It has been shown, using a model-potential analysis, that the large permanent quadrupole moment of the excited Mg+(3p) ion can play a significant role in the strong physical M+/Rg bonding observed for Mg+(3p pi).Rg[(2)Pi] ionic states. The four permanent quadrupole terms included in the model potential (two proportional to 1/R-6, two to 1/R-8) contribute substantially to Mg+(3p pi)/Rg attraction near the bond distances R-e. In fact, our analysis indicates that the leading charge/induced-dipole 1/R-4 attractive term contributes only similar to 25-30 % to the physical bonding in the Mg+(3p pi).Ar excited state, in stark contrast to the conventional wisdom that this term is usually dominant in M+/Rg bonding. Empirically derived Ae(-bR) repulsive terms also show that electron/electron repulsion for a given Mg+(3p pi).Rg excited state is less than for the analogous Mg+(3s sigma).Rg ground state, consistent with the fact that the Rg atoms approach the excited 3p pi orbital of Mg+ along its nodal axis. For the Mg+(3p sigma).Rg[(2)Sigma (+)] excited states, however, three of the permanent quadrupole terms are repulsive (with twice the magnitude) and thus contribute significantly to the extremely weak bonds and very large bond distances for the 3p sigma ionic states. In contrast, the much smaller quadrupole moments of open-shell d-orbital states of transition metal M+ ions appear to have very little effect on their physical bonding with the Ar atom, at least for the few states which have been well-characterized spectroscopically. For all the M+/Rg states discussed above, our model-potential analysis indicates that no substantial chemical or charge-transfer interactions are needed to rationalize the bond strengths, the bond lengths, and the vibrational frequencies (the "shapes" of the potential curves near their minima).