I-II boundary line of solids H 2 , HD and D 2 , whereas there is almost none for the II-III phase boundary. X-ray diffraction studies have shown that the mass centers of the molecules remain on an hcp lattice at the I-II and II-III transitions, indicating that these phases are differentiated by a molecular ordering on this lattice [6,7]. The nature of this ordering, however, is still unknown. Neutron diffraction data may rule out some theoretical predictions for phase II of D 2 but are insufficient for determination of the orientational order [6]. Numerous calculations using Density Functional Theory (DFT) have tried to examine structural changes in solid molecular hydrogen under pressure [8]. A very small energy difference between various candidate structures is obtained and the relative stability of these structures may be easily changed by including zero-point energy contributions. The most recent revision of the DFT phase diagram of hydrogen, including zero-point energy at the harmonic level, predicts the P 6 3 /m structure for phase...

Simulation and understanding of atomic and molecular quantum crystals

“…For instance, Chen et al (2014) have recently shown in a thorough PIMC benchmark study on H 2 that those cases in which good agreement between standard DFT calculations and experiments is obtained, large error cancellations are likely to be affecting the simulations. Similar conclusions have been attained also by Geneste et al (2012), Morales et al (2013), andDrummond et al (2015) by using non-standard computational approaches (e. g., non-harmonic simulation methods in combination with electronic QMC). In order to provide more conclusive estimations in solid H 2 , therefore, is necessary to employ quantum simulation methods that simultaneously describe QNE (e. g., PIMD, PIMC and PIGS, see Sec.…”

Path-integral simulation of solids

“…A strong isotope effect in phase II of solid H 2 and D 2 was reported by Geneste et al 154 . These authors investigated nuclear quantum motion at 80 K and pressures up to 160 GPa by first-principles PIMD calculations.…”

“…Experimental studies based on static compression revealed three relevant phases of solid molecular hydrogen: phase I (high-temperature, relatively lowpressure phase), phase II (low-temperature, low-pressure phase), and phase III (high-pressure phase). These H 2 phases have been studied in recent years with pathintegral simulations, using effective [147][148][149][150] and ab initio potentials [151][152][153][154][155] . A new phase IV has been recently proposed 156 .…”

The properties of hydrogen and helium under extreme conditions

“…Furthermore, even though this approach lacks rotational motion, an examination of the rotational energies of a set of candidate structures, including the P 6 3 /m structure, suggests that rotational motion in P ca2 1 is the least energetic (Moraldi, 2009). Although, recent PIMD calculations suggests the possibility that the structure of Phase II is isotope dependent (Geneste et al, 2012), with…”