Quantum Monte Carlo study of high pressure solid molecular hydrogen

Abstract

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 account for finite-size errors by combining the use of twist-averaged boundary conditions with corrections obtained using the Kwee–Zhang–Krakauer functional in density functional theory. To study the closure of the band gap with increasing pressure, we perform 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 in the quasi-harmonic approximation, 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 (2012 Phys. Rev. Lett. 108, 146402) 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 P63/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 (2010 Phys. Rev. B 82 060101), which also reported a hexagonal-close-packed arrangement of hydrogen molecules.