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The sequential enthalpies , free energies , and entropies for the hydration reaction M(H2O) n - 1 2+ + H2O = M(H2O) n 2+ were determined in the gas phase for M = Mg, Ca, Sr, Ba. The gas-phase ion hydrates were produced by electrospray, and the hydration equilibria were determined in a reaction chamber attached to a mass spectrometer. The exothermicities of the (n − 1, n) reactions at low n (n = 1 to n = 5) are very high, and the corresponding equilibria require very high temperatures and could not be determined. For these low n, good theoretical results are available for Mg2+ and Ca2+ (Siegbahn and co-workers). A combination of the theoretical data with the experimental results (from n = 6 to n = 14) provides information on the inner and outer hydration shell structure and energetics of the hydrates. Very good agreement is observed between the theoretical and experimental energies where they overlap. For Mg, Ca, and Sr the first six molecules go into the inner shell while the seventh and higher molecules go into the outer shell(s). However, the sequential energies indicate crowding in the inner shell of Mg. Six or seven molecules can be filled in the inner shell of Sr, while for Ba the inner shell number may be as high as 8 or 9. The observed entropy changes are, in general, consistent with the assigned shell structures. In particular, there is a large change of ΔS n - 1, n on transition from the inner (n = 6) to the outer (n = 7) shell for Mg, Ca, and Sr. The difference between the gas-phase total enthalpies (Ca2+) − (Mg2+) is within 3 kcal/mol of the total hydration difference (Ca2+) − (Mg2+) for liquid water. A similar result is obtained also for the hydration free energies. Extension of the determinations to ligands that model bonding and coordination in biocomplexes of Mg2+ and Ca2+ is discussed.

Several factors, attributable to the ESIMS mechanism, that can affect the assumptions of the titration method are examined: (1) The assumption that the concentrations in solution of the protein P, the ligand L, and the complex PL are proportional to the respective ion intensities observed with ESIMS, is examined with experiments in which ion intensities of two non-interacting proteins are compared with the respective concentrations. The intensities are found to be approximately proportional to the concentrations. The proportionality factors are found to increase as the mass of the protein is decreased. Very small proteins have much higher intensities. The results suggest that it is preferable to use only the intensity ratio of PL and P, whose masses are very close to each other when L is small, to determine the association constant KA in solution. (2) From the charge residue model (CRM) one expects that the solution will experience a very large increase of concentration due to evaporation of the precursor droplets, before the proteins P and PL are produced in the gas phase. This can shift the equilibrium in the droplets: P + L = PL, towards PL. Analysis of the droplet evaporation history shows that such a shift is not likely, because the time of droplet evolution is very short, only several micros, and the equilibrium relaxation time is much longer. (3) The droplet history shows that unreacted P and L can be often present together in the same droplet. On complete evaporation of such droplets L will land on P leading to PL and this effect will lead to values of KA that are too high. However, it is argued that mostly accidental, weakly bonded, complexes will form and these will dissociate in the clean up stages (heated transfer capillary and CAD region). Thus only very small errors are expected due to this cause. (4) Some PL complexes may have bonding that is too weak in the gas phase even though they have KA values in solution that predict high solution PL yields. In this case the PL complexes may decompose in the clean up stages and not be observed with sufficient intensity in the mass spectrum. This will lead to KA values that are too low. The effect is expected for complexes that involve significant hydrophobic interaction that leads to high stability of the complex in solution but low stability in the gas phase. The titration method is not suited for such systems.

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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 (Me2CO) 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-Me2CO 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 Me2CO and then H2O. 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(H2O)3 2+ and Zn(H2O)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(Me2CO) 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 Me2CO 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.