Hydration Energies and Entropies for Mg²⁺, Ca²⁺, Sr²⁺, and Ba²⁺ from Gas-Phase Ion−Water Molecule Equilibria Determinations

Abstract

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.

Role of methyl-induced polarization in ion binding

“…2. The ΔG values obtained for the set of reactions involving water molecules and methanols, for which experimental data are available (33)(34)(35), are in quantitative agreement with experimental values (Table S1). The explicit inclusion of dispersion improves the performance of PBE0 significantly.…”

Thermochemistry of Non-Covalent Ion–Molecule Interactions

“…More recently, the GIBMS studies have been extended 66,67) and Fe 2+ . 68) Hydration complexes of the latter three metals have never been studied before, whereas the results for Ca 2+ and Sr 2+ agree well with previous studies conducted either by equilibrium measurements using HPMS 69) or by blackbody infrared radiative dissociation (BIRD). 70,71) However, because these are both thermal techniques, the smallest complex these methods are capable of studying is 6 and 5 water ligands, respectively.…”

Specific Ion Binding at Phospholipid Membrane Surfaces

“…In aqueous solution, the most stable hydration states for Ca 2+ are CWT = 6, 7, consistent with experimental hydration number. 38,39 The most stable bound state for Ca 2+ is at (CWT = 2, CLP = 4), where the total coordination number is 6. Other stable bound states are at CLP = 3, 4, 5 with total coordination number of 4 ∼ 6, which are 2 ∼ 4 kcal/mol higher than the global minimum (see Table 1).…”