Path-integral Monte Carlo simulations of solid parahydrogen using two-body, three-body, and four-body ab initio interaction potential energy surfaces

TL;DR

This study uses path integral Monte Carlo simulations with advanced ab initio potentials to accurately model the equation of state of solid parahydrogen at low temperatures, highlighting the importance of many-body interactions.

Contribution

It introduces comprehensive simulations incorporating two-, three-, and four-body potentials, providing improved agreement with experimental data and insights into many-body effects in solid parahydrogen.

Findings

Four-body interactions yield equilibrium density close to experiments.

Including four-body terms improves pressure-density agreement up to a certain density.

Higher-order many-body interactions are needed at higher densities.

Abstract

We present path integral Monte Carlo simulation results for the equation of state of solid parahydrogen between $ 0.024 \, {\r{A}}^{-3} $ and $ 0.1 \, {\r{A}}^{-3} $ at $ T = 4.2 \, $ K. The simulations are performed using non-additive isotropic ab initio two-body, three-body, and four-body potential energy surfaces (PES). We apply corrections to account for both the finite size simulation errors and the Trotter factorization errors. Simulations that use only the two-body PES during sampling yield an equation of state similar to that of simulations that use both the two-body and three-body PESs during sampling. With the four-body interaction energy, we predict an equilibrium density of $ 0.02608 \, {\r{A}}^{-3} $, very close to the experimental result of $ 0.0261 \, {\r{A}}^{-3} $. The inclusion of the four-body interaction energy also brings the simulation results in excellent agreement with the experimental pressure-density data until around $ 0.065 \, {\r{A}}^{-3} $, beyond which the simulation results overestimate the pressure. These PESs overestimate the average kinetic energy per molecule at the equilibrium density by about $ 7 \% $ compared to the experimental result. Our findings suggest that, at higher densities, we require five-body and higher-order many-body interactions to quantitatively improve the agreement between the pressure-density curve produced by simulations, and that of experiment. Using the four-body PES during sampling at excessively high densities, where such higher-order many-body interactions are likely to be significant, causes an artificial symmetry breaking in the hcp lattice structure of the solid.