Binding Energies for Doubly-Charged Ions M²⁺ = Mg²⁺, Ca²⁺ and Zn²⁺ with the Ligands L = H₂O, Acetone and <i>N</i>-methylacetamide in Complexes M for <i>n</i> = 1 to 7 from Gas Phase Equilibria Determinations and Theoretical Calculations

Experimental and theoretical binding energies, entropies, and free energies are reported for M(L) n 2+ complexes, where M = Zn, Mg, Ca and L = acetone (Me 2 CO) and N -methylacetamide (MAcA), as well as water for comparison. For the theoretical binding energies, expressed as dissociation energies ( ), n extends up to 3 for the Mg-Me 2 CO system, while for the experimental binding energies, n starts as low as 5 for the Zn- and Mg-acetone systems and reaches as high as 9 for the Ca(MAcA) system. For n = 1 complexes, Zn exhibits the strongest binding (due to sdσ hybridization and charge transfer), followed by Mg and then Ca (primarily electrostatic binding, with Mg being smaller). For the ligands, the trend based on dipole and polarizability holds for n = 1, with MAcA exhibiting the strongest binding, followed by Me 2 CO and then H 2 O. However, as n increases, the bond enthalpies drop at rates that cause them to equalize within a few kcal/mol for n = 6. The observed trend of bond enthalpy equalization has been attributed to primarily ligand−ligand repulsion in the case of Mg and Ca complexes. For the Zn complexes, loss of sdσ hybridization and charge-transfer play an added role so that, for example, for Zn(H 2 O) 3 2+ and Zn(H 2 O) 4 2+, the binding energies are lower than for the Mg analogues, despite the shorter bond distance in the Zn complexes. The experimental bond enthalpy and entropy differences for M(Me 2 CO) n 2+, where M = Ca and Mg and n = 6 and 7, show a sharp drop that corresponds to a transition to an outer shell for the seventh Me 2 CO ligand. The entropies for the addition of the seventh ligand are much smaller than for the sixth ligand and correspond to a ligand that, due to the absence of ligand−ligand bonding interactions, is free to translate across the entire inner shell. The lower bond enthalpy and entropy for Zn as compared to Ca and Mg indicate that the transition to an outer shell is earlier for Zn. The strong hydrogen bonding between outer-shell and inner-shell MAcA ligands, indicated for Ca(MAcA) 7 2+, allows earlier transitions to an outer shell for Zn- and Mg-MAcA complexes as compared to their acetone analogues. Implications of the ligand interactions in the experimentally observed Ca complexes to Ca-containing proteins is also discussed.

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