High-level ab initio calculations, using the CPd-G2thaw and CP-G2 composite computational procedures (combined with spin projection techniques when appropriate), are used to explore the bonding between the metal monocations Na+, Mg+, Al+, K+, and Ca+ and the radicals H, CH3, C2H, C2H3, and C2H5. Assessment of existing and novel computational techniques for the second-row-metal-containing species Finds significantly improved performance, as ascertained by residual basis set superposition error (BSSE) values, of the new variants over standard methods, and general recommendations for calculations on second-row-metal-containing ions are established. In sharp contrast to the results obtained from many studies of bonding between metal ions and closed-shell ligands, wide variations are seen for any given radical ligand among the bond strengths of different metal ions within a given row: for example, the Na+-H bond strength is only 4.2 kJ mol(-1) while the Mg+-H bond strength (in the singlet state adduct) is 196.3 kJ mol(-1). Discrepancies between theoretical and literature experimental thermochemical values for MgH+ and Mg2H+ contrast with generally very good agreement with previous studies for other species, suggesting that the energetics of MgH+ and Mg2H+ may warrant further experimental study. Finally, the very large singlet-state adduct bond energies for Mg- and Ca-containing ions, and the notably small bond energies for Na- and K-containing adducts, suggest that radicals such as H and CH3, encountered in environments such as jovian planetary atmospheres, outflowing circumstellar envelopes, and interstellar clouds, will display a high selectivity in their propensity to react with ambient metal ions.