Simple Two-Body Cation−Water Interaction Potentials Derived from ab Initio Calculations. Comparison to Results Obtained with an Empirical Approach

Abstract

Ab initio calculations were performed on M(H2O)n systems, M being Li+, Na+, K+, Be2+, Mg2+, or Ca2+, with n = 1, 2, 4, or 6. For the most hydrated systems, parameters for the effective Lennard-Jones interaction between the cation and the water molecules were determined, so as to reproduce ab initio results. In order to compare our results to those obtained previously by J. Åqvist with a purely empirical approach, water−water interactions were assumed to be given by the TIP3P model. Different forms for the effective two-body interaction potential were tested. The best fits of ab initio data were obtained with a smooth r-7 repulsive and a classical r-4 attractive term, in addition to standard Coulombic interactions. Though better fits were obtained for alkaline cations than for alkaline-earth ones, only Be2+ obviously requires a more complicated form of the potential energy function.The corresponding parameters were tested with molecular dynamics simulations of cations in water solutions and with hydration free energy difference calculations, using the thermodynamic perturbation approach. Radial distribution functions consistent with experimental data were obtained for all cations. Free energy differences are obviously much more challenging. The most accurately reproduced value is the difference between the hydration free energies of Na+ and K+. This result is likely to be significant since effective interaction energies between Na+ or K+ and water molecules as obtained in Åqvist's and in the present work are found to be very similar, despite the fact that the corresponding sets of parameters were determined with completely different approaches.