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, Delta(h)G, 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 [J. Chem. Phys. 110, 1329 (1999)]. This method allows calculation of Delta(h)G 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 Moller-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 K-c=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 K-c=2.6 (interpolated at 0.535 g/cm(3)) 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. (C) 2003 American Institute of Physics.