Path Integral Monte Carlo simulations of solid parahydrogen using many-body interaction potentials

Abstract

We construct ab initio many-body potential energy surfaces (PES) and use them to perform high-accuracy path integral Monte Carlo (PIMC) simulations of solid parahydrogen.

We first perform PIMC simulations of solid parahydrogen using the Faruk-Schmidt-Hinde (FSH) potential, an ab initio 1D two-body PES for parahydrogen constructed by the Roy group in 2015. The simulations are successful at reproducing experimental results for the equilibrium density and for the vibrational matrix shift for solid parahydrogen. However, we find that the two-body PES on its own is too energetically repulsive at higher densities, and greatly overestimates the pressure as a function of density. To improve the accuracy of our simulations, we must include higher-order many-body interactions, such as the three-body and four-body interactions.

We then construct an isotropic ab initio three-body PES for parahydrogen. The energies are calculated using the coupled cluster method with singles, doubles, and perturbative triples excitations (CCSD(T)). The calculations are performed using an AVTZ atom-centred basis set, with additional (3s3p2d) midbond functions. We use a machine learning method called the reproducing kernel Hilbert space (RKHS) method to construct a PES from the ab initio energies. The three-body PES is attractive at short distances. We perform PIMC simulations of solid parahydrogen using both the two-body FSH potential and the new three-body PES. The inclusion of the three-body PES improves the agreement with experiment at lower densities. However, at higher densities, the attractive interaction of the three-body PES overcorrects for the repulsive wall of the two-body PES, resulting in a severe underestimation of the pressure-density curve.

Next, we construct an isotropic ab initio four-body PES for parahydrogen. The energies are calculated using the CCSD(T) method, using an AVDZ atom-centred basis set with additional (3s3p2d) midbond functions. We use a multilayer perceptron (MLP) to construct a PES from the ab initio energies. We find that the four-body PES is repulsive at short distances. We anticipate that the inclusion of the four-body PES alongside the aforementioned two-body and three-body PESs will improve the agreement of the PIMC simulations of solid parahydrogen with experiment to higher densities than previously found.