An Extended Empirical Valence Bond Model for Describing Proton Mobility in Water

In order to study the microscopic nature of the hydrated proton and its transport mechanism, we have introduced a multistate empirical valence bond model, fitted to ab initio results. This model was applied to the study, at low computational cost, of the structure and dynamics of an excess proton in liquid water. The quantum character of the proton is included by means of an effective parametrization of the model using preliminary path-integral calculations. The mechanism of proton transfer is interpreted as the translocation of a special O–H⁺–O bond along the hydrogen network, i.e., a series of reactions of the form H₅O₂⁺ + H₂O ⇌ H₂O + H₅O₂⁺, rather than H₃O⁺ + H₂O → H₂O + H₃O⁺ as usually described. The translocation of the special bond can be described as a diffusion process with a jump time of 1 ps. A time-dependent correlation function analysis of the special pair relaxation yields two timescales, 0.3 and 3.5 ps. The first time is attributed to the interconversion between a delocalized (H₅O₂⁺-like) and a localized (H₉O₄⁺-like) form of the hydrated proton within a given special pair. The second one is the relaxation time of the special pair, including return trajectories. The computed diffusion constant, as well as the isotopic substitution effect, are in good agreement with experiment. The hydration structure around the excess proton is discussed in terms of various radial distribution functions around the water molecules involved in the special pair and those in the first solvation shell. The hydrogen-bond-dynamics which accompanies the translocation process is studied statistically. The “Moses mechanism” proposed by Noam Agmon for proton mobility in water is partially verified by our simulations.