The dynamics and energetics of an excess proton in bulk phase water are examined computationally with a special emphasis on a quantum-dynamical treatment of the nuclear motion. The potential model used, the recently developed multistate empirical valence bond (MS-EVB) approach [U. W. Schmitt and G. A. Voth, J. Phys. Chem. B 102, 5547 (1998)], is also further refined and described in more detail. The MS-EVB model takes into account the interaction of an exchange charge distribution of the charge-transfer complex with the polar solvent, which qualitatively changes the nature of the solvated complex. Classical and quantum molecular dynamics simulations of the excess proton in bulk phase water reveal that quantization of the nuclear degrees of freedom results in an increased stabilization of the solvated H5O2+ (Zundel) cation relative to the H9O4+ (Eigen) cation, though the latter is still more stable, and that a species intermediate between the two also exists. The quantum proton transport rate, which is evaluated by the centroid molecular dynamics approach, is found to be on the order of two times faster compared to a purely classical treatment of the system and in good agreement with the experimental value. Calculation of the hydrogen-bonding lifetime beyond the first solvation shell of the excess proton reveals a similar quantum enhancement factor compared to the classical regime.

Building on the previously developed multistate empirical valence bond model [U. W. Schmitt and G. A. Voth, J. Chem. Phys 111, 9361 (1999)] for the dynamics and energetics of an excess proton in bulk phase water, a second generation model is described. This model is shown to produce similar dynamic and structural properties to the previous model, while allowing for the use of the full hydronium charge. This characteristic of the model is required for its implementation in a host of realistic applications beyond bulk water. An improved state selection algorithm is also presented, resulting in a significantly reduced energy drift during microcanonical molecular dynamics simulations. The unusually high self diffusion constant of an excess proton in water due to the proton hopping (Grotthuss) process is observed in the simulation data and is found to be quantitatively in the same range as the experimental value if a quantum correction is taken into consideration. Importantly, a more complete analysis of proton transport process is also presented.

By virtue of an accurate interaction model, the equilibrium and dynamical properties of an excess proton in aqueous systems are studied, in which the water and excess proton are confined to hydrophobic cylindrical channels. Solvation structures of the excess proton and its mobility along the channel are considered as a function of the channel radius. It is found that when the aqueous proton systems are sufficiently constricted there is a substantial increase in the diffusion of the excess proton charge accompanied by a decrease in the diffusion of water molecules along the channel. Such systems present clear evidence for the possible existence of "proton wires."

The vibrational properties of the hydrated proton and deuteron in bulk phase water and deuterated water are investigated spectroscopically and computationally. Mid-infrared spectra of aqueous acid solutions are measured by attenuated total reflectance-Fourier transform IR spectroscopy and compared with pure water and salt/counterion spectra to extract high-quality hydrated proton spectra at a series of concentrations. Multistate empirical valence bond simulations of the excess proton in bulk phase water are also performed, allowing the autocorrelation function of the time derivative of the dipole moment, and hence the power spectrum of the hydrated proton, to be evaluated. The experimental and theoretical spectra are found to be in very good agreement. Normal mode analysis of the bulk phase simulation data allows definitive assignment of the spectrum. The associated motions are found to be represented by both Eigen and Zundel forms of the hydrated proton.

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