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We use the diffusion quantum Monte Carlo (DMC) method to calculate the ground state phase diagram of solid molecular hydrogen and examine the stability of the most important insulating phases relative to metallic crystalline molecular hydrogen. We develop a new method to account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee-Zhang-Krakauer (KZK) functional in density functional theory. To study band-gap closure and find the metallization pressure, we perform accurate quasi-particle many-body calculations using the $GW$ method. In the static approximation, our DMC simulations indicate a transition from the insulating Cmca-12 structure to the metallic Cmca structure at around 375 GPa. The $GW$ band gap of Cmca-12 closes at roughly the same pressure. In the dynamic DMC phase diagram, which includes the effects of zero-point energy, the Cmca-12 structure remains stable up to 430 GPa, well above the pressure at which the $GW$ band gap closes. Our results predict that the semimetallic state observed experimentally at around 360 GPa [Phys. Rev. Lett. {bf 108}, 146402 (2012)] may correspond to the Cmca-12 structure near the pressure at which the band gap closes. The dynamic DMC phase diagram indicates that the hexagonal close packed $P6_3/m$ structure, which has the largest band gap of the insulating structures considered, is stable up to 220 GPa. This is consistent with recent X-ray data taken at pressures up to 183 GPa [Phys. Rev. B {bf 82}, 060101(R) (2010)], which also reported a hexagonal close packed arrangement of hydrogen molecules.
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A theoretical study is reported of the molecular-to-atomic transition in solid hydrogen at high pressure. We use the diffusion quantum Monte Carlo method to calculate the static lattice energies of the competing phases and a density-functional-theory-based vibrational self-consistent field method to calculate anharmonic vibrational properties. We find a small but significant contribution to the vibrational energy from anharmonicity. A transition from the molecular Cmca-12 direct to the atomic I4_1/amd phase is found at 374 GPa. The vibrational contribution lowers the transition pressure by 91 GPa. The dissociation pressure is not very sensitive to the isotopic composition. Our results suggest that quantum melting occurs at finite temperature.
Establishing the phase diagram of hydrogen is a major challenge for experimental and theoretical physics. Experiment alone cannot establish the atomic structure of solid hydrogen at high pressure, because hydrogen scatters X-rays only weakly. Instead our understanding of the atomic structure is largely based on density functional theory (DFT). By comparing Raman spectra for low-energy structures found in DFT searches with experimental spectra, candidate atomic structures have been identified for each experimentally observed phase. Unfortunately, DFT predicts a metallic structure to be energetically favoured at a broad range of pressures up to 400 GPa, where it is known experimentally that hydrogen is nonmetallic. Here we show that more advanced theoretical methods (diffusion quantum Monte Carlo calculations) find the metallic structure to be uncompetitive, and predict a phase diagram in reasonable agreement with experiment. This greatly strengthens the claim that the candidate atomic structures accurately model the experimentally observed phases.
We use the diffusion quantum Monte Carlo to revisit the enthalpy-pressure phase diagram of the various products from the different proposed decompositions of H$_2$S at pressures above 150~GPa. Our results entails a revision of the ground-state enthalpy-pressure phase diagram. Specifically, we find that the C2/c HS$_2$ structure is persistent up to 440~GPa before undergoing a phase transition into the C2/m phase. Contrary to density functional theory, our calculations suggest that the C2/m phase of HS is more stable than the I4$_1$/amd HS structure over the whole pressure range from 150 to 400 GPa. Moreover, we predict that the Im-3m phase is the most likely candidate for H$_3$S, which is consistent with recent experimental x-ray diffraction measurements.
This paper investigates some of the successes and failures of density functional theory in the study of high-pressure solid hydrogen at low temperature. We calculate the phase diagram, metallization pressure, phonon spectrum, and proton zero-point energy using three popular exchange-correlation functionals: the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, and the semi-local Becke-Lee-Yang-Parr (BLYP) functional. We focus on the solid molecular P$6_3$/m, C2/c, Cmca-12, and Cmca structures in the pressure range from $100<P<500$ GPa over which phases I, II and III are observed experimentally. At the static level of theory, in which proton zero-point energy is ignored, the LDA, PBE and BLYP functionals give very different structural transition and metallization pressures, with the BLYP phase diagram in better agreement with experiment. Nevertheless, all three functionals provide qualitatively the same information about the band gaps of the four structures and the phase transitions between them. Going beyond the static level, we find that the frequencies of the vibron modes observed above 3000 cm$^{-1}$ depend strongly on the choice of exchange-correlation functional, although the low-frequency part of the phonon spectrum is little affected. The largest and smallest values of the proton zero-point energy, obtained using the BLYP and LDA functionals, respectively, differ by more than 10 meV/proton. Including the proton zero-point energy calculated from the phonon spectrum within the harmonic approximation improves the agreement of the BLYP and PBE phase diagrams with experiment. Taken as a whole, our results demonstrate the inadequacy of mean-field-like density functional calculations of solid molecular hydrogen in phases I, II and III and emphasize the need for more sophisticated methods.
We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band-gap energies of the $C2/c$, $Pc$, and $P6_3/m$ structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab-initio path-integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero-point energy and temperature-induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band-gaps substantially, leading to metallization of the $C2/c$ and $Pc$ phases via band overlap; the effect on the band-gap of the $P6_3/m$ structure is less pronounced. Our combined DMC-PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the $C2/c$ and $Pc$ phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band-gap energy and vibron modes. This strong coupling induces a band-gap reduction of more than 2.46 eV in high-pressure solid molecular hydrogen. Comparing our DMC-PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen.
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