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(1,2) of structural diffusion' nearly two centuries ago. Subsequent explanations have refined this concept by invoking thermal hopping(3,4), proton tunnelling(5,6) or solvation effects(7). More recently, two main structural models have emerged for the hydrated proton. Eigen(8,9) proposed the formation of an H9O4+ complex in which an H3O+ core is strongly hydrogen-bonded to three H2O molecules. Zundel(10,11), meanwhile, supported the notion of an H5O2+ complex in which the proton is shared between two H2O molecules. Here we use ab initio path integral(12-14) 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 H9O4+ and H5O2+ occurring only in the sense 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'(15,16), 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.