The Solvation Structure of Na+ and K+ in Liquid Water Determined from High Level ab Initio Molecular Dynamics Simulations

Knowledge of the hydration structure of Na+ and K+ in the liquid phase has wide ranging implications in the field of biological chemistry. Despite numerous experimental and computational studies, even basic features such as the coordination number of these alkali ions in liquid water, thought to play a critical role in selectivity, continue to be the subject of intensive debates. Simulations based on accurate potential energy surfaces offer one approach to resolve these issues by providing reliable results on ion hydration. In this article, we report the results from molecular dynamics simulations of Na+ and K+ hydration based on a novel and rigorous strategy designed to overcome the challenges of QM/MM simulations of solvent molecules in the liquid phase. In this method, which we call Flexible Inner Region Ensemble Separator (FIRES), the ion and a fixed number of nearest water molecules form a dynamical and flexible inner region that is represented with high level ab initio quantum mechanical (QM) methods, while the water molecules from the surrounding bulk form an outer region that is represented by a polarizable molecular mechanical (MM) force field. Simulations yield rigorously correct thermodynamic averages as long as the solvent molecules in the flexible inner and outer regions are not allowed to exchange. Extensive FIRES simulations were carried out based on a QM/MM model in which the Na+ or K+ ion and the 12 nearest water molecules were represented by high level ab initio methods (RI-MP2/def2-TZVP and density functional theory with PBE/def2-TZVP), while the surrounding MM water molecules were represented by the polarizable SWM4-NDP potential. On the basis of these results, the ion coordination numbers are estimated to be within the range of 5.7-5.8 for Na+ and 6.9-7.0 for K+.