The nature of the hydrated excess proton in water

Explanations for the anomalously high mobility of protons in liquid water began with Grotthuss's idea, of `structural diffusion' nearly two centuries ago. Subsequent explanations have refined this concept by invoking thermal hopping, , proton tunnelling, or solvation effects. More recently, two main structural models have emerged for the hydrated proton. Eigen, proposed the formation of an H<sub>9</sub>O<sub>4</sub><sup>+</sup> complex in which an H<sub>3</sub>O<sup>+</sup> core is strongly hydrogen-bonded to three H<sub>2</sub>O molecules. Zundel, , meanwhile, supported the notion of an H<sub>5</sub>O<sub>2</sub><sup>+</sup> complex in which the proton isshared between two H<sub>2</sub>O molecules. Here we use ab initio path integral simulations to address this question. These simulations include time-independent equilibrium thermal and quantum fluctuations of all nuclei, and determine interatomic interactions from the electronic structure. We find that the hydrated proton forms a fluxional defect in the hydrogen-bonded network, with both H<sub>9</sub>O<sub>4</sub><sup>+</sup> and H<sub>5</sub>O<sub>2</sub><sup>+</sup> occurring only in thesense of `limiting' or `ideal' structures. The defect can become delocalized over several hydrogen bonds owing to quantum fluctuations. Solvent polarization induces a small barrier to proton transfer, which is washed out by zero-point motion. The proton can consequently be considered part of a `low-barrier hydrogen bond', , in which tunnelling is negligible and the simplest concepts of transition-state theory do not apply. The rate of proton diffusion is determined by thermally induced hydrogen-bond breaking in the second solvation shell.