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 $C2/c-24$ 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 $C2/c-24$ and $P{6}_{1}22-36$, we apply the diffusion Monte Carlo (DMC) method to optimize the percentage $\alpha$ of exact exchange in the trial many-body wave function. We found that the optimized $\alpha$ 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 $\alpha =25\%$, 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 $C2/c-24$. Hence, we predict that phase III of high-pressure solid hydrogen is polymorphic.

Figure 1

The static relative enthalpy-pressure phase diagram for solid molecular hydrogen as calculated by the SCAN XC functional. There are four phase transitions: $P{6}_3/m-16$ to $C2/c-24$ at 129 GPa, $C2/c-24$ to $P{6}_{1}22-36$ at 190 GPa, $P{6}_{1}22-36$ to $Cmca-24$ at 343 GPa, and $Cmca-24$ to $Cmca-8$ at 442 GPa. The number after the hyphen indicates the number of hydrogen atoms in the primitive cell used in our DFT calculations.

Figure 2

The static relative enthalpy-pressure phase diagram of solid molecular hydrogen. The phase diagram is separated into four pressure ranges of 100–200, 200–300, 300–400, and 400–450 GPa, respectively. The reference zero line corresponds to the $P{6}_{1}22-36$ phase. The energy difference between the $P{6}_{1}22-36$ and $C2/c-24$ structures is less than 1 meV/atom. The observed phase transitions are $P{6}_3/m-16$ to $C2/c-24$ at 129 GPa, $C2/c-24$ to $P{6}_{1}22-36$ at 190 GPa, $P{6}_{1}22-36$ to $Cmca-24$ at 343 GPa, and $Cmca-24$ to $Cmca-8$ at 442 GPa.

Figure 3

DMC relative energy as a function of the percentage of exact exchange parameter $\alpha$ in the trial wave function. For $\alpha =0\%$, our PBE1 XC functional is identical to the PBE functional. The error bars are smaller than 0.1 meV/atom.

Figure 4

Relative DFT and DMC enthalpies of $C2/c$ and $P{6}_{1}22$ structures as function of exchange weight. The reference point at each $r_S$ is the enthalpy of $C2/c$ phase.

Figure 5

Relative stability of $P{6}_{1}22$ with respect to the $C2/c$ structure. The enthalpy is obtained using the DMC energy and the DFT-$\mathit{PV}$ term at $\alpha =40\%$. The $P{6}_{1}22$ phase transforms into $C2/c$ at a pressure of around 210–220 GPa. The widths of the H-P lines indicates the estimated uncertainties in the enthalpy calculations, which is about $\sim 3$ meV/atom.