Coupled electron-ion Monte Carlo simulation of hydrogen molecular crystals

Abstract

We performed simulations for solid molecular hydrogen at high pressures (250GPa≤P≤500GPa) along two isotherms at T=200 K (phases III and VI) and at T=414 K (phase IV). At T=200K we considered likely candidates for phase III, the C2c and Cmca12 structures, while at T=414K in phase IV we studied the Pc48 structure. We employed both Coupled Electron-Ion Monte Carlo (CEIMC) and Path Integral Molecular Dynamics (PIMD) based on Density Functional Theory (DFT) using the vdW-DF approximation. The comparison between the two methods allows us to address the question of the accuracy of the xc approximation of DFT for thermal and quantum protons without recurring to perturbation theories. In general, we find that atomic and molecular fluctuations in PIMD are larger than in CEIMC which suggests that the potential energy surface from vdW-DF is less structured than the one from Quantum Monte Carlo. We find qualitatively different behaviors for systems prepared in the C2c structure for increasing pressure. Within PIMD the C2c structure is dynamically partially stable for P≤250GPa only: it retains the symmetry of the molecular centers but not the molecular orientation; at intermediate pressures it develops layered structures like Pbcn or Ibam and transforms to the metallic Cmca-4 structure at P≥450GPa. Instead, within CEIMC, the C2c structure is found to be dynamically stable at least up to 450GPa; at increasing pressure the molecular bond length increases and the nuclear correlation decreases. For the other two structures the two methods are in qualitative agreement although quantitative differences remain. We discuss various structural properties and the electrical conductivity. We find these structures become conducting around 350GPa but the metallic Drude-like behavior is reached only at around 500GPa, consistent with recent experimental claims.

Plasma phase transition (by the fiftieth anniversary of the prediction)

“…[28,29,31,32] We do not insist on the quantitative accuracy of the position of pressure and density range of the phase equilibria on the phase diagram of hydrogen. [40,44,56] and we suggest that it leads to almost the same conclusions as in the given work. The approach used in the given work and also in ref.…”

“…The spatial arrangement of hydrogen atoms, averaged over time, in the resulting Cmca-12 molecular phase is shown in Figure 3(b). [56]. The possibility of the existence of this structure was also shown in refs.…”

Local structure in dense hydrogen at the liquid–liquid phase transition by coupled electron–ion Monte Carlo

“…The nuclear configuration space is sampled with a multi‐level Metropolis scheme and the Penalty method . Quantum nuclei within the Path Integral formalism are sampled with specialized procedures, which made the method computationally affordable, as explained in Pierleoni et al Within this method, a few proton slices are enough to accurately simulate systems above T = 600 K in the relevant range of densities. For example, the transition pressure converged with eight proton slices at T = 600 K, the lowest temperature we considered (see the SM of Pierleoni et al).…”

Metastable molecular fluid hydrogen at high pressures

“…[26] While most theoretical works suggest that it is a first-order transition, [1][2][3][4][5][6][7][8][9][10] there is an uncertainty in the experimental verification. [26] While most theoretical works suggest that it is a first-order transition, [1][2][3][4][5][6][7][8][9][10] there is an uncertainty in the experimental verification.…”

“…[1][2][3][4][5][6][7][8][9][10][11] The methods also include density functional theory (DFT), [12] path-integral molecular dynamics (PIMD) based on DFT, coupled electron-ion Monte Carlo (CEIMC), [13] and the quantum Monte Carlo molecular dynamics (QMCMD). [1][2][3][4][5][6][7][8][9][10][11] The methods also include density functional theory (DFT), [12] path-integral molecular dynamics (PIMD) based on DFT, coupled electron-ion Monte Carlo (CEIMC), [13] and the quantum Monte Carlo molecular dynamics (QMCMD).…”