Given the recent developments in methodology associated with the accurate computation of molecular systems with weak interactions, it is of particular interest to revisit systems that are notoriously challenging for determining reliable potential energy surface (PES) descriptions. Additionally, challenges associated with carrying out complete basis set extrapolation procedures and treatment of basis set superposition error (BSSE) are of importance in these descriptions. In this work, investigation into the ability to accurately predict the potential energy surfaces of the main Rg3 molecules (Rg ) He, Ne, Ar) is made across a range of wave function types and large basis sets, including the use of several established extrapolation procedures and counterpoise corrections. Wave function types span most classes of density functional types, including the newest DFT-D schemes, and are benchmarked against high accuracy CCSD(T)/CBS methodology. Study of such systems is valuable, as they serve as simple models for many complex properties, most importantly n-body weak interaction energies.