Dissociation of High-Pressure Solid Molecular Hydrogen: A Quantum Monte Carlo and Anharmonic Vibrational Study

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 $Cmca\text{−}12$ direct to the atomic $I{4}_1/amd$ 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.

Figure 1

Enthalpy as a function of pressure for the $Cmca\text{−}12$, $Cmca\text{−}4$, and $I{4}_1/amd$ phases, relative to the $I{4}_1/amd$ phase. Top: Static phase diagram from DMC calculations. Bottom: Phase diagram including the ZP enthalpy from the harmonic and anharmonic vibrational calculations. The inset shows the harmonic ZP enthalpy as a function of pressure.

Figure 2

Top: Harmonic (dashed black lines) and anharmonic (solid red lines) Born-Oppenheimer (BO) energy surfaces and corresponding wave function densities $|{\mathrm{\Phi }}_{\text{har}}{|}^2$ and $|{\mathrm{\Phi }}_{\text{anh}}{|}^2$ for an optical mode at the $\mathrm{\Gamma }$ point of the $I{4}_1/amd$ structure. Bottom: A supercell of the $I{4}_1/amd$ structure with arrows indicating the proton motion corresponding to the phonon mode in the top figure. Alternate planes move in antiphase.