Hydration energies of divalent beryllium and magnesium ions: An ab initio molecular orbital study

Ab initio molecular orbital calculations have been used to investigate contributions of water molecules in the first and second coordination shells to the overall hydration energy of divalent beryllium and magnesium cations. Enthalpy and free energy changes at 298 K have been calculated at a variety of computational levels for the reactions M(2+) + [H2O](p) --> M(2+) . nH(2)O . mH(2)O, where M = Be or Mg, [H2O](p) (p = 2, 4, 6, 8; p = n + m) are water clusters, and M(2+) . nH(2)O . mH(2)O are ion-water complexes with n and m water molecules in the first and second coordination shells, respectively. These reactions involve the disruption of the water cluster and naturally include the competitive effects of ion-water and water-water interactions inherent in the hydration process. At the MP2(FULL)/6-311++G**//RHF/6-31G* computational level, the values of Delta G(298) for the reactions which complete the first hydration shells, Be2+ + [H2O](4) --> Be2+ . 4H(2)O and Mg2+ + [H2O](6) --> Mg2+ . 6H(2)O, are -352.0 and -266.7 kcal/mol, accounting for 61.2% and 60.7% of the experimental free energies of hydration of Be2+ and Mg2+. Reactions that incorporate two additional water molecules into a second hydration shell only change Delta G(298) by -43.0 and -24.2 kcal/mol, whereas the values of Delta G(298) for the corresponding reactions that incorporate the first two water molecules in the primary hydration shell are -244.6 and -135.2 kcal/mol, respectively. The calculated values of Delta G(298) for the formation of the complexes Be2+ . 4H(2)O . 4H(2)O and Mg2+ . 6H(2)O . 2H(2)O from eight-water clusters account for approximately 73.2% and 66.2% of the overall free energies for Be2+ and Mg2+, respectively, but convergence toward the experimental hydration energies will be quite slow as additional water molecules are added to the outer hydration shells. This is consistent with the concept of the importance of long-range interactions to the hydration energy.