Infrared Spectrum of the Pyrene Anion in the CH Stretching Region.

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.

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.

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).

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.

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.

A wave function correction-based approach to the identification of resonances for vibrational perturbation theory.

An approach for identifying 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 is 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 H2CO. The approach is also compared to the Martin test [J. M. L. Martin et al., J. Chem. Phys. 103, 2589-2602 (1995)] for calculations of the vibrational spectra of H2CO and cc-HOONO.

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.

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 ΔrOH and ΔrOH2 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.

A flexible approach to vibrational perturbation theory using sparse matrix methods.

A sparse linear algebra based implementation of Rayleigh-Schrödinger vibrational perturbation theory is presented. This implementation allows for flexibility in the coordinates used to expand the vibrational Hamiltonian as well as the order to which the perturbation theory is performed. It also provides a powerful tool for investigating the origin of spectral intensity and transition frequencies. Specifically, this flexibility allows for the analysis of which terms in the expansions of the Hamiltonian and dipole surface lead to the largest corrections to the energies and transition intensities, and how these conclusions depend on the coordinates used for these expansions. Comparisons of corrections to transition frequencies are reported for the Morse oscillator when the potential is expanded in Δr and Morse coordinates as well as for water, water dimer, and peroxynitrous acid when the molecular Hamiltonians and dipole surfaces are expanded in Cartesian displacement coordinates and in the displacements of the bond-angle-dihedral internal coordinates. Further comparisons of the corrections to the transitions moments are made for H2O and (H2O)2. It is found that while the transition frequencies and intensities are independent of coordinate choice, a good choice of coordinates leads to a cleaner interpretation of the origins of the anharmonicities in these systems.

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.