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

Abstract

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(+).

Absolute proton hydration free energy, surface potential of water, and redox potential of the hydrogen electrode from first principles: QM/MM MD free-energy simulations of sodium and potassium hydration

“…7 and 8 as well as Table I. For the QM/MM simulations, they are in line with those of previous experimental 269,270 and theoretical 155,219 studies reported in the literature (see also other references in Table I). …”

“…The QM/MM MD simulations rely on the quantum-mechanical charge field (QMCF) approach, 158,159 which belongs to the family of adaptive QM/MM methods 148,149,160 and has been applied with success in the past to investigations of solvated ions, 153,154 molecules, 161,162 coordination complexes, 163,164 and biomolecular systems. 165,166 Single-determinantal approaches such as ab initio HartreeFock 167,168 (HF) or DFT 169,170 have a limited accuracy/reliability 120,[123][124][125][126][127]155,[171][172][173][174][175][176] in the description of hydration phenomena. Thus, a correlated ab initio method is employed here to describe the QM subsystem (ion and first hydration shell), namely, resolution-of-identity secondorder Møller-Plesset perturbation 177,178 (RIMP2).…”

“…Although the MP2 level of theory is only the first scheme in a hierarchy of approaches to account for electron-correlation effects, 179 it has been shown to provide a good compromise between accuracy and computational effort in the context of ion-water interactions. 66,67,77,78,130,155,180,181 Recent simulations of the bulk water dynamics at this level of theory [123][124][125][126][127] also suggest that it is adequate for the representation of the liquid properties.…”

“…For example, the adaptive QM/MM studies of Refs. 155 and 182 characterized the solvation structure at the MP2 level, 155 but could calculate relative ionic hydration free energies at the DFT level only. 182 For this reason, a different approach is employed here.…”

Computer simulations of alkali-acetate solutions: Accuracy of the forcefields in difference concentrations

“…Ab initio molecular dynamics of ions in solutions can be performed, and many such studies have been reported (e.g., [48][49][50][51][52] ). Unfortunately, such simulations are limited to small systems and short periods.…”