Evaluation of Hydration Enthalpies of Monatomic Cations by Considering Both Long-Range and Short-Range Interactions

The standard hydration enthalpy, ΔH°_hyd, of a monatomic cation was calculated as the sum of (1) the enthalpy due to the long-range interaction between a hydrated ion and bulk water, ΔH°_LR, (2) the enthalpy due to the short-range interaction between the ion and water molecules in the first hydration shell, ΔH°_SR, and (3) the enthalpy due to the ligand field stabilization of an ion, ΔH°_LF, which arises for a transition-metal ion. ΔH°_LR was estimated on the basis of the Born theory assuming the radius of the hydrated ion as the interatomic distance between the ion and the oxygen atom of a water molecule in the first hydration shell, r_M-O, determined experimentally. ΔH°_SR was evaluated on the basis of the donor−acceptor interaction between an ion and a water molecule coordinating to the ion, which was evaluated by the molecular orbital calculation of a monohydrated cluster of an ion combined with the Mulliken population analysis. ΔH°_LF was calculated on the basis of the crystal field theory. Hydration enthalpies of 48 monatomic cations thus calculated agreed well with those observed experimentally.