Three-body potential energy surface for parahydrogen

We present a 3D isotropic ab initio three-body (para-H$_2$)$_3$ interaction potential energy surface (PES). The electronic structure calculations are carried out at the correlated coupled-cluster theory level, with single, double, and perturbative triple excitations. The calculations use an augmented correlation-consistent triple zeta basis set and a supplementary midbond function. We construct the PES using the Reproducing-Kernel Hilbert Space toolkit [J. Chem. Inf. Model. 57, 1923 (2017)] with phenomenological and empirical adjustments to account for short-range and long-range behaviour. The (para-H$_2$)$_3$ interaction energies deviate drastically from the Axilrod-Teller-Muto (ATM) potential at short intermolecular separations. We find that the configuration of three para-H$_2$ molecules at the corners of an equilateral triangle is responsible for the majority of the (para-H$_2$)$_3$ interaction energy contribution in a hexagonal-close-packed lattice. In cases where two para-H$_2$ molecules are close to one another while the third is far away, the (para-H$_2$)$_3$ interaction PES takes the form of a modified version of the ATM potential. We expect the combination of this PES together with a first principles para-H$_2$--para-H$_2$ Adiabatic Hindered Rotor potential to outperform a widely-used effective pair potential for condensed many-body systems of para-H$_2$.