Unconventional phase III of high-pressure solid hydrogen

We reassess the phase diagram of high-pressure solid hydrogen using mean-filed and many-body wave function based approaches to determine the nature of phase III of solid hydrogen. To discover the best candidates for the phase III, Density Functional Theory with meta-generalized-gradient approximation (meta-GGA) non-empirical strongly constrained and appropriately normed (SCAN) exchange-correlation (XC) is employed. We study eleven molecular structures with different symmetry, which are the most competitive phases, within the pressure range of 100 to 500 GPa. The SCAN phase diagram predicts that the $C2/c-24$ and $P6_122-36$ structures are the best candidates for the phase III with energy difference of less than 1 meV/atom. To verify the stability of the competitive insulator structures of $C2/c-24$ and $P6_122-36$, we apply the diffusion quantum Monte Carlo (DMC) to optimise the percentage of the exact exchange ($\alpha$) in the trial many-body wave function. We found that the optimised $\alpha$ equals to $40 \%$, and the corresponding XC functional is named PBE$_{1x}$. The energy gain with respect to the conventional hybrid functional (PBE$_0$) with $\alpha = 25\%$ varies with density and structure. The PBE$_{1x}$-DMC enthalpy-pressure phase diagram predicts that the $P6_122-36$ structure is stable up to 210 GPa where it transforms to the $C2/c-24$. We predict that the phase III of high-pressure solid hydrogen is polymorphic.