The ground state Ar-Br₂ potential energy surface is predicted from ab initio calculations and from an atom-atom model using empirical ArBr potentials and the (evaluated ab initio) perturbation of the interaction between Ar and Br within Br₂. At all levels of modelling, the surface has a double-minimum topology, with a well for the linear (L) geometry in addition to a well for the T-shaped geometry. This differs from the single-minimum topology predicted by the commonly used pairwise additive Lennard-Jones potential. For both ab initio and atom-atom model surfaces, the L-well is found to be significantly deeper than the T-well; this relative behaviour is unchanged by zero-point vibrations. Spectroscopic parameters are predicted for the present surfaces. The final surfaces result from a scaling to reproduce the estimated bond energy of the system. Possible reflections of the surface topology in experimental observables are discussed.