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.

Water Self-Dissociation is Insensitive to Nanoscale Environments

Nanoconfinement effects on water dissociation and reactivity remain controversial, despite their importance to understand the aqueous chemistry at interfaces, pores, or aerosols. The pKw in confined environments has been assessed from experiments and simulations in a few specific cases, leading to dissimilar conclusions. Here, with the use of carefully designed ab initio simulations, we demonstrate that the energetics of bulk water dissociation is conserved intact to unexpectedly small length-scales, down to aggregates of only a dozen molecules or pores of widths below 2 nm. The reason is that most of the free-energy involved in water autoionization comes from breaking the O-H covalent bond, which has a comparable barrier in the bulk liquid, in a small droplet of nanometer size, or in a nanopore in the absence of strong interfacial interactions. Thus, dissociation free-energy profiles in nanoscopic aggregates or in 2D slabs of 1 nm width reproduce the behavior corresponding to the bulk liquid, regardless of whether the corresponding nanophase is delimited by a solid or a gas interface. The present work provides a definite and fundamental description of the mechanism and thermodynamics of water dissociation at different scales with broader implications on reactivity and self-ionization at the air-liquid interface.