| Abstract
| - Ab initio molecular orbital calculations have been usedto investigate contributions of water molecules in thefirst and second coordination shells to the overall hydration energy ofdivalent beryllium and magnesiumcations. Enthalpy and free energy changes at 298 K have beencalculated at a variety of computationallevels for the reactions M2+ +[H2O]p →M2+·nH2O·mH2O,where M = Be or Mg, [H2O]p(p = 2, 4, 6, 8;p = n + m) are water clusters, andM2+·nH2O·mH2Oare ion−water complexes with n and m watermoleculesin the first and second coordination shells, respectively. Thesereactions involve the disruption of the watercluster and naturally include the competitive effects of ion−waterand water−water interactions inherent inthe hydration process. At theMP2(FULL)/6-311++G**//RHF/6-31G* computational level, thevalues ofΔG298 for the reactions which complete thefirst hydration shells, Be2+ +[H2O]4 →Be2+·4H2O and Mg2++[H2O]6 →Mg2+·6H2O, are −352.0 and −266.7kcal/mol, accounting for 61.2% and 60.7% of theexperimentalfree energies of hydration of Be2+ andMg2+. Reactions that incorporate two additionalwater molecules intoa second hydration shell only change ΔG298 by−43.0 and −24.2 kcal/mol, whereas the values ofΔG298 forthe corresponding reactions that incorporate the first two watermolecules in the primary hydration shell are−244.6 and −135.2 kcal/mol, respectively. The calculatedvalues of ΔG298 for the formation of thecomplexesBe2+·4H2O·4H2O andMg2+·6H2O·2H2O fromeight-water clusters account for approximately 73.2% and66.2% of the overall free energies for Be2+ andMg2+, respectively, but convergence toward theexperimentalhydration energies will be quite slow as additional water molecules areadded to the outer hydration shells.This is consistent with the concept of the importance oflong-range interactions to the hydration energy.
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