Unconventional phase III of high-pressure solid hydrogen
We reassess the phase diagram of high-pressure solid hydrogen using mean-field and many-body wave function-based approaches to determine the nature of phase III of solid hydrogen. To discover the best candidates for phase III, density functional theory calculations within the metageneralized gradient approximation by means of the strongly constrained and appropriately normed (SCAN) semilocal density functional are employed. We study 11 molecular structures with different symmetries, which are the most competitive phases, within the pressure range of 100 to 500 GPa. The SCAN phase diagram predicts that the $C2/c\ensuremath{-}24$ and $P{6}_{1}22\ensuremath{-}36$ structures are the best candidates for phase III with an energy difference of less than 1 meV/atom. To verify the stability of the competitive insulator structures of $C2/c\ensuremath{-}24$ and $P{6}_{1}22\ensuremath{-}36$, we apply the diffusion Monte Carlo (DMC) method to optimize the percentage $\ensuremath{\alpha}$ of exact exchange in the trial many-body wave function. We found that the optimized $\ensuremath{\alpha}$ equals $40%$ and denote the corresponding exchange and correlation functional as PBE1. The energy gain with respect to the well-known hybrid functional PBE0, where $\ensuremath{\alpha}=25%$, varies with density and structure. The PBE1-DMC enthalpy-pressure phase diagram predicts that the $P{6}_{1}22\ensuremath{-}36$ structure is stable up to 210 GPa, where it transforms to the $C2/c\ensuremath{-}24$. Hence, we predict that phase III of high-pressure solid hydrogen is polymorphic.