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 meta-generalized gradient approximation by means of the strongly constrained and appropriately normed ( SCAN ) semilocal density functional are employed .
We study eleven 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 C 2 / c - 24 and P 6 _ { 1 } 22 - 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 C 2 / c - 24 and P 6 _ { 1 } 22 - 36 , we apply the diffusion Monte Carlo ( DMC ) method to optimise the percentage \alpha of exact-exchange in the trial many-body wave function .
We found that the optimised \alpha equals to 40 \% , and denote the corresponding exchange and correlation functional as PBE1 .
The energy gain with respect to the well-known hybrid functional PBE0 , where \alpha = 25 \% , varies with density and structure .
The PBE1-DMC enthalpy-pressure phase diagram predicts that the P 6 _ { 1 } 22 - 36 structure is stable up to 210 GPa , where it transforms to the C 2 / c - 24 .
Hence , we predict that the phase III of high-pressure solid hydrogen is polymorphic .