Rate-limiting step of proton transport in liquid water

For an excess proton in liquid water at $300\,\mathrm{K}$, identify the rate-limiting step of structural (Grotthuss) diffusion, the relay of the proton from molecule to molecule: hydrogen-bond breaking or forming in the second solvation shell, or motion along the proton-transfer coordinate. An answer is a simulation with path-integral nuclei on a near-quantum-chemical potential that reproduces the measured proton diffusion coefficient (about $9.3 \times 10^{-5}\,\mathrm{cm}^2/\mathrm{s}$) and its H/D isotope effect and identifies the step from the trajectories.

Path-integral molecular dynamics on a coupled-cluster-quality potential reproducing diffusion and isotope effect, with a committor or rate analysis of the transfer events.