Given the critical role of the aqueous excess proton in redox chemistry, determining its structure and the mechanism of its transport in water are intense areas of experimental and theoretical research. The ultrafast dynamics of the proton's hydration structure has made it extremely challenging to study experimentally. Using ultrafast broadband two-dimensional infrared spectroscopy, we show that the vibrational spectrum of the aqueous proton is fully consistent with a protonated water complex broadly defined as a Zundel-like HO motif. Analysis of the inhomogeneously broadened proton stretch two-dimensional lineshape indicates an intrinsically asymmetric, low-barrier O-H-O potential that exhibits surprisingly persistent distributions in both its asymmetry and O-O distance. This structural characterization has direct implications for the extent of delocalization exhibited by a proton's excess charge and for the possible mechanisms of proton transport in water.

Hydrogen bonds (H-bonds) can be interpreted as a classical electrostatic interaction or as a covalent chemical bond if the interaction is strong enough. As a result, short strong H-bonds exist at an intersection between qualitatively different bonding descriptions, with few experimental methods to understand this dichotomy. The [F-H-F]− ion represents a bare short H-bond, whose distinctive vibrational potential in water is revealed with femtosecond two-dimensional infrared spectroscopy. It shows the superharmonic behavior of the proton motion, which is strongly coupled to the donor-acceptor stretching and disappears on H-bond bending. In combination with high-level quantum-chemical calculations, we demonstrate a distinct crossover in spectroscopic properties from conventional to short strong H-bonds, which identify where hydrogen bonding ends and chemical bonding begins.

The local environmental sensitivity of infrared (IR) spectroscopy to a hydrogen-bonding structure makes it a powerful tool for investigating the structure and dynamics of excess protons in water. Although of significant interest, the line broadening that results from the ultrafast evolution of different solvated proton-water structures makes the assignment of liquid-phase IR spectra a challenging task. In this work, we apply a normal mode analysis using density functional theory of thousands of proton-water clusters taken from reactive molecular dynamics trajectories of the latest generation multistate empirical valence bond proton model (MS-EVB 3.2). These calculations are used to obtain a vibrational density of states and IR spectral density, which are decomposed on the basis of solvated proton structure and the frequency dependent mode character. Decompositions are presented on the basis of the proton sharing parameter δ, often used to distinguish Eigen and Zundel species, the stretch and bend character of the modes, the mode delocalization, and the vibrational mode symmetry. We find there is a wide distribution of vibrational frequencies spanning 1200-3000 cm for every local proton configuration, with the region 2000-2600 cm being mostly governed by the distorted Eigen-like configuration. We find a continuous red shift of the special-pair O⋯H⋯O stretching frequency, and an increase in the flanking water bending intensity with decreasing δ. Also, we find that the flanking water stretch mode of the Zundel-like species is strongly mixed with the flanking water bend, and the special pair proton oscillation band is strongly coupled with the bend modes of the central HO2+moiety.