Ab initio calculations have been carried out to generate a potential energy surface for the Ar-H2S weakly bonded cluster. The surface displays a low energy trough with small barriers for the "orbit" of Ar about H2S. Basis set and correlation effects have been analyzed through a series of calculations at different levels, and the feature of a low energy trough seems assured. The nature of this surface has only little to do with electrostatic interaction, and so, a fairly good fit of the nonelectrical part of the potential surface is obtained with atom-atom Lennard-Jones potential terms. With different surface fits and a fully anharmonic analysis of the ground vibrational state, on-average rotational constants were calculated via rigid-body diffusion quantum Monte Carlo. These calculations show that certain intriguing spectroscopic manifestations of deuterium substitution are associated primarily with the trough feature of the surface.