  Acid solutions exhibit a variety of complex structural and dynamical features
arising from the presence of multiple interacting reactive proton defects and
counterions. However, disentangling the transient structural motifs of proton
defects in the water hydrogen bond network and the mechanisms for their
interconversion remains a formidable challenge. Here, we use simulations
treating the quantum nature of both the electrons and nuclei to show how the
experimentally observed spectroscopic features and relaxation timescales can be
elucidated using a physically transparent coordinate that encodes the overall
asymmetry of the solvation environment of the proton defect. We demonstrate
that this coordinate can be used both to discriminate the extremities of the
features observed in the linear vibrational spectrum and to explain the
molecular motions that give rise to the interconversion timescales observed in
recent nonlinear experiments. This analysis provides a unified condensed-phase
picture of proton structure and dynamics that, at its extrema, encompasses
proton sharing and spectroscopic features resembling the limiting Eigen
[H$_{3}$O(H$_{2}$O)$_{3}$]$^{+}$ and Zundel [H(H$_{2}$O)$_{2}$]$^{+}$ gas-phase
structures, while also describing the rich variety of interconverting
environments in the liquid phase.
