  We present a detailed study of proton dynamics in the hydrogen-bonded
superprotonic conductor CsHSO4 from first-principles molecular dynamics
simulations, isolating the subtle interplay between the dynamics of the O--H
chemical bonds, the O...H hydrogen bonds, and the SO4 tetrahedra in promoting
proton diffusion. We find that the Grotthus mechanism of proton transport is
primarily responsible for the dynamics of the chemical bonds, whereas the
reorganization of the hydrogen-bond network is dominated by rapid angular hops
in concert with small reorientations of the SO4 tetrahedra. Frequent proton
jumping across the O--H...O complex is countered by a high rate of jump
reversal, which we show is connected to the dynamics of the SO4 tetrahedra,
resulting in a diminished CsHSO4/CsDSO4 isotope effect. We also find evidence
of multiple timescales for SO4 reorientation events, leading to distinct
diffusion mechanisms along the different crystal lattice directions. Finally,
we employ graph-theoretic techniques to characterize the topology of the
hydrogen-bond network and demonstrate a clear relationship between certain
connectivity configurations and the likelihood for diffusive jump events.
