Quantum and classical simulations of an excess proton in water

ZundEig: The Structure of the Proton in Liquid Water from Unsupervised Learning

The structure of the excess proton in liquid water has been the subject of lively debate on both experimental and theoretical fronts for the last century. Fluctuations of the proton are typically interpreted in terms of limiting states referred to as the Eigen and Zundel species. Here, we put these ideas under the microscope, taking advantage of recent advances in unsupervised learning that use local atomic descriptors to characterize environments of acidic water combined with advanced clustering techniques. Our agnostic approach leads to the observation of only one charged cluster and two neutral ones. We demonstrate that the charged cluster involving the excess proton is best seen as an ionic topological defect in water's hydrogen bond network, forming a single local minimum on the global free-energy landscape. This charged defect is a highly fluxional moiety, where the idealized Eigen and Zundel species are neither limiting configurations nor distinct thermodynamic states. Instead, the ionic defect enhances the presence of neutral water defects through strong interactions with the network. We dub the combination of the charged and neutral defect clusters as ZundEig, demonstrating that the fluctuations between these local environments provide a general framework for rationalizing more descriptive notions of the proton in the existing literature.

A polarizable multistate empirical valence bond model for proton transport in aqueous solution

A multistate empirical valence bond model for proton transport in water, which explicitly includes solvent polarization, is presented. Polarization is included for each valence-bond state via induced point dipoles, and the model is parametrized to be used with an effective path integral derived potential surface, so as to include quantum effects of the transferring proton. The new model is shown to reproduce ab initio geometries and energetics for small protonated clusters. It is also shown that the new model gives a diffusion constant for the excess proton in water, which is in good agreement with experiment, and that the qualitative features of ab initio path integral simulations [D. Marx, M. E. Tuckerman, J. Hutter, and M. Parrinello, Nature (London) 397, 601 (1999)] are well reproduced.