Hydration free energy and potential of mean force for a model of the sodium chloride ion pair in supercritical water with ab initio solute–solvent interactions

The free energy of hydration, ΔhG, and the potential of mean force (PMF) of a quantum-mechanical (QM)–molecular mechanical (MM) model of the NaCl ion pair at 973 K with 0.535 g/cm3 has been calculated using the ab initio/classical free-energy perturbation (ABC-FEP) method proposed by Wood et al. [J. Chem. Phys. 110, 1329 (1999)]. This method allows calculation of ΔhG and the PMF of a QM-MM model in which Na+-Cl−, Na+-H2O, and Cl−-H2O interactions are calculated by ab initio QM methods and only the H2O-H2O interactions are calculated by a MM model [Rick, Stuart, and Berne, J. Chem. Phys. 101, 6141 (1994)]. The only simulations required are of an approximate MM model. The free energy of the QM-MM model is obtained from a relatively small number of QM energy calculations via free-energy perturbation theory. These QM energies are obtained by calculating pair-wise interactions at the second-order Møller–Plesset/ 6-311++G(3df,3pd) level, and multibody interactions at the B3LYP/ 6-311++G(3df,3pd) level. The PMF predicts an association constant, log Kc=2.3±0.3, for the NaCl ion pair. This compares favorably with the experimental value of Quist and Marshall [J. Phys. Chem. 72, 684 (1968)], log Kc=2.6 (interpolated at 0.535 g/cm3) and demonstrates the ability of the ABC-FEP method to predict the PMF and the association constant of an ion pair. There are important contributions to the PMF from non-pairwise-additive contributions to the Na+-Cl− interaction. While previous calculations have accounted for these non-pairwise-additive contributions through effective pairwise-additive models, the ABC-FEP method includes them exactly, within the accuracy of an ab initio calculation.