Decoding the spectroscopic features and timescales of aqueous proton defects

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.