Extended Data Fig. 4: Random walk modeling of the diffusion coefficient.

(A) Stable proton hopping time-correlation function \(1-C{ij}(t)=1-\langle pi(0)pj(t)\rangle\) (see definition in ref. 59) from our revPBE0-D3/TRPMD H + ,H2O simulation at 300 K. Shaded regions show the 95% confidence interval derived from 20 independent trajectories. (B) Distribution of Oa-Ob distances in Eigen-like (3a,4b) (green) and Zundel-like (3a,3b) (purple) H-bond arrangements from our revPBE0-D3/TRPMD H + ,H2O simulation at 300 K. Shaded regions show the 95% confidence interval derived from 20 independent trajectories. (C) Distribution of (Oa-Ob)2 squared distances in our revPBE0- D3/TRPMD H + ,H2O simulation at 300 K. Shaded regions show the 95% confidence interval derived from 20 independent trajectories.