Resolving Heterogeneous Dynamics of Excess Protons in Aqueous Solution with Rate Theory

Rate theories have found great utility across the chemical sciences by providing a physically transparent way to analyze dynamical processes. Here we demonstrate the benefits of using transition state theory and Marcus theory to study the rate of proton transfer in HCl solutions. By using long ab initio molecular dynamics simulations, we show that good agreement is obtained between these two different formulations of rate theory and how they can be used to study the pathways and lifetime of proton transfer in aqueous solution. Since both rate theory formulations utilize identical sets of molecular data, this provides a self-consistent theoretical picture of the rates of aqueous phase proton transfer. Specifically, we isolate and quantify the rates of proton transfer, ion-pair dissociation, and solvent exchange in concentrated HCl solutions. Our analysis predicts a concentration dependence to both proton transfer and ion-pairing. Moreover, our estimate of the lifetime for the Zundel species is 0.8 and 1.3 ps for 2 M and 8 M HCl, respectively. We demonstrate that concentration effects can indeed be quantified through the combination of state-of-the-art simulation and theory and provides a picture of the important correlations between the cation (hydronium) and the counterion in acid solutions.