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 ${({\mathrm{H}}_2\mathrm{O})}_2$ . 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.

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

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.

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.

The vibrational spectra of gas phase tert-butyl hydroperoxide have been recorded in the OH-stretching fundamental and overtone regions (Δv_OH = 1–5) at room temperature using conventional Fourier transform infrared (Δv_OH = 1–3) and cavity ring-down (Δv_OH = 4–5) spectroscopy. In hydroperoxides, the OH-stretching and COOH torsion vibrations are strongly coupled. The double-well nature of the COOH torsion potential leads to tunneling splitting of the energy levels and, combined with the low frequency of the torsional vibration, results in spectra in the OH-stretching regions with multiple vibrational transitions. In each of the OH-stretching regions, both an OH-stretching and a stretch–torsion combination feature are observed, and we show direct evidence for the tunneling splitting in the OH-stretching fundamental region. We have developed two complementary vibrational models to describe the spectra of the OH-stretching regions, a reaction path model and a reduced dimensional local mode model, both of which describe the features of the vibrational spectra well. We also explore the torsional dependence of the OH-stretching transition dipole moment and show that a Franck–Condon treatment fails to capture the intensity in the region of the stretch–torsion combination features. The accuracy of the Franck–Condon treatment of these features improves with increasing Δv_OH.

The infrared (IR) spectrum of tert-butyl hydroperoxide (TBHP) in the region of the first OH-stretching overtone has been observed under jet-cooled and thermal (300 K, 3 Torr) conditions at ∼7017 cm⁻¹. The jet-cooled spectrum is recorded by IR multiphoton excitation with UV laser-induced fluorescence detection of OH radical products, while direct IR absorption is utilized under thermal conditions. Prior spectroscopic studies of TBHP and other hydroperoxides have shown that the OH-stretch and XOOH (X = H or C) torsion vibrations are strongly coupled, resulting in a double well potential associated with the torsional motion about the OO bond that is different for each of the OH-stretching vibrational states. A low barrier between the wells on the torsional potential results in tunneling split energy levels, which leads to four distinct transitions associated with excitation of the coupled OH-stretch-torsion states. In order to interpret the experimental results, two theoretical models are used that include the OH-stretch-torsion coupling in TBHP. Both methods are utilized to compute the vibrational transitions associated with the coupled OH-stretch-torsion states of TBHP, revealing the underlying transitions that compose the experimentally observed features. A comparison between theory and experiment illustrates the necessity for treatments that include OH-stretch and COOH torsion in order to unravel the spectral features observed in the first OH-stretching overtone region of TBHP.