  Imidazole is a promising anhydrous proton conductor with a high conductivity
comparable to that of water at a similar temperature relative to its melting
point. Previous theoretical studies of the mechanism of proton transport in
imidazole have relied either on empirical models or on ab initio trajectories
that have been too short to draw significant conclusions. Here, we present the
results of ab initio molecular dynamics simulations of an excess proton in
liquid imidazole reaching 1 nanosecond in total simulation time. We find that
the proton transport is dominated by structural diffusion, and the diffusion
constant of the proton defect is ~8 times higher than the self-diffusion of the
imidazole molecules. By using correlation function analysis, we decompose the
mechanism for proton transport into a series of first-order processes and show
that the proton transport mechanism occurs over three distinct time and length
scales. Although the mechanism at intermediate times is dominated by hopping
along pseudo one-dimensional chains, at longer times, the overall rate of
diffusion is limited by the reformation of these chains, thus providing a more
complete picture of the traditional, idealized Grotthuss structural diffusion
mechanism.
