Reaction Rate Theory in Coordination Number Space: An Application to Ion Solvation

Understanding reaction mechanisms in many chemical and biological processes requires application of rare event theories. In these theories, an effective choice of a reaction coordinate to describe a reaction pathway is essential. To this end, we study ion solvation in water using molecular dynamics simulations and explore the utility of coordination number (n = number of water molecules in the first solvation shell) as the reaction coordinate. Here, we compute the potential of mean force (W(n)) using umbrella sampling, predicting multiple metastable n-states for both cations and anions. With increasing ionic size, we find these states become more stable and structured for cations when compared to anions. We have extended transition state theory (TST) to calculate transition rates between n states. TST overestimates the rate constant due to solvent-induced barrier recrossings that are not accounted for. We correct the TST rates by calculating transmission coefficients using the reactive flux method. This approach enables a new way of understanding rare events involving coordination complexes.