Isolating the Contributions of Specific Network Sites to the Diffuse Vibrational Spectrum of Interfacial Water with Isotopomer-Selective Spectroscopy of Cold Clusters

The Near-Sightedness of Many-Body Interactions in Anharmonic Vibrational Couplings

Couplings between vibrational motions are driven by electronic interactions, and these couplings carry special significance in vibrational energy transfer, multidimensional spectroscopy experiments, and simulations of vibrational spectra. In this investigation, the many-body contributions to these couplings are analyzed computationally in the context of clathrate-like alkali metal cation hydrates, including Cs+(H2O)20, Rb+(H2O)20, and K+(H2O)20, using both analytic and quantum-chemistry potential energy surfaces. Although the harmonic spectra and one-dimensional anharmonic spectra depend strongly on these many-body interactions, the mode-pair couplings were, perhaps surprisingly, found to be dominated by one-body effects, even in cases of couplings to low-frequency modes that involved the motion of multiple water molecules. The origin of this effect was traced mainly to geometric distortion within water monomers and cancellation of many-body effects in differential couplings, and the effect was also shown to be agnostic to the identity of the ion. These outcomes provide new understanding of vibrational couplings and suggest the possibility of improved computational methods for the simulation of infrared and Raman spectra.

Correlations between the Structures and Spectra of Protonated Water Clusters

Badger's rule-like correlations between OH stretching frequencies and intensities and the OH bond length are used to develop a spectral mapping procedure for studies of pure and protonated water clusters. This approach utilizes the vibrationally averaged OH bond lengths, which were obtained from diffusion Monte Carlo simulations that were performed using the general potential developed by Yu and Bowman. Good agreement is achieved between the spectra obtained using this approach and previously reported spectra for H+(H2O)n clusters, with n = 3, 4, and 5, as well as their perdeuterated analogues. The analysis of the spectra obtained by this spectral mapping approach supports previous work that assigned the spectrum of H+(H2O)6 to a mixture of Eigen and Zundel-like structures. Analysis of the calculated spectra also suggests a reassignment of the frequency of one of the transitions that involves the OH stretching vibration of the OH bonds in the hydronium core in the Eigen-like structure of H+(H2O)6 from 1917 cm-1 to roughly 2100 cm-1. For D+(D2O)6, comparison of the measured spectrum to those obtained by using the spectral mapping approach suggests that the carrier of the measured spectrum is one or more of the isomers of D+(D2O)6 that contain a four-membered ring and two flanking water molecules. While there are several candidate structures, the two flanking water molecules most likely form a chain that is bound to the hydronium core.

Pitfalls in the n-mode representation of vibrational potentials

Simulations of anharmonic vibrational motion rely on computationally expedient representations of the governing potential energy surface. The n-mode representation (n-MR)-effectively a many-body expansion in the space of molecular vibrations-is a general and efficient approach that is often used for this purpose in vibrational self-consistent field (VSCF) calculations and correlated analogues thereof. In the present analysis, a lack of convergence in many VSCF calculations is shown to originate from negative and unbound potentials at truncated orders of the n-MR expansion. For cases of strong anharmonic coupling between modes, the n-MR can both dip below the true global minimum of the potential surface and lead to effective single-mode potentials in VSCF that do not correspond to bound vibrational problems, even for bound total potentials. The present analysis serves mainly as a pathology report of this issue. Furthermore, this insight into the origin of VSCF non-convergence provides a simple, albeit ad hoc, route to correct the problem by "painting in" the full representation of groups of modes that exhibit these negative potentials at little additional computational cost. Somewhat surprisingly, this approach also reasonably approximates the results of the next-higher n-MR order and identifies groups of modes with particularly strong coupling. The method is shown to identify and correct problematic triples of modes-and restore SCF convergence-in two-mode representations of challenging test systems, including the water dimer and trimer, as well as protonated tropine.

Intra-cluster Charge Migration upon Hydration of Protonated Formic Acid Revealed by Anharmonic Analysis of Cold Ion Vibrational Spectra

The rates of many chemical reactions are accelerated when carried out in micron-sized droplets, but the molecular origin of the rate acceleration remains unclear. One example is the condensation reaction of 1,2-diaminobenzene with formic acid to yield benzimidazole. The observed rate enhancements have been rationalized by invoking enhanced acidity at the surface of methanol solvent droplets with low water content to enable protonation of formic acid to generate a cationic species (protonated formic acid or PFA) formed by attachment of a proton to the neutral acid. Because PFA is the key feature in this reaction mechanism, vibrational spectra of cryogenically cooled, microhydrated PFA·(H2O)n=1-6 were acquired to determine how the extent of charge localization depends on the degree of hydration. Analysis of these highly anharmonic spectra with path integral ab initio molecular dynamics simulations reveals the gradual displacement of the excess proton onto the water network in the microhydration regime at low temperatures with n = 3 as the tipping point for intra-cluster proton transfer.

Accelerating Anharmonic Spectroscopy Simulations via Local-Mode, Multilevel Methods

Ab initio computer simulations of anharmonic vibrational spectra provide nuanced insight into the vibrational behavior of molecules and complexes. The computational bottleneck in such simulations, particularly for ab initio potentials, is often the generation of mode-coupling potentials. Focusing specifically on two-mode couplings in this analysis, the combination of a local-mode representation and multilevel methods is demonstrated to be particularly symbiotic. In this approach, a low-level quantum chemistry method is employed to predict the pairwise couplings that should be included at the target level of theory in vibrational self-consistent field (and similar) calculations. Pairs that are excluded by this approach are "recycled" at the low level of theory. Furthermore, because this low-level pre-screening will eventually become the computational bottleneck for sufficiently large chemical systems, distance-based truncation is applied to these low-level predictions without substantive loss of accuracy. This combination is demonstrated to yield sub-wavenumber fidelity with reference vibrational transitions when including only a small fraction of target-level couplings; the overhead of predicting these couplings, particularly when employing distance-based, local-mode cutoffs, is a trivial added cost. This combined approach is assessed on a series of test cases, including ethylene, hexatriene, and the alanine dipeptide. Vibrational self-consistent field (VSCF) spectra were obtained with an RI-MP2/cc-pVTZ potential for the dipeptide, at approximately a 5-fold reduction in computational cost. Considerable optimism for increased accelerations for larger systems and higher-order couplings is also justified, based on this investigation.

Exploring the Origins of the Intensity of the OH Stretch-HOH Bend Combination Band in Water

While the intensity of the OH stretching fundamental transition is strongly correlated to hydrogen-bond strength, the intensity of the corresponding transition to the state with one quantum of excitation in both the OH stretching and HOH bending vibrations in the same water molecule shows a much weaker sensitivity to the hydrogen-bonding environment. The origins of this difference are explored through analyses of the contributions of terms in the expansion of the dipole moment to the calculated intensity. It is found that the leading contribution to the stretch-bend intensity involves the second derivative of the dipole moment with respect to the OH bond length and HOH angle. While this is not surprising, the insensitivity of this derivative to the hydrogen-bonding environment is unexpected. Possible contributions of mode mixing are also explored. While mode mixing leads to splittings of the energies of nearly degenerate excited states, it does not result in significant changes in the sum of the intensities of these transitions. Analysis of changes in the partial charges on the hydrogen atoms upon displacement of the HOH angles shows that these charges generally increase with increasing HOH angle. This effect is partially canceled by a decrease in the charge of the hydrogen atom when a hydrogen bond is broken. The extent of this cancellation increases with the hydrogen bond strength, which is reflected in the observed insensitivity of the intensity of the stretch-bend transition to hydrogen-bond strength.

Observation of Slow Eigen-Zundel Interconversion in H+(H2O)6 Clusters upon Isomer-Selective Vibrational Excitation and Buffer Gas Cooling in a Cryogenic Ion Trap

The formation of isomers when trapping floppy cluster ions in a temperature-controlled ion trap is a generally observed phenomenon. This involves collisional quenching of the ions initially formed at high temperature by buffer gas cooling until their internal energies fall below the barriers in the potential energy surface that separate them. Here we explore the kinetics at play in the case of the two isomers adopted by the H⁺(H₂O)₆ cluster ion that differ in the proton accommodation motif. One of these is most like the Eigen cation with a tricoordinated hydronium motif (denoted E), and the other is most like the Zundel ion with the proton equally shared between two water molecules (denoted Z). After initial cooling to about 20 K in the radiofrequency (Paul) trap, the relative populations of these two spectroscopically distinct isomers are abruptly changed through isomer-selective photoexcitation of bands in the OH stretching region with a pulsed (∼6 ns) infrared laser while the ions are in the trap. We then monitor the relaxation of the vibrationally excited clusters and reformation of the two cold isomers by recording infrared photodissociation spectra with a second IR laser as a function of delay time from the initial excitation. The latter spectra are obtained after ejecting the trapped ions into a time-of-flight photofragmentation mass spectrometer, thus enabling long (∼0.1 s) delay times. Excitation of the Z isomer is observed to display long-lived vibrationally excited states that are collisionally cooled on a ms time scale, some of which quench into the E isomer. These excited E species then display spontaneous interconversion to the Z form on a ∼10 ms time scale. These qualitative observations set the stage for a series of experimental measurements that can provide quantitative benchmarks for theoretical simulations of cluster dynamics and the potential energy surfaces that underlie them.

Character of the OH Bend-Stretch Combination Band in the Vibrational Spectra of the "Magic" Number H3O+(H2O)20 and D3O+(D2O)20 Cluster Ions

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 H₃O⁺(H₂O)₂₀ and D₃O⁺(D₂O)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.

Electronic and mechanical anharmonicities in the vibrational spectra of the H-bonded, cryogenically cooled X- · HOCl (X=Cl, Br, I) complexes: Characterization of the strong anionic H-bond to an acidic OH group

We report vibrational spectra of the H₂-tagged, cryogenically cooled X^- · HOCl (X = Cl, Br, and I) ion-molecule complexes and analyze the resulting band patterns with electronic structure calculations and an anharmonic theoretical treatment of nuclear motions on extended potential energy surfaces. The complexes are formed by "ligand exchange" reactions of X^- · (H₂O)_n clusters with HOCl molecules at low pressure (∼10^-2 mbar) in a radio frequency ion guide. The spectra generally feature many bands in addition to the fundamentals expected at the double harmonic level. These "extra bands" appear in patterns that are similar to those displayed by the X^- · HOD analogs, where they are assigned to excitations of nominally IR forbidden overtones and combination bands. The interactions driving these features include mechanical and electronic anharmonicities. Particularly intense bands are observed for the v = 0 → 2 transitions of the out-of-plane bending soft modes of the HOCl molecule relative to the ions. These involve displacements that act to break the strong H-bond to the ion, which give rise to large quadratic dependences of the electric dipoles (electronic anharmonicities) that drive the transition moments for the overtone bands. On the other hand, overtone bands arising from the intramolecular OH bending modes of HOCl are traced to mechanical anharmonic coupling with the v = 1 level of the OH stretch (Fermi resonances). These interactions are similar in strength to those reported earlier for the X^- · HOD complexes.

Water Network Shape-Dependence of Local Interactions with the Microhydrated -NO2- and -CO2- Anionic Head Groups by Cold Ion Vibrational Spectroscopy

We report the structural evolutions of water networks and solvatochromic response of the CH₃NO₂^- radical anion in the OH and CH stretching regions by analysis of the vibrational spectra displayed by cryogenically cooled CH₃NO₂^-·(H₂O)_n=1-6 clusters. The OH stretching bands evolve with a surprisingly large discontinuity at n = 6, which features the emergence of an intense, strongly red-shifted band along with a weaker feature that appears in the region assigned to a free OH fundamental. Very similar behavior is displayed by the perdeuterated carboxylate clusters, RCO₂^-·(H₂O)_n=5-7 (R = CD₃CD₂), indicating that this behavior is a general feature in the microhydration of the triatomic anionic domain and not associated with CH oscillators. Electronic structure calculations trace this behavior to the formation of a "book" isomer of the water hexamer that adopts a configuration in which one of the water molecules resides in an acceptor-acceptor-donor (AAD) (A = acceptor, D = donor) H-bonding site. Excitation of the bound OH in the AAD site explores the local network topology best suited to stabilize an incipient -XO₂H-OH^-(H₂O)₂ intracluster proton-transfer reaction. These systems thus provide particularly clear examples where the network shape controls the potential energy landscape that governs water network-mediated, intracluster proton transfer. The CH stretching bands of the CH₃NO₂^-·(H₂O)_n=1-6 clusters also exhibit strong solvatochromic shifts, but in this case, they smoothly blue-shift with increasing hydration with no discontinuity at n = 6. This behavior is analyzed in the context of the solute-ion polarizability response and partial charge transfer to the water networks.

Preparation and Characterization of the Halogen-Bonding Motif in the Isolated Cl-·IOH Complex with Cryogenic Ion Vibrational Spectroscopy

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^-·(H₂O)_n clusters with HOCl vapor and measure its vibrational spectrum by IR photodissociation of the H₂-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.

Vibrational Signatures of HNO3 Acidity When Complexed with Microhydrated Alkali Metal Ions, M+·(HNO3)(H2O)n=5 (M = Li, K, Na, Rb, Cs), at 20 K

The speciation of strong acids like HNO₃ under conditions of restricted hydration is an important factor in the rates of chemical reactions at the air-water interface. Here, we explore the trade-offs at play when HNO₃ is attached to alkali ions (Li⁺-Cs⁺) with four water molecules in their primary hydration shells. This is achieved by analyzing the vibrational spectra of the M⁺·(HNO₃)(H₂O)₅ clusters cooled to about 20 K in a cryogenic photofragmentation mass spectrometer. The local acidity of the acidic OH group is estimated by the extent of the red shift in its stretching frequency when attached to a single water molecule. The persistence of this local structural motif (HNO₃-H₂O) in all of these alkali metal clusters enables us to determine the competition between the effect of the direct complexation of the acid with the cation, which acts to enhance acidity, and the role of the water network in the first hydration shell around the ions, which acts to counter (screen) the intrinsic effect of the ion. Analysis of the vibrational features associated with the acid molecule, as well as those of the water network, reveals how cooperative interactions in the microhydration regime conspire to effectively offset the intrinsic enhancement of HNO₃ acidity afforded by attachment to the smaller cations.

Exploring the Origins of Spectral Signatures of Strong Hydrogen Bonding in Protonated Water Clusters

The effects of anharmonicity on the spectral features of strong ionic hydrogen bonds are explored through reduced dimensional studies of the couplings between the hydrogen bonding OH and the donor-acceptor OO stretching vibrations in protonated water clusters with 2-4 water molecules. Specifically, this study focuses on how the anharmonicities and couplings in these ions are reflected in the vibrational spectra by exploring the intensities of the transitions to states with excitation in both the OH and the OO stretching vibrations and changes in the frequency of the OO stretching vibration when the OH stretching vibration is excited. These questions are addressed through the application of several approximate treatments that are based on an adiabatic separation of the high-frequency OH and low-frequency OO stretching vibrations as well as low-order expansions of the potential and dipole surfaces. While an adiabatic approximation captures most of the trends found in the spectra and from an analysis of the two-dimensional model, a vibrational Franck-Condon approach fails to capture the intensities of these transitions. Of the terms in the expansion of the dipole moment function, those that are proportional to Δr_OH and Δr_OH² are found to provide the largest contributions to the calculated intensities of the transitions involving excitation of both the OH and the OO stretches. This leads to the conclusion that the intensities of these transitions encode information about the frequency and anharmonicity of the OH stretching vibration and how they are affected by changes in the OO distance. The anharmonicity of the potential also leads to changes in the OO stretching frequency with excitation of the OH stretching vibration. The direction of this change in frequency encodes additional information about the strength of the ionic hydrogen bond.