Anharmonicity and the Eigen-Zundel Dilemma in the IR Spectrum of the Protonated 21 Water Cluster

Magic Numbers and Stabilities of Photoionized Water Clusters: Computational and Experimental Characterization of the Nanosolvated Hydronium Ion

The stability and distributions of small water clusters generated in a supersonic beam expansion are interrogated by tunable vacuum ultraviolet (VUV) radiation generated at a synchrotron. Time-of-flight mass spectrometry reveals enhanced population of various protonated water clusters (H⁺(H₂O)_n) based upon ionization energy and photoionization distance from source, suggesting there are "magic" numbers below the traditional n = 21 that predominates in the literature. These intensity distributions suggest that VUV threshold photoionization (11.0-11.5 eV) of neutral water clusters close to the nozzle exit leads to a different nonequilibrium state compared to a skimmed molecular beam. This results in the appearance of a new magic number at 14. Metadynamics conformer searches coupled with modern density functional calculations are used to identify the global minimum energy structures of protonated water clusters between n = 2 and 21, as well as the manifold of low-lying metastable minima. New lowest energy structures are reported for the cases of n = 5, 6, 11, 12, 16, and 18, and special stability is identified by several measures. These theoretical results are in agreement with the experiments performed in this work in that n = 14 is shown to exhibit additional stability, based on the computed second-order stabilization energy relative to most cluster sizes, though not to the extent of the well-known n = 21 cluster. Other cluster sizes that show some additional energetic stability are n = 7, 9, 12, 17, and 19. To gain insight into the balance between ion-water and water-water interactions as a function of the cluster size, an analysis of the effective two-body interactions (which sum exactly to the total interaction energy) was performed. This analysis reveals a crossover as a function of cluster size between a water-hydronium-dominated regime for small clusters and a water-water-dominated regime for larger clusters around n = 17.

Towards complete assignment of the infrared spectrum of the protonated water cluster H+(H2O)21

The spectroscopic features of protonated water species in dilute acid solutions have been long sought after for understanding the microscopic behavior of the proton in water with gas-phase water clusters H⁺(H₂O)_n extensively studied as bottom-up model systems. We present a new protocol for the calculation of the infrared (IR) spectra of complex systems, which combines the fragment-based Coupled Cluster method and anharmonic vibrational quasi-degenerate perturbation theory, and demonstrate its accuracy towards the complete and accurate assignment of the IR spectrum of the H⁺(H₂O)₂₁ cluster. The site-specific IR spectral signatures reveal two distinct structures for the internal and surface four-coordinated water molecules, which are ice-like and liquid-like, respectively. The effect of inter-molecular interaction between water molecules is addressed, and the vibrational resonance is found between the O-H stretching fundamental and the bending overtone of the nearest neighboring water molecule. The revelation of the spectral signature of the excess proton offers deeper insight into the nature of charge accommodation in the extended hydrogen-bonding network underpinning this aqueous cluster.

Protonated water species have been the subject of numerous experimental and computational studies. Here the authors provide a nearly complete assignment of the experimental IR spectrum of the H⁺(H₂O)₂₁ water cluster based on high-level wavefunction theory and anharmonic vibrational quasi-degenerate perturbation theory.

Demystifying the Diffuse Vibrational Spectrum of Aqueous Protons Through Cold Cluster Spectroscopy

The ease with which the pH is routinely determined for aqueous solutions masks the fact that the cationic product of Arrhenius acid dissolution, the hydrated proton, or H⁺(aq), is a remarkably complex species. Here, we review how results obtained over the past 30 years in the study of H⁺⋅(H₂O)_n cluster ions isolated in the gas phase shed light on the chemical nature of H⁺(aq). This effort has also revealed molecular-level aspects of the Grotthuss relay mechanism for positive-charge translocation in water. Recently developed methods involving cryogenic cooling in radiofrequency ion traps and the application of two-color, infrared-infrared (IR-IR) double-resonance spectroscopy have established a clear picture of how local hydrogen-bond topology drives the diverse spectral signatures of the excess proton. This information now enables a new generation of cluster studies designed to unravel the microscopic mechanics underlying the ultrafast relaxation dynamics displayed by H⁺(aq).

Unusually strong hydrogen bond cooperativity in particular (H2O)20 clusters

Drawing upon an intuitive charge-transfer-based picture of hydrogen bonding, we demonstrate that cooperativity effects acting in concert can lead to unusually strong hydrogen bonds in neutral water clusters. The structure, vibrational, and NMR properties of a (H2O)20 pentagonal dodecahedron cluster containing such a strong hydrogen bond were studied using second-order perturbation theory and density functional theory. The hydrogen bond length was found to be shorter than 2.50 Å. A large redshift of over 2000 cm-1 with respect to the isolated water molecule was predicted for the OH stretching frequency of the donor water molecule. A large downfield shift to 13.5 ppm of the isotropic part of the 1H magnetic shielding tensor together with an unusually large shielding anisotropy of 49.9 ppm was obtained. The hydrogen bond energy was calculated using symmetry-adapted perturbation theory and was found to be more than three times stronger than a typical hydrogen bond in liquid water.

Revisit the landscape of protonated water clusters H+(H2O)n with n = 10-17: An ab initio global search

Using a genetic algorithm incorporated with density functional theory, we explore the ground state structures of protonated water clusters H⁺(H₂O)_n with n = 10-17. Then we re-optimize the isomers at B97-D/aug-cc-pVDZ level of theory. The extra proton connects with a H₂O molecule to form a H₃O⁺ ion in all H⁺(H₂O)_10-17 clusters. The lowest-energy structures adopt a monocage form at n = 10-16 and core-shell structure at n = 17 based on the MP2/aug-cc-pVTZ//B97-D/aug-cc-pVDZ+ZPE single-point-energy calculation. Using second-order vibrational perturbation theory, we further calculate the infrared spectra with anharmonic correction for the ground state structures of H⁺(H₂O)_10-17 clusters at the PBE0/aug-cc-pVDZ level. The anharmonic correction to the spectra is crucial since it reproduces the experimental results quite well. The extra proton weakens the O-H bond strength in the H₃O⁺ ion since the Wiberg bond order of the O-H bond in the H₃O⁺ ion is smaller than that in H₂O molecules, which causes a red shift of the O-H stretching mode in the H₃O⁺ ion.

Structures and Spectroscopic Properties of F-(H2O) n with n = 1-10 Clusters from a Global Search Based On Density Functional Theory

Using a genetic algorithm incorporated in density functional theory, we explore the ground state structures of fluoride anion-water clusters F^-(H₂O) _n with n = 1-10. The F^-(H₂O) _n clusters prefer structures in which the F^- anion remains at the surface of the structure and coordinates with four water molecules, as the F^-(H₂O) _n clusters have strong F^--H₂O interactions as well as strong hydrogen bonds between H₂O molecules. The strong interaction between the F^- anion and adjacent H₂O molecule leads to a longer O-H distance in the adjacent molecule than in an individual water molecule. The simulated infrared (IR) spectra of the F^-(H₂O)_1-5 clusters obtained via second-order vibrational perturbation theory (VPT2) and including anharmonic effects reproduce the experimental results quite well. The strong interaction between the F^- anion and water molecules results in a large redshift (600-2300 cm^-1) of the adjacent O-H stretching mode. Natural bond orbital (NBO) analysis of the lowest-energy structures of the F^-(H₂O)_1-10 clusters illustrates that charge transfer from the lone pair electron orbital of F^- to the antibonding orbital of the adjacent O-H is mainly responsible for the strong interaction between the F^- anion and water molecules, which leads to distinctly different geometric and vibrational properties compared with neutral water clusters.

How the Zundel (H5O2+) Potential Can Be Used to Predict the Proton Stretch and Bend Frequencies of Larger Protonated Water Clusters

From a series of seminal experiments on the IR spectra of protonated water clusters and associated theoretical analyses, it is clear that the energies and spectral features of the proton stretch and bend modes are very sensitive functions of the cluster size. Here we show that this dynamic range can be understood by examining the sensitivity of these modes in the potential of the Zundel cation, H₅O₂⁺, as the separation of the two water monomers is varied. As this distance increases, the proton increasingly localizes on a monomer, and this is encoded in the IR spectrum of the proton vibrational modes. The quantitative predictions from this simple correlation are verified for the H₇O₃⁺ and H₉O₄⁺ clusters, for which new benchmark harmonic frequencies are reported. The predictions are also in good accord with trends seen experimentally and previous calculations for these and five other clusters, including H⁺(H₂O)₂₁.

Vibrational spectral signature of the proton defect in the three-dimensional H⁺(H₂O)₂₁ cluster

The way in which a three-dimensional network of water molecules accommodates an excess proton is hard to discern from the broad vibrational spectra of dilute acids. The sharper bands displayed by cold gas-phase clusters, H(+)(H2O)n, are therefore useful because they encode the network-dependent speciation of the proton defect and yet are small enough to be accurately treated with electronic structure theory. We identified the previously elusive spectral signature of the proton defect in the three-dimensional cage structure adopted by the particularly stable H(+)(H2O)21 cluster. Cryogenically cooling the ion and tagging it with loosely bound deuterium (D2) enabled detection of its vibrational spectrum over the 600 to 4000 cm(-1) range. The excess charge is consistent with a tricoordinated H3O(+) moiety embedded on the surface of a clathrate-like cage.

Infrared spectroscopy of large-sized neutral and protonated ammonia clusters

Size selective IR spectroscopy shows the nature of hydrogen bond networks in neutral and protonated ammonia clusters.

Solvation Energies of the Proton in Methanol

pKa's, proton affinities, and proton dissociation free energies characterize numerous properties of drugs and the antioxidant activity of some chemical compounds. Even with a higher computational level of theory, the uncertainty in the proton solvation free energy limits the accuracy of these parameters. We investigated the thermochemistry of the solvation of the proton in methanol within the cluster-continuum model. The scheme used involves up to nine explicit methanol molecules, using the IEF-PCM and the strategy based on thermodynamic cycles. All computations were performed at B3LYP/6-31++G(dp) and M062X/6-31++G(dp) levels of theory. It comes out from our calculations that the functional M062X is better than B3LYP, on the evaluation of gas phase clustering energies of protonated methanol clusters, per methanol stabilization of neutral methanol clusters and solvation energies of the proton in methanol. The solvation free energy and enthalpy of the proton in methanol were obtained after converging the partial solvation free energy of the proton in methanol and the clustering free energy of protonated methanol clusters, as the cluster size increases. Finally, the recommended values for the solvation free energy and enthalpy of the proton in methanol are -257 and -252 kcal/mol, respectively.