Equation of state of solid parahydrogen using ab initio two-body and three-body interaction potentials

TL;DR

This study calculates the equation of state of solid parahydrogen at low temperature using advanced ab initio simulations with two- and three-body interactions, revealing the importance of higher-order many-body effects.

Contribution

It introduces a comprehensive simulation approach incorporating two- and three-body interactions and evaluates their effects on solid parahydrogen's properties.

Findings

Three-body interactions have minor effects on structure.

Two-body interactions alone overestimate pressure.

Including three-body interactions underestimates pressure.

Abstract

We present the equation of state (EOS) of solid parahydrogen between $ 0.024 \, {\r{A}}^{-3} $ and $ 0.1 \, {\r{A}}^{-3} $ at $ T = 4.2 $ K, calculated using path-integral Monte Carlo simulations, with ab initio two-body and three-body interaction potentials. We correct for finite size simulation errors using potential tail corrections. Trotter factorization errors are accounted for, either via extrapolation, or by using a suitably small imaginary time step. We incorporate the three-body interaction using two methods; the full inclusion method, where pair and three-body interactions are used in both Monte Carlo sampling and in the energy estimators, and the perturbative method, where three-body interactions are omitted from sampling but are still present in energy estimations. Both treatments of the three-body interaction return very similar total energies and pressures. The presence of three-body interactions has only minor effects on the structural properties of the solid. Whereas the pair interaction, on its own, significantly overestimates the pressure of solid parahydrogen, the additional presence of the three-body interaction causes a severe underestimation of the pressure. Our findings suggest that accurate simulations of solid parahydrogen require four-body and possibly higher-order many-body interactions. It may also be the case that static interaction potentials are entirely unsuitable for simulations of solid parahydrogen at high densities.