Snapshots of Proton Accommodation at a Microscopic Water Surface: Understanding the Vibrational Spectral Signatures of the Charge Defect in Cryogenically Cooled H + (H 2 O) n=2-28 Clusters Joseph A. Fournier, Conrad T. Wolke, and Mark A. Johnson* Sterling Chemistry Laboratory, Yale University, New Haven, Connecticut 06520, United States Tuguldur T. Odbadrakh and Kenneth D. Jordan* Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15620, United States Shawn M. Kathmann and Sotiris S. Xantheas* Physical Sciences Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, Richland, Washington 99352, United States * S Supporting Information ABSTRACT: We review the role that gas-phase, size-selected protonated water clusters, H + (H 2 O) n , have played in unraveling the microscopic mechanics responsible for the spectroscopic behavior of the excess proton in bulk water. Because the larger (n ≥ 10) assemblies are formed with three-dimensional cage morphologies that more closely mimic the bulk environment, we report the spectra of cryogenically cooled (10 K) clusters over the size range 2 ≤ n ≤ 28, over which the structures evolve from two-dimensional arrangements to cages at around n = 10. The clusters that feature a complete second solvation shell around a surface-embedded hydronium ion yield spectral signatures of the proton defect similar to those observed in dilute acids. The origins of the large observed shifts in the proton vibrational signature upon cluster growth were explored with two types of theoretical analyses. First, we calculate the cubic and semidiagonal quartic force constants and use these in vibrational perturbation theory calculations to establish the couplings responsible for the large anharmonic red shifts. We then investigate how the extended electronic wave functions that are responsible for the shapes of the potential surfaces depend on the nature of the H-bonded networks surrounding the charge defect. These considerations indicate that, in addition to the sizable anharmonic couplings, the position of the OH stretch most associated with the excess proton can be traced to large increases in the electric fields exerted on the embedded hydronium ion upon formation of the first and second solvation shells. The correlation between the underlying local structure and the observed spectral features is quantified using a model based on Badger’s rule as well as via the examination of the electric fields obtained from electronic structure calculations. ■ INTRODUCTION In spite of the fact that acid-base behavior lies at the foundation of aqueous chemistry, the fundamental cationic species created when an Arrhenius acid releases a proton into water has proven remarkably difficult to capture at the molecular level. 1-7 The complexity arises from the fact that the excess proton can be associated with a single water molecule, thereby becoming indistinguishable from the original OH bonds of that water molecule, or it may be delocalized between two water molecules. When this process occurs in bulk water, it results in a “charge defect” that is manifested through distortions in the proximal hydrogen bonding network. The spectroscopic characterization of the molecular entity that carries the excess charge in water 8-12 is hampered by the fact that the vibrational spectrum cor- responding to the OH stretching motions in pure water extends over hundreds of wavenumbers. 5,13-16 Attempts to isolate the absorptions due to the excess proton in dilute acids (e.g., by subtraction of the counterion spectral features, etc. 5,17 ) have yielded similarly diffuse absorptions, which provide little structural information about the local molecular environment of the embedded proton. Indeed, the diffuse background absorption attributed to the positive charge is often referred to as the “Zundel continuum” 9,18,19 in honor of Georg Zundel, who introduced a polarizable H 2 O···H + ···H 2 O model (hereafter called the H 5 O 2 + Zundel ion), in which a proton is trapped between two water molecules, to conceptually understand the Received: May 6, 2015 Revised: June 30, 2015 Feature Article pubs.acs.org/JPCA © XXXX American Chemical Society A DOI: 10.1021/acs.jpca.5b04355 J. Phys. Chem. A XXXX, XXX, XXX-XXX