We provide a consistent set of interaction energy curves for the group 2 (IIA) and group 12 (IIB) metal cation/rare gas complexes, M+-RG, where M+ = Be+-Ra+ and Zn+-Hg+ and RG = He-Rn. We report spectroscopic constants derived from these, compare them with available data, and discuss trends in the values. We gain insight into the interactions that occur using a range of approaches: reduced potential energy curves; charge and population analyses; molecular orbital diagrams and contour plots; and Birge-Sponer plots. Although sp hybridization occurs in the Be+-RG, Mg+-RG and group 12 M+-RG complexes, this appears to be minimal and covalency is the main aspect of the interaction. However, major sd hybridization occurs in the heavier group 2 M+-RG systems, which increases their interaction energies but there is minimal covalency. Examination of Birge-Sponer plots reveals significant curvature in many cases, which we ascribe to the changing amounts of hybridization or covalency as a function of internuclear separation. This suggests why the use of a simple electrostatics-based model potential to describe the interactions is inadequate.