Theoretical study of H+ translocation along a model proton wire

The mechanism of proton translocation along linear hydrogen-bonded water chains is investigated. Classical and discretized Feynman path integral molecular dynamics simulations are performed on protonated linear chains of 4, 5, and 9 water molecules. The dissociable and polarizable water model PM6 of Stillinger and co-workers is used to represent the potential energy surface of the systems. The simulations show that quantum and thermal effects are both important because the height of the barriers opposing proton transfer are strongly coupled to the configuration of the chain, which is, in turn, affected by the presence of an excess proton. For characterization of the quantum effects, the energy levels of the hydrogen nucleus located at the center of a protonated tetrameric water chain are calculated by solving the Schroedinger equation for an ensemble of configurations which were generated with path integral simulations. Analysis shows that the first excitation energies are significantly larger than the thermal energy k(B)T and that quantum effects are dominated by the zero-point energy of the proton. The quantum correlations between the different proton nuclei are found to be negligibly small, suggesting that an effective one-particle description could be valid. Potential of mean force surfaces for proton motion in relation to the donor-acceptor separation are calculated with classical and path integral simulations for tetrameric and pentameric water chains. The mechanism for long-range proton transfer is illustrated with a simulation of a hydrogen-bonded chain of nine water molecules, During the simulation, cooperative fluctuations which modulate the asymmetry of the chain enable the spontaneous translocation of protons over half of the length of the chain.