Hydration energies and entropies for Mg2+, Ca2+, Sr2+, and Ba2+ from gas-phase ion-water molecule equilibria determinations

The sequential enthalpies Delta H(n-1,n)degrees free energies Delta G(n-1, n)degrees, and entropies Delta S-n-1,S- (n)degrees for the hydration reacti on M(H2O)(n-1)(2+) + H2O = M(H2O)(n)(2+) were determined in the gas phase f or M = Mg, Ca, Sr, Ba. The gas-phase ion hydrates were produced by electros pray, and the hydration equilibria were determined in a reaction chamber at tached to a mass spectrometer. The exothermicities of the (n - 1, n) reacti ons st low n (n = 1 to n = 5) are very high, and the corresponding equilibr ia require very high temperatures and could not be determined. For these lo w n, good theoretical results are available for Mg2+ and Ca2+ (Siegbahn and coworkers). A combination of the theoretical data with the experimental re sults (from n = 6 to n = 14) provides information on the inner and outer hy dration shell structure and energetics of the hydrates. Very good agreement is observed between the theoretical and experimental energies where they o verlap. 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 i nner shelf number may be as high as 8 or 9. The observed entropy changes ar e, in general, consistent with the assigned shell structures. In particular , there is a large change of Delta S-n-1,S- n, on transition from the inner (n = 6) to the outer (n = 7) shell for Mg, Ca, and Sr. The difference betw een the gas-phase total enthalpies Delta H(0, 14)degrees(Ca2+) - Delta H(0. 14)degrees(Mg2+) is within 3 kcal/mol of the total hydration difference Del ta H(h)degrees(Ca2+) - Delta H(h)degrees(Mg2+) for liquid water. A similar result is obtained also for the hydration free energies. Extension of the d eterminations to ligands that model bending and coordination in biocomplexe s of Mg2+ and Ca2+ is discussed.