Probing Ion-Receptor Interactions in Halide Complexes of Octamethyl Calix[4]Pyrrole

Ion receptors are molecular hosts that bind ionic guests, often with great selectivity. The interplay of solvation and ion binding in anion host-guest complexes in solution governs the binding efficiency and selectivity of such ion receptors. To gain molecular-level insight into the intrinsic binding properties of octamethyl calix[4]pyrrole (omC4P) host molecules with halide guest ions, we performed cryogenic ion vibrational spectroscopy (CIVS) of omC4P in complexes with fluoride, chloride, and bromide ions. We interpret the spectra using density functional theory, describing the infrared spectra of these complexes with both harmonic and anharmonic second-order vibrational perturbation theory (VPT2) calculations. The NH stretching modes of the pyrrole moieties serve as sensitive probes of the ion binding properties, as their frequencies encode the ion-receptor interactions. While scaled harmonic spectra reproduce the experimental NH stretching modes of the chloride and bromide complexes in broad strokes, the high proton affinity of fluoride introduces strong anharmonic effects. As a result, the spectrum of F-·omC4P is not even qualitatively captured by harmonic calculations, but it is recovered very well by VPT2 calculations. In addition, the VPT2 calculations recover the intricate coupling of the NH stretching modes with overtones and combination bands of CH stretching and NH bending modes and with low-frequency vibrations of the omC4P macrocycle, which are apparent for all of the halide ion complexes investigated here. A comparison of the CIVS spectra with infrared spectra of solutions of the same ion-receptor complexes in d3-acetonitrile and d6-acetone shows how ion solvation changes the ion-receptor interactions for the different halide ions.

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.

Characterization of the Oxazolone and Macrocyclic Motifs in the bn (n = 2-5) Product Ions from Collision-Induced Dissociation of Protonated Oligoglycine Peptides with Isomer-Selective, Cryogenic Vibrational Spectroscopy

Collision-induced dissociation (CID) of small, protonated peptides leads to the formation of b-type fragment ions that can occur with several structural motifs driven by different covalent intramolecular bonding arrangements. Here, we characterize the so-called "oxazolone" and "macrocycle" bn ion structures that occur upon CID of oligoglycine peptides (Gn) ions (n = 2-6). This is determined by acquiring the vibrational band patterns of the cryogenically cooled, D2-tagged bn ions obtained using isomer-selective, two-color IR-IR photobleaching and analyzing them with predicted (DFT) harmonic spectra for the candidate structures. Both oxazolone and macrocyclic isomers are formed by b4, whereas only oxazolone species are created for b2 and b3 and the macrocycle is created for b5. As such, n = 4 corresponds to the minimum size where both Oxa and MC forms are present.

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.

Isotope Effects in the Zundel-Eigen Isomerization of H+(H2O)6

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⁺(H₂O)₆ and D⁺(D₂O)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⁺(H₂O)₆ and D⁺(D₂O)₆ are also discussed.

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.

High-Resolution Photoelectron Spectroscopy of Vibrationally Excited Vinoxide Anions

High-resolution photoelectron spectra of vibrationally pre-excited vinoxide anions (CH₂CHO^-) are reported using the recently developed IR-cryo-SEVI technique. This method is combined with a newly developed implementation of vibrational perturbation theory that can readily identify relevant anharmonic couplings among nearly degenerate vibrational states. IR-cryo-SEVI spectra are obtained by resonant infrared excitation of vinoxide anions via the fundamental C-O (ν₄, 1566 cm^-1) or isolated C-H (ν₃, 2540 cm^-1) stretching vibrations prior to photodetachment. Excitation of the ν₄ mode leads to a well-resolved photoelectron spectrum that is in excellent agreement with a harmonic Franck-Condon simulation. Excitation of the higher-energy ν₃ mode results in a more complicated spectrum that requires consideration of the calculated anharmonic resonances in both the anion and the neutral. From this analysis, information about the zeroth-order states that contribute to the nominal ν₃ wave function in the anion is obtained. In the neutral, we observe anharmonic splitting of the ν₃ fundamental into a polyad feature with peaks at 2737(22), 2 835(18), and 2910(12) cm^-1, for which only the center frequency has been previously reported. Overall, 9 of the 12 fundamental frequencies of the vinoxy radical are extracted from the IR-cryo-SEVI and ground-state cryo-SEVI spectra, most of which are consistent with previous measurements. However, we provide a new estimate of the ν₅ (CH₂ scissoring) fundamental frequency at 1395(11) cm^-1 and attribute the discrepancy with previously reported values to a Fermi resonance with the 2ν₁₁ overtone (CH₂ wagging).

Isotope Effects on Ground and Excited States of Ethyl Cation, H+(C2H4)

The structure and spectra of ethyl cation, H⁺(C₂H₄), and its deuterated analogues are investigated using diffusion Monte Carlo (DMC). These calculations all show that the ground state wave function for H⁺(C₂H₄) is localized near the minimum energy configuration in which the excess proton is in a bridging configuration, although the amplitude of the vibrational motions of the bridging proton is large. Deuteration of the bridging proton reduces the amplitude of this motion, while deuteration of only the ethylenic hydrogen atoms in H⁺(C₂D₄) has little effect on the amplitude of the motion of the bridging proton. Excited states that are accessed by spectroscopically observed transitions in H⁺(C₂H₄) are calculated using fixed-node DMC. The calculated and measured frequencies for the states with one quantum of excitation in the ethylenic CH stretching vibrations show good agreement. We also explore the excited state with one quantum of excitation in the proton transfer vibration of the bridging proton and obtain a frequency of 616 cm^-1 for H⁺(C₂H₄). This frequency increases to 629 cm^-1 in H⁺(C₂D₄). Deuteration decreases this frequency to 491 and 495 cm^-1 in D⁺(C₂H₄) and D⁺(C₂D₄), respectively. The effects of partial deuteration on the frequencies of the CH stretching vibrations, and the corresponding probability amplitudes are also explored. Finally, we report the vibrationally averaged rotational constants for the four isotopologues of ethyl cation considered in this study.

Exploring Expansions of the Potential and Dipole Surfaces Used for Vibrational Perturbation Theory

A scheme for evaluating expansions of the potential and dipole moment surfaces for vibrational perturbation theory is described. The approach is based on numerical differentiation of the Hessian in the coordinates of interest. It is shown that performing these calculations in internal coordinates generates expansions that are transferable among isotopologues of the molecule of interest. Additionally, re-expressing the expansion of the potential in terms of functions of the internal coordinates, for example, cosines of angles or exponential functions of the bond length displacements, provides expansions that can be used for higher-order perturbation theory calculations. The approach is explored and the results are discussed for water, HOD, ammonia, isomers of HNO₃, and halogenated methane.

A Wave Function Correction-Based Approach to the Identification of Resonances for Vibrational Perturbation Theory

An approach for idenifying resonances in vibrational perturbation theory calculations is introduced. This approach makes use of the corrections to the wave functions that are obtained from non-degenerate perturbation theory calculations to identify spaces of states that must be treated with degenerate perturbation theory. Pairs of states are considered to be in resonance if the magnitude of expansion coefficients in the corrections to the wave functions in the non-degenerate perturbation theory calculation are greater than a specified threshold, χmax. This approach is applied to calculations of the vibrational spectra of CH4, H2CO, HNO3 and cc-HOONO. The question of how the identified resonances depend on the value of χmax and how the choice of the resonance spaces affects the calculated vibrational spectrum is further explored for \formaldehyde. The approach is also compared to the Martin test [J. Chem. Phys. 103, 2589-2602 (1995)] for calculations of the vibrational spectra of H2CO and cc-HOONO.

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.

Fast Near Ab Initio Potential Energy Surfaces Using Machine Learning

A machine-learning based approach for evaluating potential energies for quantum mechanical studies of properties of the ground and excited vibrational states of small molecules is developed. This approach uses the molecular-orbital-based machine learning (MOB-ML) method to generate electronic energies with the accuracy of CCSD(T) calculations at the same cost as a Hartree-Fock calculation. To further reduce the computational cost of the potential energy evaluations without sacrificing the CCSD(T) level accuracy, GPU-accelerated Neural Network Potential Energy Surfaces (NN-PES) are trained to geometries and energies that are collected from small-scale Diffusion Monte Carlo (DMC) simulations, which are run using energies evaluated using the MOB-ML model. The combined NN+(MOB-ML) approach is used in variational calculations of the ground and low-lying vibrational excited states of water and in DMC calculations of the ground states of water, CH₅⁺, and its deuterated analogues. For both of these molecules, comparisons are made to the results obtained using potentials that were fit to much larger sets of electronic energies than were required to train the MOB-ML models. The NN+(MOB-ML) approach is also used to obtain a potential surface for C₂H₅⁺, which is a carbocation with a nonclassical equilibrium structure for which there is currently no available potential surface. This potential is used to explore the CH stretching vibrations, focusing on those of the bridging hydrogen atom. For both CH₅⁺ and C₂H₅⁺ the MOB-ML model is trained using geometries that were sampled from an AIMD trajectory, which was run at 350 K. By comparison, the structures sampled in the ground state calculations can have energies that are as much as ten times larger than those used to train the MOB-ML model. For water a higher temperature AIMD trajectory is needed to obtain accurate results due to the smaller thermal energy. A second MOB-ML model for C₂H₅⁺ was developed with additional higher energy structures in the training set. The two models are found to provide nearly identical descriptions of the ground state of C₂H₅⁺.

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.

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.

Infrared spectroscopic signature of a hydroperoxyalkyl radical (•QOOH)

Infrared (IR) action spectroscopy is utilized to characterize a prototypical carbon-centered hydroperoxyalkyl radical (•QOOH) transiently formed in the oxidation of volatile organic compounds. The •QOOH radical formed in isobutane oxidation, 2-hydroperoxy-2-methylprop-1-yl, •CH₂(CH₃)₂COOH, is generated in the laboratory by H-atom abstraction from tert-butyl hydroperoxide (TBHP). IR spectral features of jet-cooled and stabilized •QOOH radicals are observed from 2950 to 7050 cm^-1 at energies that lie below and above the transition state barrier leading to OH radical and cyclic ether products. The observed •QOOH features include overtone OH and CH stretch transitions, combination bands involving OH or CH stretch and a lower frequency mode, and fundamental OH and CH stretch transitions. Most features arise from a single vibrational transition with band contours well simulated at a rotational temperature of 10 K. In each case, the OH products resulting from unimolecular decay of vibrationally activated •QOOH are detected by UV laser-induced fluorescence. Assignments of observed •QOOH IR transitions are guided by anharmonic frequencies computed using second order vibrational perturbation theory, a 2 + 1 model that focuses on the coupling of the OH stretch with two low-frequency torsions, as well as recently predicted statistical •QOOH unimolecular decay rates that include heavy-atom tunneling. Most of the observed vibrational transitions of •QOOH are readily distinguished from those of the TBHP precursor. The distinctive IR transitions of •QOOH, including the strong fundamental OH stretch, provide a general means for detection of •QOOH under controlled laboratory and real-world conditions.

Using Diffusion Monte Carlo Wave Functions to Analyze the Vibrational Spectra of H7O3+ and H9O4. J Phys Chem A 2021;125:7185-7197. [PMID: 34433268 DOI: 10.1021/acs.jpca.1c05025]

An approach for evaluating spectra from ground state probability amplitudes (GSPA) obtained from diffusion Monte Carlo (DMC) simulations is extended to improve the description of excited state energies and allow for coupling among vibrational excited states. This approach is applied to studies of the protonated water trimer and tetramer, and their deuterated analogs. These ions provide models for solvated hydronium, and analysis of these spectra provides insights into spectral signatures of proton transfer in aqueous environments. In this approach, we obtain a separable set of internal coordinates from the DMC ground state probability amplitude. A basis is then developed from products of the DMC ground state wave function and low-order polynomials in these internal coordinates. This approach provides a compact basis in which the Hamiltonian and dipole moment matrix are evaluated and used to obtain the spectrum. The resulting spectra are in good agreement with experiment and in many cases provide comparable agreement to the results obtained using much larger basis sets. In addition, the compact basis allows for interpretation of the spectral features and how they evolve with cluster size and deuteration.

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

Diffusion Monte Carlo (DMC) provides a powerful method for understanding the vibrational landscape of molecules that are not well-described by conventional methods. The most computationally demanding step of these calculations is the evaluation of the potential energy. In this work, a general approach is developed in which a neural network potential energy surface is trained by using data generated from a small-scale DMC calculation. Once trained, the neural network can be evaluated by using highly parallelizable calls to a graphics processing unit (GPU). The power of this approach is demonstrated for DMC simulations on H₂O, CH₅⁺, and (H₂O)₂. The need to include permutation symmetry in the neural network potentials is explored and incorporated into the molecular descriptors of CH₅⁺ and (H₂O)₂. It is shown that the zero-point energies and wave functions obtained by using the neural network potentials are nearly identical to the results obtained when using the potential energy surfaces that were used to train the neural networks at a substantial savings in the computational requirements of the simulations.

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

Decoding the structural information contained in the interfacial vibrational spectrum of water requires understanding how the spectral signatures of individual water molecules respond to their local hydrogen bonding environments. In this study, we isolated the contributions for the five classes of sites that differ according to the number of donor (D) and acceptor (A) hydrogen bonds that characterize each site. These patterns were measured by exploiting the unique properties of the water cluster cage structures formed in the gas phase upon hydration of a series of cations M⁺·(H₂O)_n (M = Li, Na, Cs, NH₄, CH₃NH₃, H₃O, and n = 5, 20-22). This selection of ions was chosen to systematically express the A, AD, AAD, ADD, and AADD hydrogen bonding motifs. The spectral signatures of each site were measured using two-color, IR-IR isotopomer-selective photofragmentation vibrational spectroscopy of the cryogenically cooled, mass selected cluster ions in which a single intact H₂O is introduced without isotopic scrambling, an important advantage afforded by the cluster regime. The resulting patterns provide an unprecedented picture of the intrinsic line shapes and spectral complexities associated with excitation of the individual OH groups, as well as the correlation between the frequencies of the two OH groups on the same water molecule, as a function of network site. The properties of the surrounding water network that govern this frequency map are evaluated by dissecting electronic structure calculations that explore how changes in the nearby network structures, both within and beyond the first hydration shell, affect the local frequency of an OH oscillator. The qualitative trends are recovered with a simple model that correlates the OH frequency with the network-modulated local electron density in the center of the OH bond.

The Role of Tunneling in the Spectra of H5+ and D5+ up to 7300 cm-1

The spectra for H₅⁺ and D₅⁺ are extended to cover the region between 4830 and 7300 cm^-1. These spectra are obtained using mass-selected photodissociation spectroscopy. To understand the nature of the states that are accessed by the transitions in this and prior studies, we develop a four-dimensional model Hamiltonian. This Hamiltonian is expressed in terms of the two outer H₂ stretches, the displacement of the shared proton from the center of mass of these two H₂ groups, and the distance between the H₂ groups. This choice is motivated by the large oscillator strength associated with the shared proton stretch and the fact that the spectral regions that have been probed correspond to zero, one, and two quanta of excitation in the H₂ stretches. This model is analyzed using an adiabatic separation of the H₂ stretches from the other two vibrations and includes the non-adiabatic couplings between H₂ stretch states with the same total number of quanta of excitation in the H₂ stretches. Based on the analysis of the energies and wave functions obtained from this model, we find that when there are one or more quanta of excitation in the H₂ stretches the states come in pairs that reflect tunneling doublets. The states accessed by the transitions in the spectrum with the largest intensity are assigned to the members of the doublets with requisite symmetry that are localized on the lowest-energy adiabat for a given level of H₂ excitation.

Spectroscopic Signatures of Mode-Dependent Tunnel Splitting in the Iodide-Water Binary Complex

The gas-phase vibrational spectrum of the isolated iodide-water cluster ion (I^-·H₂O), first reported in 1996, presents one of the most difficult, long-standing spectroscopic puzzles involving ion microhydration. Although the spectra of the smaller halides are well described in the context of an asymmetrical ground-state structure in which only one OH group is hydrogen-bonded to the ion, the I^-·H₂O spectrum displays multiplet structures with partially resolved rotational patterns that are additionally influenced by quantum nuclear spin statistics. In this study, this complex behavior is unraveled with a combination of experimental methods, including ion preparation in a temperature-controlled ion trap and spectral simplification through applications of tag-free, two-color IR-IR double-resonance spectroscopy. Analysis of the double-resonance spectra reveals a vibrational ground-state tunneling splitting of about 20 cm^-1, which is on the same order as the spacing between the peaks that comprise the multiplet structure. These findings are further supported by the results obtained from a fully coupled, six-dimensional calculation of the vibrational spectrum. The underlying level structure can then be understood as a consequence of experimentally measurable, vibrational mode-dependent tunneling splittings (which, in the case of the ground vibrational state, is comparable to the rotational energy spacing between levels with K_a = 0 and 1), as well as Fermi resonance interactions. The latter include the hydrogen-bonded OH stretches and combination bands that involve the HOH bend overtones and soft-mode excitations of frustrated translation and rotation displacements of the water molecule relative to the ion. These anharmonic couplings yield closely spaced bands that are activated in the IR by borrowing intensity from the OH stretch fundamentals.

Disentangling the Complex Vibrational Mechanics of the Protonated Water Trimer by Rational Control of Its Hydrogen Bonds

The vibrational spectrum of the protonated water trimer, H⁺(H₂O)₃, is surprisingly complex, with many strong features in the expected region of the fundamentals associated with two H-bonded OH groups on the H₃O⁺ core ion. Here we follow how the bands in this region of the spectrum evolve when the energies of the fundamentals in the H-bonded OH stretches are systematically increased by the attachment of increasingly strongly bound "tag" molecules (He, Ar, D₂, N₂, CO, and H₂O) to the free OH position on the hydronium core ion of H⁺(H₂O)₃, as well as by replacement of the hydrogen atom in the nonbonded OH group on hydronium with methyl and ethyl groups. This allows for the incremental transformation of the complex band pattern observed in H⁺(H₂O)₃ into that of the "Eigen" structure of the protonated water tetramer. Differences among the trajectories of the various bands provide an empirical way to disentangle features primarily due to the displacements of the OH stretches bound to the hydronium core from those arising from anharmonic coupling to states involving one or more quanta in lower frequency modes. The latter are found to be dramatically enhanced when the nominal frequencies of the intermolecular OH stretching modes approach those of the intramolecular bends of the H₃O⁺ and H₂O constituents in both H and D isotopologues.

Deconstructing water's diffuse OH stretching vibrational spectrum with cold clusters

The diffuse vibrational envelope displayed by water precludes direct observation of how different hydrogen-bond topologies dictate the spectral response of individual hydroxy group (OH) oscillators. Using cold, isotopically labeled cluster ions, we report the spectral signatures of a single, intact water (H₂O) molecule embedded at various sites in the clathrate-like cage structure adopted by the Cs⁺·(D₂O)₂₀ ion. These patterns reveal the site-dependent correlation between the frequencies of the two OH groups on the same water molecule and establish that the bound OH companion of the free OH group exclusively accounts for bands in the lower-energy region of the spectrum. The observed multiplet structures reveal the homogeneous linewidths of the fundamentals and quantify the anharmonic contributions arising from coupling to both the intramolecular bending and intermolecular soft modes.

Beyond Badger's Rule: The Origins and Generality of the Structure-Spectra Relationship of Aqueous Hydrogen Bonds

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.