Four-Body Nonadditive Potential Energy Surface and the Fourth Virial Coefficient of Helium

The four-body nonadditive contribution to the energy of four helium atoms is calculated and fitted for all geometries for which the internuclear distances exceed a small minimum value. The interpolation uses an active learning approach based on Gaussian processes. Asymptotic functions are used to calculate the nonadditive energy when the four helium atoms form distinct subclusters. The resulting four-body potential is used to compute the fourth virial coefficient D(T) for helium, at temperatures from 10 to 2000 K, with a path-integral approach that fully accounts for quantum effects. The results are in reasonable agreement with the limited and scattered experimental data for D(T), but our calculated results have much smaller uncertainties.