The CH stretch region is a good candidate as a probe of structure and local environment. The functional groups are ubiquitous and their vibration spectra exhibit a surprising sensitivity to molecular structure. In this talk we briefly review our theoretical model Hamiltonian [J. Chem. Phys. 138 064308 (2013)] for describing vibrational spectra associated with the CH stretch of CH₂ groups and then describe an extension of it to molecules containing methyl and methoxy groups. Results are compared to the infrared spectroscopy of four molecules studied under supersonic expansion cooling in gas phase conditions. The molecules include 1,1-diphenylethane, 1,1-diphenylpropane, 2-methoxyphenol (guaiacol), and 1,3-dimethoxy-2-hydroxybenzene (syringol). The curvilinear local-mode Hamiltonian predicts most of the major spectral features considered in this study and provides insights into mode mixing. We conclude by returning to CH₂ groups and explain both why the CH stretch spectrum of cyclohexane is substantially modified when it forms a complex with an alkali metal and what these spectra tell us about the structure of the complex.

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase-space localized (PSL) basis functions. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. Iterative methods are imperative if one wishes to avoid storing matrices which is important for larger molecules. RecentlyJ. Brown and T. Carrington Jr., Phys. Rev. Lett. 114, 058901 (2015).e showed it was possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. Here, we present calculated vibrational energies of CH₂O and CH₃CN using the iterative Arnoldi algorithm and PSL functions, and show that our PSL basis is competitive with other previously used basis sets for these molecules.

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Footnotes:

J. Brown and T. Carrington Jr., Phys. Rev. Lett. 114, 058901 (2015).w

By optimizing sum-of-products (SOP) basis functions, it is possible to compute vibrational spectra, using a direct product basis, without storing vectors with as many components as there are product basis functions. These ideas are presented in a recent paper: Leclerc and Carrington, J. Chem. Phys 140 174111 (2014). In that paper, the SOP basis functions are products of factors that depend on a single coordinate. When using factors that depend on one coordinate the number of terms (rank) in the SOP basis functions increases with the size of the molecule and the coupling strength. Using multi-dimensional factors makes it possible to incorporate some of the coupling into the factors and to calculate spectra of molecules with more than a dozen atoms. We use multi-dimensional factors that are eigenfunctions of reduced-dimension Hamiltonians. These can be constructed, in different ways, by organizing the factors into a multiple layer tree. Each node in a layer of a tree represents eigenfunctions of a reduced-dimension Hamiltonian for a group of coordinates. We have done calculations with tensor-train and binary tree structures. Efficiency is significantly enhanced by representing the potential with the same tree structure. The ideas are tested by computing energy levels of a 64-D model coupled oscillator Hamiltonian and of CH3CN (12 dimensions) with a realistic potential.

Convergent hierarchies of theories for calculating many-body vibrational ground and excited-state wave functions, such as Møller-Plesset perturbation theory or coupled cluster theory, tend to rely on matrix-algebraic manipulations of large, high-dimensional arrays of anharmonic force constants, tasks which require large amounts of computer storage space and which are very difficult to implement in a parallel-scalable fashion. On the other hand, existing quantum Monte Carlo (QMC) methods for vibrational wave functions tend to lack robust techniques for obtaining excited-state energies, especially for large systems. By exploiting analytical identities for matrix elements of position operators in a harmonic oscillator basis, we have developed stochastic implementations of the size-extensive vibrational self-consistent field (MC-XVSCF) and size-extensive vibrational Møller-Plesset second-order perturbation (MC-XVMP2) theories which do not require storing the potential energy surface (PES). The programmable equations of MC-XVSCF and MC-XVMP2 take the form of a small number of high-dimensional integrals evaluated using Metropolis Monte Carlo techniques. The associated integrands require independent evaluations of only the value, not the derivatives, of the PES at many points, a task which is trivial to parallelize. However, unlike existing vibrational QMC methods, MC-XVSCF and MC-XVMP2 can calculate anharmonic frequencies directly, rather than as a small difference between two noisy total energies, and do not require user-selected coordinates or nodal surfaces. MC-XVSCF and MC-XVMP2 can also directly sample the PES in a given approximation without analytical or grid-based approximations, enabling us to quantify the errors induced by such approximations.

A diagrammatic vibrational coupled-cluster method for calculation of zero-point energies and an equation-of-motion coupled-cluster method for calculation of anharmonic vibrational frequencies are developed. The methods, which we refer to as XVCC and EOM-XVCC respectively, rely on the size-extensive vibrational self-consistient field (XVSCF) method for reference wave functions. The methods retain the efficiency advantages of XVSCF making them suitable for applications to large molecules and solids, while they are numerically shown to accurately predict zero-point energies and frequencies of small molecules as well. In particular, EOM-XVCC is shown to perform well for modes which undergo Fermi resonance where traditional perturbative methods fail. Rules for the systematic generation and interpretation of the XVCC and EOM-XVCC diagrams to any order are presented.

The Jahn-Teller theorem H. A.  Jahn, and E. Teller, Proc. R. Soc. Lond. A. 161, 220, (1937).tates that “All non-linear nuclear configurations are therefore unstable for an orbitally degenerate electronic state.” In 1982, Kellman M. E.  Kellman, Chem. Phys. Lett. 87, 171, (1982).ealized that the Jahn-Teller theorem also applies to nonlinear molecular species in non-degenerate electronic states when there are high-frequency vibrations that are degenerate at a symmetrical reference geometry. When those high frequencies can be considered as adiabatic functions of degenerate low-frequency coordinates, there is a spontaneous Jahn-Teller distortion that lifts the degeneracy of the high-frequency vibrations. Kellman applied the vibrational Jahn-Teller (vJT) concept to the Van der Waals dimer (SF₆)₂. In this talk, the vJT concept is applied to E ⊗ e systems that are small bound molecules in non-degenerate electronic states. The first case considered in systems for which the global minimum of the electronic potential has C_3v symmetry.For such systems, including (C₆H₆)Cr(CO)₃ and CH₃CN, the vJT effect leads to a significant splitting of the degenerate high-frequency vibrations (CH or CO stretches), but the spontaneous vJT distortion is exceptionally small. The second case in systems for which the global minimum of the electronic potential is substantially distorted from the C_3v reference geometry. For the second case systems, including CH₃OH and CH₃SH, the vJT splitting of the degenerate CH stretches is much larger, on the order of several 10Äôs of cm⁻¹). For both cases, there is the symmetry-required vibrational conical intersection at the C_3v reference geometry. For the second case systems, there are additional symmetry-allowed vibrational conical intersections far from the C_3v geometry but energetically accessible to the molecule at thermal energies. For both cases, the vibrationally adiabatic surfaces, including the multiple conical intersections, are well described by modest extensions to a high-order Hamiltonian that was developed for the electronic Jahn-Teller problem.A.  Viel, and W. Eisfeld, J. Chem. Phys. 120, 4603, (2004).html:<hr /><h3>Footnotes: H. A.  Jahn, and E. Teller, Proc. R. Soc. Lond. A. 161, 220, (1937).s M. E.  Kellman, Chem. Phys. Lett. 87, 171, (1982).r A.  Viel, and W. Eisfeld, J. Chem. Phys. 120, 4603, (2004).

Nowadays the task of spectra processing is as relevant as ever in molecular spectroscopy. Nevertheless, existing techniques of vibrational energy levels and wave functions computation often come to a dead-lock. Application of standard quantum-mechanical approaches often faces inextricable difficulties. Variational method requires unimaginable computational performance. On the other hand perturbational approaches beat against divergent series. That’s why this problem faces an urgent need in application of specific resummation techniques. In this research Rayleigh–Schrödinger perturbation theory is applied to vibrational energy levels calculation of excited vibrational states of H₂CO. It is known that perturbation series diverge in the case of anharmonic resonance coupling between vibrational states [1]. Nevertheless, application of advanced divergent series summation techniques makes it possible to calculate the value of energy with high precision (more than 10 true digits) even for highly excited states of the molecule [2]. For this purposes we have applied several summation techniques based on high-order Pade-Hermite approximations. Our research shows that series behaviour completely depends on the singularities of complex energy function inside unit circle. That's why choosing an approximation function modelling this singularities allows to calculate the sum of divergent series. Our calculations for formaldehyde molecule show that the efficiency of each summation technique depends on the resonant type.
REFERENCES
1. J. Cizek, V. Spirko, and O. Bludsky, ON THE USE OF DIVERGENT SERIES IN VIBRATIONAL SPECTROSCOPY. TWO- AND THREE-DIMENSIONAL OSCILLATORS, J. Chem. Phys. 99, 7331 (1993).
2. A. V. Sergeev and D. Z. Goodson, SINGULARITY ANALYSIS OF FOURTH-ORDER MÖLLER-PLESSET PERTURBATION THEORY, J. Chem. Phys. 124, 4111 (2006).

Triacetylene, HC₆H, is the longest poly-acetylene chain found in space, and is believed to be involved in the formation of longer chain molecules and polycyclic aromatic hydrocarbons (PAHs). However, abundances are expected to be low, and observational confirmation requires knowledge of the gas-phase spectra, which up to now has been incomplete with only the weak, low lying bending modes being known. We present new infrared (IR) spectra in the C-H stretch region obtained using ultra-sensitive and highly precise IR continuous wave cavity ring-down spectroscopy (cw-CRDS), combined with supersonic plasma expansionsD. Zhao, J. Guss, A. Walsh, H. Linnartz, Chem. Phys. Lett., 565, 132 (2013) The talk reviews the accurate determination of the rotational constants of the asymmetric fundamental mode, ν₅, including discussion on the perturber state, and associated hot bandsK.D. Doney, D. Zhao, H. Linnartz, in preparation The determined molecular parameters are accurate enough to aid astronomical searches with such facilities as ALMA (Atacama Large Millimeter Array) or the upcoming JWST (James Webb Space Telecscope), which can now probe even trace molecules (abundances of  ∼  10⁻⁶ - 10⁻¹⁰ with respect to H₂).

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Footnotes:

D. Zhao, J. Guss, A. Walsh, H. Linnartz, Chem. Phys. Lett., 565, 132 (2013). K.D. Doney, D. Zhao, H. Linnartz, in preparation.

Ionic liquids (ILs) are a highly variable and potentially game-changing class of molecules for a number of Air Force applications such as satellite propulsion, but the complex nature of IL structure and intermolecular interactions makes it difficult to adequately predict structure-property relationships in order to make new IL-based technology a reality. For example, methylation of imidazolium ionic liquids leads to a substantial increase in viscosity but the underlying physical mechanism is not understood. In addition, the role of hydrogen bonding in ILs, and especially its relationship to macroscopic properties, is a matter of ongoing research. Here we describe the gas-phase spectroscopy of a series of imidazolium- and pyridinium-based ILs, using a combination of infrared spectroscopy and density functional theory to establish the intermolecular interactions present in various ILs, to assess how well they are described by theory, and to relate microscopic structure to macroscopic properties.

Vibrational spectra of alkanes in the CH stretch region are often complicated by Fermi resonance with the overtone of the CH bends. This complication has made the CH stretch region difficult to use as a spectroscopic tool for assigning structures to experimental infrared spectra. A first-principles model accounting for Fermi resonance has been developed by Sibert and co-workers, and has been successfully implemented to predict the CH stretch region of alkyl groups in a variety of settings (both -CH₂- and -CH₃). We have recorded jet-cooled, single-conformation infrared spectra of a series of straight chain alkylbenzenes having chain lengths of two carbons and longer, serving as a foundation for further tests and refinement of the theoretical model. Ground and excited state IR spectra of these alkylbenzenes were acquired using fluorescence dip infrared spectroscopy. A novel approach for taking the excited state spectra that utilizes the gain of a second, infrared-induced fluorescence peak will be discussed and compared to the typical depletion spectra, using ethylbenzene as a prototypical system.

M⁺(H₂O)Ar and M⁺(H₂O)Ne clusters (M=V, Nb) were produced in a laser vaporization/pulsed nozzle source. The clusters were then mass selected in a time-of-flight mass spectrometer and studied with infrared photodissociation spectroscopy in the OH stretching region. Spectra showed two bands, with the asymmetric band showing k-type rotational structure. Previous work has shown that most metal-water rare gas-tagged systems adopt C_2v geometry and exhibit the well-known 3:1 ortho:para ratio in the k-type rotational structure in asymmetric stretch band. However these two metals display a pattern that indicates a breaking of the C_2v symmetry. Computational work confirms the breaking of C_2v symmetry giving an Ar-M⁺-O angle of 163.7 degrees for V and 172.1 degrees for Nb. In the ground state we obtain rotational constants that match up well with obtained spectra using 166 degrees for V and 175 degrees for Nb.

Acetylacetone (acac) is the simplest of the beta-diketones. which have both keto and enol tautomers with multiple protonation sites. We readily produce the protonated forms in the gas phase and the current investigation uses vibrational spectroscopy coupled with argon tagging to determine which protonated isomers are present in clusters of acac and the effects of solvation on the isomers observed.

We use Ar predissociation and vibrational autodetachment below 2100 cm⁻¹to obtain vibrational spectra of the low-energy modes of nitromethane anion. We interpret the spectra using anharmonic calculations, which reveal strong mode coupling and Fermi resonances. Not surprisingly, the number of evaporated Ar atoms varies with photon energy, and we follow the propensity of evaporating two versus one Ar atoms as photon energy increases. The photodetachment spectrum is discussed in the context of threshold effects and the importance of hot bands.

We report the observation of a dipole-bound state and a high-resolution photoelectron imaging study of cryogenically cooled acetate anions (CH₃COO⁻). Both high-resolution non-resonant and resonant photoelectron spectra via the dipole-bound state of CH₃COO⁻ are obtained. The binding energy of the dipole-bound state relative to the detachment threshold is determined to be 53 ±8 cm⁻¹. The electron affinity of the CH₃COO• neutral radical is measured accurately as 26 236 ±8 cm⁻¹(3.2528 ± 0.0010 eV) using high-resolution photoelectron imaging. This accurate electron affinity is validated by observation of autodetachment from two vibrational levels of the dipole-bound state of CH₃COO⁻. Excitation spectra to the dipole-bound states yield rotational profiles, allowing the rotational temperature of the trapped CH₃COO⁻ anions to be evaluated ¹. [1] D. L. Huang, G. Z. Zhu and L. S. Wang, J. Chem. Phys., 2015, 142, 091103