Multi-State Reactive Molecular DynamicsSimulations of Proton Diffusion in WaterClusters and in Bulk

The molecular mechanics with proton transfer (MMPT) force field is combined withmulti state adiabatic reactive molecular dynamics (MS-ARMD) to describe protontransport in the condensed phase. Parametrization for small protonated water clustersbased on electronic structure calculations at the MP2/6-311+G(2d,2p) level of theoryand refinement by comparing with infrared spectra for protonated water tetramer yieldsa force field which faithfully describes minimum energy structures of small protonatedwater clusters. In protonated water clusters up to (H2O)100H+the proton hopping rateis around 100 hops/ns. Convergence of such rates is already found for 21≤n≤31and no further speedup in bulk water is found. This indicates that bulk-like behaviourrequires solvation of a Zundel motif by∼25 water molecules which corresponds tothe second solvation sphere. For smaller cluster sizes the number of available states,i.e. the number of proton acceptors, is too small and slows down proton transfer rates. The cluster simulations confirm that the excess proton is typically located on the surface.  The free energy surface as a function of the weights of the two lowest statesand a configurational parameter suggest that the “special pair” plays a central role inrapid proton transport. The barriers between this minimum energy structure and theZundel and Eigen minima are sufficiently low (∼1 kcal/mol,consistent with recentexperiments andcommensurate with a hopping rate of∼100/ns or 1 every 10 ps)which lead to a highly dynamical environment. These findings are also consistent withrecent experiments which find that Zundel-type hydration geometries are prevalent inbulk water.