High-level ab initio calculations, including the recently formulated CP-dG2thaw methodology, are used to explore the bonding between Mg2+ and a representative assembly of small inorganic and organic molecules. Assessment of existing and novel computational techniques shows that both Mg 2s and 2p electron correlation, and correction for basis set superposition error (BSSE), have a significant influence on calculated magnesium dication affinity (MgDA) values. These two effects are opposed, so that techniques which neglect both (such as G2) are actually found to perform better than techniques in which innervalence correlation, but not BSSE, is treated (such as G2thaw). As shown by comparison of sodium cation affinity (SCA) and MgDA values, we find that Mg2+ has a somewhat greater propensity for binding to "soft" ligands containing second-row donor atoms than does Na+. This trend is attributable to the increased influence of the ion/induced dipole term with increasing cation charge. Dipole induction is, in some circumstances, sufficient to very significantly lengthen other bonds to the donor atom: for example, the F-CH3 bond is extended by over 0.25 Angstrom upon coordination to Mg2+, while structural factors substantially dampen the corresponding effect for the HO-CH3 and H2N-CH3 CH3 bonds.