A Flexible Approach to Vibrational Perturbation Theory using Sparse Matrix Methods

Infrared spectroscopy of the syn-methyl-substituted Criegee intermediate: A combined experimental and theoretical study

An IR-vacuum ultraviolet (VUV) ion-dip spectroscopy method is utilized to examine the IR spectrum of acetaldehyde oxide (CH3CHOO) in the overtone CH stretch (2νCH) spectral region. IR activation creates a depletion of the ground state population that reduces the VUV photoionization signal on the parent mass channel. IR activation of the more stable and populated syn-CH3CHOO conformer results in rapid unimolecular decay to OH + vinoxy products and makes the most significant contribution to the observed spectrum. The resultant IR-VUV ion-dip spectrum of CH3CHOO is similar to that obtained previously for syn-CH3CHOO using IR action spectroscopy with UV laser-induced fluorescence detection of OH products. The prominent IR features at 5984 and 6081 cm-1 are also observed using UV + VUV photoionization of OH products. Complementary theoretical calculations utilizing a general implementation of second-order vibrational perturbation theory provide new insights on the vibrational transitions that give rise to the experimental spectrum in the overtone CH stretch region. The introduction of physically motivated small shifts of the harmonic frequencies yields remarkably improved agreement between experiment and theory in the overtone CH stretch region. The prominent features are assigned as highly mixed states with contributions from two quanta of CH stretch and/or a combination of CH stretch with an overtone in mode 4. The generality of this approach is demonstrated by applying it to three different levels of electronic structure theory/basis sets, all of which provide spectra that are virtually indistinguishable despite showing large deviations prior to introducing the shifts to the harmonic frequencies.

Direct Probe of Vibrational Fingerprint and Combination Band Coupling

Vibrational fingerprints and combination bands are a direct measure of couplings that control molecular properties. However, most combination bands possess small transition dipoles. Here we use multiple, ultrafast coherent infrared pulses to resolve vibrational coupling between CH3CN fingerprint modes at 918 and 1039 cm-1 and combination bands in the 2750-6100 cm-1 region via doubly vibrationally enhanced (DOVE) coherent multidimensional spectroscopy (CMDS). This approach provides a direct probe of vibrational coupling between fingerprint modes and near-infrared combination bands of large and small transition dipoles in a molecular system over a large frequency range.

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.

Extending the Large Molecule Limit: The Role of Fermi Resonance in Developing a Quantum Functional Group

Polyatomic molecules equipped with optical cycling centers (OCCs), enabling continuous photon scattering during optical excitation, are exciting candidates for advancing quantum information science. However, as these molecules grow in size and complexity, the interplay of complex vibronic couplings on optical cycling becomes a critical but relatively unexplored consideration. Here, we present an extensive exploration of Fermi resonances in large-scale OCC-containing molecules using high-resolution dispersed laser-induced fluorescence and excitation spectroscopy. These resonances manifest as vibrational coupling leading to intensity borrowing by combination bands near optically active harmonic bands, which require additional repumping lasers for effective optical cycling. To mitigate these effects, we explore altering the vibrational energy level spacing through substitutions on the phenyl ring or changes in the OCC itself. While the complete elimination of vibrational coupling in complex molecules remains challenging, our findings highlight significant mitigation possibilities, opening new avenues for optimizing optical cycling in large polyatomic molecules.

Vibrational heat-bath configuration interaction with semistochastic perturbation theory using harmonic oscillator or VSCF modals

Vibrational heat-bath configuration interaction (VHCI)-a selected configuration interaction technique for vibrational structure theory-has recently been developed in two independent works [J. H. Fetherolf and T. C. Berkelbach, J. Chem. Phys. 154, 074104 (2021); A. U. Bhatty and K. R. Brorsen, Mol. Phys. 119, e1936250 (2021)], where it was shown to provide accuracy on par with the most accurate vibrational structure methods with a low computational cost. Here, we eliminate the memory bottleneck of the second-order perturbation theory correction using the same (semi)stochastic approach developed previously for electronic structure theory. This allows us to treat, in an unbiased manner, much larger perturbative spaces, which are necessary for high accuracy in large systems. Stochastic errors are easily controlled to be less than 1 cm-1. We also report two other developments: (i) we propose a new heat-bath criterion and an associated exact implicit sorting algorithm for potential energy surfaces expressible as a sum of products of one-dimensional potentials; (ii) we formulate VHCI to use a vibrational self-consistent field (VSCF) reference, as opposed to the harmonic oscillator reference configuration used in previous reports. Our tests are done with quartic and sextic force fields, for which we find that with VSCF, the minor improvements to accuracy are outweighed by the higher computational cost associated the matrix element evaluations. We expect VSCF-based VHCI to be important for more general potential representations, for which the harmonic oscillator basis function integrals are no longer analytic.

Spectroscopy of Radicals, Clusters, and Transition States Using Slow Electron Velocity-Map Imaging of Cryogenically Cooled Anions

Slow electron velocity-map imaging of cryogenically cooled anions (cryo-SEVI) is a high-resolution variant of anion photoelectron spectroscopy that has been applied with considerable success over the years to the study of radicals, size-selected clusters, and transition states for unimolecular and bimolecular reactions. Cryo-SEVI retains the versatility of conventional anion photoelectron spectroscopy while offering sub-meV resolution, thereby enabling the resolution of vibrational structure in the photoelectron spectra of complex anions. This Feature Article describes recent experiments in our laboratory using cryo-SEVI, including a new research direction in which anions are vibrationally pre-excited with an infrared laser pulse prior to photodetachment.

Multidimensional Quantum Dynamical Simulation of Infrared Spectra under Polaritonic Vibrational Strong Coupling

Recent experimental and theoretical studies demonstrate that the chemical reactivity of molecules can be modified inside an optical cavity. Here, we provide a theoretical framework for conducting multidimensional quantum simulations of the infrared (IR) spectra for molecules interacting with cavity modes. A single water molecule under polaritonic vibrational strong coupling serves as an illustrative example. Combined with accurate potential energy and dipole moment surfaces, our cavity vibrational self-consistent field/virtual state configuration interaction (cav-VSCF/VCI) approach can predict the IR spectra when the molecule is inside or outside the cavity. The spectral signatures of Rabi splittings and shifts of certain bands are found to be strongly dependent on the frequency and polarization direction of the cavity modes. Analyses of the simulated spectra show that polaritonic vibrational strong coupling can induce unconventional couplings among the molecule's vibrational modes, suggesting that intramolecular vibrational energy transfer can be significantly accelerated by the cavity.

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.

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.