  In this work a series of analyses are performed on ab initio molecular
dynamics (AIMD) simulations of a hydrated excess proton in water to quantify
the relative occurrence of concerted hopping events and <span>rattling</span>
events, and thus to further elucidate the hopping mechanism of proton transport
in water. Contrary to results reported in certain earlier papers, the new
analysis finds that concerted hopping events do occur in all simulations, but
that the majority of events are the product of proton rattling, where the
excess proton will rattle between two or more waters. The results are
consistent with the proposed <span>special-pair dance</span> model of the
hydrated excess proton, wherein the acceptor water molecule for the proton
transfer will quickly change (resonate between three equivalent special pairs)
until a decisive proton hop occurs. To remove the misleading effect of simple
rattling, a filter was applied to the trajectory such that hopping events that
were followed by back hops to the original water are not counted. A steep
reduction in the number of multiple hopping events is found when the filter is
applied, suggesting that many multiple hopping events that occur in the
unfiltered trajectory are largely the product of rattling, contrary to prior
suggestions. Comparing the continuous correlation function of the filtered and
unfiltered trajectories, we find agreement with experimental values for the
proton hopping time and Eigen-Zundel interconversion time, respectively.
