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.