Transport and spectroscopy of the hydrated proton: A molecular dynamics study

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Abstract
In order to study the microscopic nature of the hydrated proton and its transport mechanism, we have introduced a multi-state empirical valence bond model, fitted to ab-initio results [J. Phys. Chem. B 102, 4261 (1998) and references therein]. The model makes it possible to take into account an arbitrary number N of valence states for the system proton+water and the electronic ground-state is obtained by diagonalization of a N×N interaction matrix. The resulting force field 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 a preliminary path-integral calculation. In the light of the simulations, the mechanism of proton transfer is interpreted as the translocation of a privileged H5O2+ structure along the hydrogen bond network, with at any time a special O–H+–O bond, rather than a series of H3O++H2O→H2O+H3O+ reactions. The translocation of the special bond can be described as a diffusion process with a jump time of 1 ps on average and distributed according to a Poisson law. A time dependent correlation function analysis of the special pair relaxation yields two times scales, 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 (8×10−5 cm2/s) as well as the isotopic substitution effect (1.15), are in good agreement with experiment. The broad infrared absorption spectrum which characterizes the excess proton in liquid water is also computed and interpreted. The main contribution to the broad bands between 1000 and 1800 cm−1 is a combination of the bends and asymmetric O–H+ stretch of the H5O2+ complex. The continuum of absorption between 2000 and 3000 cm−1 is attributed to the interconversion between symmetric and asymmetric structures within a given special bond.