The computer simulation of proton transport in water

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 ${\mathrm{H}}_{\mathrm{5}}{\mathrm{O}}_2^{+}$ (Zundel) cation relative to the ${\mathrm{H}}_{\mathrm{9}}{\mathrm{O}}_4^{+}$ (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.