Stochastic Model of Solvent Exchange in the First Coordination Shell of Aqua Ions

Ion microsolvation is a basic, yet fundamental, process of ionicsolutions underlying many relevant phenomena in either biological ornanotechnological applications, such as solvent reorganization energy, iontransport, catalytic activity, and so on. As a consequence, it is a topic of extensiveinvestigations by various experimental techniques, ranging from X-ray diffractionto NMR relaxation and from calorimetry to vibrational spectroscopy, andtheoretical approaches, especially those based on molecular dynamics (MD)simulations. The conventional microscopic view of ion solvation is usuallyprovided by a"static"cluster model representing thefirst ion-solventcoordination shell. Despite the merits of such a simple model, however, ioncoordination in solution should be better regarded as a complex population ofdynamically interchanging molecular configurations. Such a more comprehen-sive view is more subtle to characterize and often elusive to standard approaches. In this work, we report on an effectivecomputational strategy aiming at providing a detailed picture of solvent coordination and exchange around aqua ions, thus includingthe main structural, thermodynamic, and dynamic properties of ion microsolvation, such as the most probablefirst-shell complexstructures, the corresponding free energies, the interchanging energy barriers, and the solvent-exchange rates. Assuming the solventcoordination number as an effective reaction coordinate and combining MD simulations with enhanced sampling and master-equation approaches, we propose a stochastic model suitable for properly describing, at the same time, the thermodynamics andkinetics of ion-water coordination. The model is successfully tested toward various divalent ions (Ca2+,Zn2+,Hg2+, and Cd2+)inaqueous solution, considering also the case of a high ionic concentration. Results show a very good agreement with those issuingfrom brute-force MD simulations, when available, and support the reliable prediction of rare ion-water complexes and slow waterexchange rates not easily accessible to usual computational methods.