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Here we analyze cryogenic ion vibrational spectra of tagged protonated formic acid (PFA) with electronic structure and anharmonic vibrational calculations to establish the isomers generated by electrospray ionization (ESI) followed by buffer gas cooling to ∼25 K. Two isomers are identified (the trans form (E,Z) and the cis form (E,E)) and generated in comparable abundance despite the fact that the calculated E,E structure lies 6.40 kJ mol -1 above the E,Z form. A large (∼60 kJ mol -1 ) barrier separates them such that the E,E form can be kinetically trapped upon cooling in the ion trap. The anticooperativity between the H-bonds of the OH groups is explored by measuring the shift in the D 2 -bound OH fundamental when a second D 2 is attached. Both isomers are observed in the N 2 -tagged counterparts, displaying the expected red-shifted OH bands. These results indicate that ESI generates both isomers and both must be considered when analyzing cluster spectra based on the PFA core ion.

The isomerization pathway between the energetically low-lying Zundel and Eigen isomers of the protonated water hexamer was investigated using high-level ab initio calculations including a treatment of zero-point corrections. On the basis of these calculations, the Zundel-Eigen isomerization was found to proceed through a stable intermediate isomer, which consists of a four-membered ring with two single acceptor water molecules. The inclusion of vibrational zero-point energy is shown to be important for accurately establishing the relative energies of the three relevant isomers involved in the Zundel-Eigen isomerization. Diffusion Monte Carlo calculations including anharmonic vibrational effects show that all three isomers of H + (H 2 O) 6 and D + (D 2 O) 6 have well-defined structures. The energetic ordering of the three isomers changes upon deuteration. The implications of these results for the vibrational spectra of H + (H 2 O) 6 and D + (D 2 O) 6 are also discussed.

The fundamental transitions that contribute to the diffuse OH stretching spectrum of water are known to increase in width and intensity with increasing red shift from the free OH frequency. In contrast, the profile of the higher-energy combination band involving the OH stretching and the intramolecular HOH bending modes displays a qualitatively different spectral shape with a much faster falloff on the lower-energy side. We elucidate the molecular origin of this difference by analyzing the shapes of the combination bands in the IR spectra of cryogenically cooled H 3 O + (H 2 O) 20 and D 3 O + (D 2 O) 20 clusters. The difference in the shapes of the bands is traced to differences in the dependence of their transition dipole matrix elements on the hydrogen-bonding environment. The fact that individual transitions across the combination band envelope have similar intensities makes it a useful way to determine the participation of various sites in extended H-bonding networks.

In the presence of a halide ion, hypohalous acids can adopt two binding motifs upon formation of the ion-molecule complexes [XHOY] - (X, Y = Cl, Br, I): a hydrogen (HB) bond to the acid OH group and a halogen (XB) bond between the anion and the acid halogen. Here we isolate the X-bonded Cl - ·IOH ion-molecule complex by collisions of I - ·(H 2 O) n clusters with HOCl vapor and measure its vibrational spectrum by IR photodissociation of the H 2 -tagged complex. Anharmonic analysis of its vibrational band pattern reveals that formation of the XB complex results in dramatic lowering of the HOI bending fundamental frequency and elongation of the O-I bond (by 168 cm -1 and 0.13 Å, respectively, relative to isolated HOI). The frequency of the O-I stretch (estimated 436 cm -1 ) is also encoded in the spectrum by the weak v = 0 → 2 overtone transition at 872 cm -1 .

The structure of hydrogen bonded networks is intimately intertwined with their dynamics. Despite the incredibly wide range of hydrogen bond strengths encountered in water clusters, ion-water clusters, and liquid water, we demonstrate that the previously reported correlation between the change in the equilibrium bond length of the hydrogen bonded OH covalent bond and the corresponding shift in its harmonic frequency in water clusters is much more broadly applicable. Surprisingly, this correlation describes the ratios for both the equilibrium OH bond length/harmonic frequency and the vibrationally averaged bond length/anharmonic frequency in water, hydronium water, and halide water clusters. Consideration of harmonic and anaharmonic data leads to a correlation of -19 ± 1 cm -1 /0.001 Å. The fundamental nature of this correlation is further confirmed through the analysis of ab initio Molecular Dynamics (AIMD) trajectories for liquid water. We demonstrate that this simple correlation for both harmonic and anharmonic systems can be modeled by the response of an OH bond to an external field. Treating the OH bond as a Morse oscillator, we develop analytic expressions, which relate the ratio of the shift in the vibrational frequency of the hydrogen-bonded OH bond to the shift in OH bond length, to parameters in the Morse potential and the ratio of the first and second derivatives of the field-dependent projection of the dipole moment of water onto the hydrogen-bonded OH bond. Based on our analysis, we develop a protocol for reconstructing the AIMD spectra of liquid water from the sampled distribution of the OH bond lengths. Our findings elucidate the origins of the relationship between the molecular structure of the fleeting hydrogen-bonded network and the ensuing dynamics, which can be probed by vibrational spectroscopy.

Near-infrared spectroscopy measurements are presented for protonated water clusters, H + (H 2 O) n , in the size range of n = 1-8. Clusters are produced in a pulsed-discharge supersonic expansion, mass selected, and studied with infrared laser photodissociation spectroscopy in the regions of 3600-4550 and 4850-7350 cm -1 . Although there is some variation with cluster size, the main features of these spectra are a broad absorption near 5300 cm -1 , a sharp doublet near 7200 cm -1 , as well as a structured absorption near 4100 cm -1 for n ≥ 2. The vibrational patterns measured for the hydronium, Zundel, and Eigen ions are compared to those predicted by different forms of anharmonic theory. Second-order vibrational perturbation theory (VPT2) and a local mode treatment of the OH stretches both capture key aspects of the spectra but suffer understandable deficiencies in the quantitative description of band positions and intensities.

Vibrational spectroscopy of the protonated water trimer provides a stringent constraint on the details of the potential energy surface (PES) and vibrational dynamics governing excess proton motion far from equilibrium. Here we report the linear spectrum of the cold, bare H + (H 2 O) 3 ion using a two-color, IR-IR photofragmentation technique and follow the evolution of the bands with increasing ion trap temperature. The key low-energy features are insensitive to both D 2 tagging and internal energy. The D 2 -tagged D + (D 2 O) 3 spectrum is reported for the first time, and the isotope dependence of the band pattern is surprisingly complex. These spectra are reproduced by large-scale vibrational configuration interaction calculations based on a new full-dimensional PES, which treat the anharmonic effects arising from large amplitude motion. The results indicate such extensive mode mixing in both isotopologues that one should be cautious about assigning even the strongest features to particular motions, especially for the absorptions that occur close to the intramolecular bending mode of the water molecule.