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The p K a 's of acids are known to depend on the ionic strength of an electrolyte solution, an effect that qualitatively results from electrostatic interactions of the acid and conjugate base with proximal ions. Here, we explore an intramolecular variation on this theme in which a carboxylic acid group is tethered to a pyridinium cationic charge center with increasingly long alkyl linkages in the series Py + -(CH 2 ) n -COOH, with n = 1-7. The effective acidities of the carboxylic acid group in the isolated cations are determined by recording the red-shifts in the frequencies of the acid OH stretches upon attachment to D 2 and N 2 molecules, measured by using cryogenic ion spectroscopy. The short chains indeed lead to substantial increases in acidity, with the effect falling off in the range of n = 4-5. The response of the CO stretch on the acid head group is surprisingly strong and, in contrast to the expected red shift of the OH, displays a blue shift as the chain length is reduced. Electronic structure calculations recover these trends and indicate that the proximal cationic charge center acts to draw electron density away from the acid C═O bond. This acts to blue-shift the CO stretch while weakening the C-C bond that attaches the head group to the chain.

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.

In this work, we report the infrared spectrum of the pyrene anion, measured using messenger tagging with up to three Ar atoms. We assign the spectrum using density functional theory and vibrational perturbation theory. We discuss our results in the context of computed and experimental spectra from the literature as well as recent observations from astronomical sources, addressing the question of whether polycyclic aromatic hydrocarbon anions could contribute to the strong infrared emission bands at 3.29 μm from carbon-rich regions of space.

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 d 3 -acetonitrile and d 6 -acetone shows how ion solvation changes the ion-receptor interactions for the different halide ions.

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 + (H 2 O) 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 + (H 2 O) 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 + (H 2 O) 6 from 1917 cm -1 to roughly 2100 cm -1 . For D + (D 2 O) 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 + (D 2 O) 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.

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.

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.

High-resolution photoelectron spectra of vibrationally pre-excited vinoxide anions (CH 2 CHO - ) 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 (ν 4 , 1566 cm -1 ) or isolated C-H (ν 3 , 2540 cm -1 ) stretching vibrations prior to photodetachment. Excitation of the ν 4 mode leads to a well-resolved photoelectron spectrum that is in excellent agreement with a harmonic Franck-Condon simulation. Excitation of the higher-energy ν 3 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 ν 3 wave function in the anion is obtained. In the neutral, we observe anharmonic splitting of the ν 3 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 ν 5 (CH 2 scissoring) fundamental frequency at 1395(11) cm -1 and attribute the discrepancy with previously reported values to a Fermi resonance with the 2ν 11 overtone (CH 2 wagging).

The structure and spectra of ethyl cation, H + (C 2 H 4 ), and its deuterated analogues are investigated using diffusion Monte Carlo (DMC). These calculations all show that the ground state wave function for H + (C 2 H 4 ) 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 + (C 2 D 4 ) has little effect on the amplitude of the motion of the bridging proton. Excited states that are accessed by spectroscopically observed transitions in H + (C 2 H 4 ) 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 + (C 2 H 4 ). This frequency increases to 629 cm -1 in H + (C 2 D 4 ). Deuteration decreases this frequency to 491 and 495 cm -1 in D + (C 2 H 4 ) and D + (C 2 D 4 ), 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.

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 HNO 3 , and halogenated methane.

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.

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, CH 5 + , 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 C 2 H 5 + , 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 CH 5 + and C 2 H 5 + 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 C 2 H 5 + 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 C 2 H 5 + .

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 speciation of strong acids like HNO 3 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 HNO 3 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 + ·(HNO 3 )(H 2 O) 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 (HNO 3 -H 2 O) 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 HNO 3 acidity afforded by attachment to the smaller cations.

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 Δ r OH and Δ r OH 2 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.

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.

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 H 2 O, CH 5 + , and (H 2 O) 2 . The need to include permutation symmetry in the neural network potentials is explored and incorporated into the molecular descriptors of CH 5 + and (H 2 O) 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.

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 + ·(H 2 O) n (M = Li, Na, Cs, NH 4 , CH 3 NH 3 , H 3 O, 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 H 2 O 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.

Diffusion Monte Carlo provides an effective and efficient approach for calculating ground state properties of molecular systems based on potential energy surfaces. The approach has been shown to require increasingly large ensembles when intra- and intermolecular vibrations are weakly coupled. We recently proposed a guided variant of diffusion Monte Carlo to address these challenges for water clusters [Lee, V. G. M.; McCoy, A. B. J. Phys. Chem. A 2019, 123, 8063-8070]. In the present study, we extend this approach and apply it to more strongly bound molecular ions, specifically CH 5 + and H + (H 2 O) n =1-4 . For the protonated water systems, we show that the guided DMC approach that was developed for studies of (H 2 O) n can be used to describe the OH stretches and HOH bends in the solvating water molecules, as well as the free OH stretches in the hydronium core. For the hydrogen bonded OH stretches in the H 3 O + core of H + (H 2 O) n and the CH stretches in CH 5 + , we develop adaptive guiding functions based on the instantaneous structure of the ion of interest. Using these guiding functions, we demonstrate that we are able to obtain converged zero-point energies and ground state wave functions using ensemble sizes that are as small as 10% the size that is needed to obtain similar accuracy from unguided calculations.

The ground-state structures of water hexamer and several deuterated variants are studied by using the diffusion Monte Carlo (DMC) method. We demonstrate that a recently developed guided DMC approach allows us to study these systems using substantially smaller ensembles than are required for standard DMC approaches. DMC calculations of the ground states of (H 2 O) 6 and (D 2 O) 6 using the MB-pol potential with 50 000 walkers and a 1 au time step show that for (H 2 O) 6 the cage structure is 51 ± 7 cm -1 lower in energy than the prism structure. In the case of (D 2 O) 6 , the two structures have nearly equal energies (Δ E = 9 ± 11 cm -1 ). The structures of the singly substituted, (H 2 O)(D 2 O) 5 and (H 2 O) 5 (D 2 O), variants of water hexamer are also explored to identify the impact of the location of the unique water molecule on the relative stability of the possible structure. The effect on the stability of the hydrogen bond on whether a hydrogen bond has an OD or OH bond as the donor is also explored.

The spectra for H 5 + and D 5 + 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 H 2 stretches, the displacement of the shared proton from the center of mass of these two H 2 groups, and the distance between the H 2 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 H 2 stretches. This model is analyzed using an adiabatic separation of the H 2 stretches from the other two vibrations and includes the non-adiabatic couplings between H 2 stretch states with the same total number of quanta of excitation in the H 2 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 H 2 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 H 2 excitation.

The gas-phase vibrational spectrum of the isolated iodide-water cluster ion (I - ·H 2 O), 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 - ·H 2 O 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.

An efficient and accurate approach for using diffusion Monte Carlo (DMC) to study molecular clusters is described and applied to an investigation of (H 2 O) n with n = 1, 2, 3. In this approach, importance sampled DMC is used to describe the intramolecular degrees of freedom of the water monomers. The intermolecular degrees of freedom are treated using standard unguided DMC approaches. This hybrid approach allows us to use significantly smaller simulations to obtain converged zero-point energies and ground state wave functions than would be required for a fully unguided simulation of the same system. We demonstrate the efficiency, accuracy, and utility of this approach through a study of nine isotopologues of water trimer, focusing on how the ground state probability amplitude for these clusters samples the various low-energy minima on the potential surface.

The vibrational spectrum of the protonated water trimer, H + (H 2 O) 3 , is surprisingly complex, with many strong features in the expected region of the fundamentals associated with two H-bonded OH groups on the H 3 O + 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, D 2 , N 2 , CO, and H 2 O) to the free OH position on the hydronium core ion of H + (H 2 O) 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 + (H 2 O) 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 H 3 O + and H 2 O constituents in both H and D isotopologues.

Statistical approaches are applied to an investigation of how deuterated forms of CH 5 + sample the potential energy surface for this ion. In its ground state, CH 5 + has been shown to have amplitude in all of the 120 equivalent minima in the potential as well as in the region of each of the 180 low-energy saddle points that connect these minima. Although deuteration quenches this delocalization, the multidimensional nature of the isomerization pathways makes it difficult to visualize and quantify the delocalization of the ground state wave function. In this work, the localization of the ground state wave function is explored through an analysis of projections of the ground state probability amplitude onto various atom-atom distances. Specifically, analysis of two-dimensional projections of the ground state probability amplitude on to the distances between pairs of hydrogen atoms reveals that the ground state probability amplitude is localized near structures in which the hydrogen atoms in the ion can be divided into those that make up a CH 3 + part and those that make up in a H 2 part. Analysis of fits of projections of the probability amplitude onto distances between pairs of hydrogen atoms, between pairs of deuterium atoms, and between hydrogen and deuterium atoms to sums of Gaussian functions allows us to quantify the increased localization of hydrogen and deuterium atoms in the CH 3 + and H 2 parts of the ion. In addition, the amplitude of the wave function in the regions of the potential that correspond to the transition state for exchange of hydrogen or deuterium atoms between these two parts of the ion is found to decrease in the partially deuterated forms of CH 5 + and is smallest for CH 2 D 3 + and CH 3 D 2 + .

Approaches for using diffusion Monte Carlo (DMC) to evaluate matrix elements involving two vibrational wave functions are explored. In the first part of this study, overlaps between a wave function obtained using DMC and one that can be calculated analytically are evaluated. In this case, the analytical wave function is used as the guiding function for an importance sampled DMC simulation. The accuracy of the calculated overlaps is found to depend strongly on the accuracy of the calculated descendant weights, which are obtained in the DMC simulation. While a single evaluation of the descendant weights is sufficient for obtaining projected probability amplitudes or expectation values of multiplicative operators, averages of multiple independent evaluations of the descendant weights are required to obtain accurate matrix elements. This approach is investigated for one-dimensional model systems as well as H 2 CO, H 2 D + , and D 2 H + . The approach is extended to the evaluation of matrix elements of the dipole moment operator between the ground state and states with one quantum of excitation in one of the OH stretching vibrations in H 3 O 2 - . For these calculations, the wave functions for both the ground and excited states are evaluated using DMC. The described methodology opens the possibility of evaluating matrix elements involving two different states, both of which are obtained using DMC.

Alkene ozonolysis, an important source of hydroxyl (OH) radicals in the Earth's troposphere, proceeds through unimolecular decay of Criegee intermediates. In this work, infrared activation of the methyl-substituted Criegee intermediate, syn-CH 3 CHOO, in the CH stretch fundamental region (2850-3150 cm -1 ) is shown to result in unimolecular decay to OH radical products. These excitation energies correspond to only half of the transition state barrier height, and thus the resultant 1,4 H atom transfer that leads to OH products occurs exclusively by quantum mechanical tunneling. Infrared action spectra recorded with UV laser-induced fluorescence detection of the OH products reveal the four CH stretch fundamentals and CO stretch overtone predicted to have strong transition strength. The vibrational band origins, relative intensities, and transition types derived from rotational band contour analyses are in good accord with theory. Distinctly different Lorentzian line broadening of the observed features is attributed to mode-specific anharmonic couplings predicted theoretically between spectroscopically bright and nearby dark states. The measured OH product state distribution shows a strong λ-doublet preference arising from pπ orbital alignment, which is indicative of the vinyl hydroperoxide intermediate along the reaction pathway. The unimolecular decay of syn-CH 3 CHOO at ca. 3000 cm -1 is predicted to be quite slow (ca. 10 5 s -1 ) using statistical Rice-Ramsperger-Kassel-Marcus theory with tunneling and much slower than observed at higher energies.

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.

We report vibrational spectra of the cryogenically cooled H 9 O 4 + cation along with those of the D 2 tagged HD 8 O 4 + isotopomers using two variations on a two-color, IR-IR double-resonance photoexcitation scheme. The spectrum of the isolated H 9 O 4 + ion consists of two sharp features in the OH stretching region that indicate exclusive formation of the "Eigen" cation, the H 3 O + ·(H 2 O) 3 isomer that corresponds to the filled hydration shell around the hydronium ion. Consistent with this structural assignment, the spectrum of the HD 8 O 4 + isotopologue is resolved into contributions from two isotopomers: one with the single OH group on one of the three solvent water molecules and another in which it resides on the hydronium core ion. The latter spectrum is dominated by a broad feature assigned to the isolated hydronium OH stretching fundamental with an envelope that is similar to that displayed by the H 3 O + ·(H 2 O) 3 isotopologue. The feature appears with a diffuse band ∼380 cm -1 above it, which is assigned to a combination band involving the hydronium OH stretching vibration and the frustrated translation mode of the HD 2 O + core and one of the solvating water molecules. These trends are analyzed with anharmonic calculations involving four-mode coupling on a realistic potential surface and interpreted in the context of vibrationally adiabatic potentials based on insights acquired from analysis of the ground state probability amplitudes obtained from diffusion Monte Carlo calculations.

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.