Vibration-rotation Spectra Research Articles

Treating linear molecules in calculations of rotation-vibration spectra.

In this article, a numerical implementation of the exact kinetic energy operator (KEO) for triatomic molecules (symmetric of XY2-type and asymmetric of YXZ-type) is presented. The implementation is based on the valence coordinates with the bisecting (XY2-type molecules) and bond-vector (YXZ) embeddings and includes the treatment of the singularity at linear geometry. The KEO is represented in a sum-of-product form. The singularity caused by the undetermined angle at the linear configuration is resolved with the help of the associated Legendre and Laguerre polynomials used as parameterized bending basis functions in the finite basis set representation. The exact KEO implementation is combined with the variational solver theoretical rovibrational energies, equipped with a general automatic symmetry-adaptation procedure and efficient basis step contraction schemes, providing a powerful computational solver of triatomic molecules for accurate computations of highly excited ro-vibrational spectra. The advantages of different basis set choices are discussed. Examples of specific applications for computing hot spectra of linear molecules are given.

Toward standardization of Raman spectroscopy: Accurate wavenumber and intensity calibration using rotational Raman spectra of H2, HD, D2, and vibration–rotation spectrum of O2

AbstractWavenumber and intensity calibration of a Raman spectrometer is performed with the use of pure rotational Raman bands (Δν = 0, ΔJ = ± 2) of H2, HD, D2, and vibration–rotation Raman bands (Δν = 1, ΔJ = ± 2) of O2 as primary standards. Wavenumber calibration is based on reference transition wavenumbers available from accurate theoretical and experimental results. Intensity calibration is based on ratios of accurate theoretical Raman intensities for transitions from common rotational states to eliminate temperature effects. Polarization dependence is corrected to ensure that all of these bands have the correct depolarization ratio, ρ = 0.75. The calibrated Raman spectrometer is used to measure standard Raman spectra of carbon tetrachloride, benzene, cyclohexane, toluene, and benzonitrile, for which the relative Raman intensities and depolarization ratios are determined with carefully estimated uncertainties. Vibrational frequencies of indene used for routine wavenumber calibration are updated.

W2020: A Database of Validated Rovibrational Experimental Transitions and Empirical Energy Levels of H216O

A detailed understanding of the complex rotation–vibration spectrum of the water molecule is vital for many areas of scientific and human activity, and thus, it is well studied in a number of spectral regions. To enhance our perception of the spectrum of the parent water isotopologue, H216O, a dataset of 270 745 non-redundant measured transitions is assembled, analyzed, and validated, yielding 19 204 rovibrational energy levels with statistically reliable uncertainties. The present study extends considerably an analysis of the rovibrational spectrum of H216O, published in 2013, by employing an improved methodology, considering about one-third more new observations (often with greatly decreased uncertainties), and using a highly accurate first-principles energy list for validation purposes. The database of experimental rovibrational transitions and empirical energy levels of H216O created during this study is called W2020. Some of the new transitions in W2020 allow the improved treatment of many parts of the dataset, especially considering the uncertainties of the experimental line positions and the empirical energy values. The W2020 dataset is examined to assess where measurements are still lacking even for this most thoroughly studied isotopologue of water, and to provide definitive energies for the lower and upper states of many yet-to-be-measured transitions. The W2020 dataset allows the evaluation of several previous compilations of spectroscopic data of water and the accuracy of previous effective Hamiltonian fits.

Identification of a vibrationally excited level in methyl formate through microwave and far-infrared spectroscopy

Methyl formate (HCOOCH3) is an important interstellar molecule. More than 1000 rotational transitions including those from the ground state, torsionally excited states, and of its isotopologues have been observed towards several astrophysical sources. The laboratory spectra of methyl formate in the microwave spectral region contain many unassigned transitions and many of them are likely to be due to rotational transitions in the low-lying excited states. We report the laboratory identification of new rotational transitions in the COC deformation (ν12) excited state. The identification was made possible by combining the microwave data with rotation–vibration spectra taken in the far-infrared region at the Canadian Light Source synchrotron.

Vibrational-rotational spectra of even–even nuclei with quadrupole and octupole deformations

Vibrational-rotation levels of the yrast and first nonyrast alternating-parity bands of the lanthanide [Formula: see text]Nd, [Formula: see text]Sm, [Formula: see text]Gd, [Formula: see text]Er and actinide [Formula: see text]Th, [Formula: see text]U, [Formula: see text]Pu nuclei are studied in the framework of a nonadiabatic collective model of even–even nuclei with quadrupole and octupole deformations. The theoretical spectra are obtained through the use of Gauss and harmonic-oscillator (HO) potentials in the radial part of the Schrödinger equation which is taken in polar coordinates. The change of the surface deformation of the nucleus with the collective excitation energy is taken into account. The [Formula: see text] staggering structure of the yrast alternating-parity bands is also considered. The theoretically obtained energy bands and staggering diagrams are in good agreement with the corresponding experimental data and point out the soft character of the collective quadrupole–octupole deformation mode manifesting in these nuclei.

Algebraic Study of diatomic Molecules: homonuclear molecules H2 and N2

It is the aim of this study to discuss for two-body systems like homonuclear molecules in which eigenvalues and eigenfunctions are obtained by exact solutions of the solvable models based on SU(1, 1) Lie algebras. Exact solutions of the solvable Hamiltonian regarding the relative motion in a two-body system on Lie algebras were obtained. The U(1) ↔ O(2), U(3) ↔ O(4) and Uq(3) ↔ Oq(4) transitional Hamiltonians are employed to described for H2 and N2 molecules. Applications to the rotation-vibration spectrum for the diatomic molecule indicate that complicated Hamiltonian can be easily determined via the exactly solvable method. The results confirm the mixing of both vibrating and rotating structures in H2 and N2 molecules.

HIGH-RESOLUTION IR SPECTRUM MEASUREMENT OF THE LINE PARAMETERS OF HYDROGEN FLUORIDE IN GAS PHASE

In this paper we present an unique high resolution FTIR rotation-vibration spectrum of H19F molecule and derived most necessary line by line parameters of the title complex. The formation mechanisms of the vibration-rotation infrared spectrum of the hydrogen fluoride have been explained. Optimal geometry and total electron density surface 3D have been mapped with electrostatic potential determined for (HF)3 cluster with mp2=full/6-311++g(3df,3pd) levels of theory.

The high-temperature rotation-vibration spectrum and rotational clustering of silylene (SiH2)

A rotation-vibration line list for the electronic ground state (X˜1A1) of SiH2 is presented. The line list, named CATS, is suitable for temperatures up to 2000 K and covers the wavenumber range 0–10 000 cm−1 (wavelengths > 1.0 µm) for states with rotational excitation up to J=52. Over 310 million transitions between 593 804 energy levels have been computed variationally with a new empirically refined potential energy surface, determined by refining to 75 empirical term values with J ≤ 5 and a newly computed high-level ab initio dipole moment surface. This is the first, comprehensive high-temperature line list to be reported for SiH2 and it is expected to aid the study of silylene in plasma physics, industrial processes and possible astronomical detection. Furthermore, we investigate the phenomenon of rotational energy level clustering in the spectrum of SiH2. The CATS line list is available from the ExoMol database (www.exomol.com) and the CDS database.

QUANTUM ALGEBRAIC SYMMETRIES IN NUCLEAR AND MOLECULAR PHYSICS

The first realizations of quanttun algebraic symmetries in nuclear and molecular spectra are presented. Rotational spectra of even-even nuclei are described by the quantum algebra SUq(2). The two parameter formula given by the algebra is equivalent to an expan- sion in terms of powers of j(j + 1), similar to the expansion given by the Variable Moment of Inertia (VMI) model. The moment of inertia parameter in the two models, as well as the small parameter of the expansion, are found to have very similar numerical values. The same formalism is found to give very good results for superdeformed nuclear bands, which are closer to the classical SU(2) limit, as well as for rotational bands of diatomic molecules, in which a partial summation of the Dunham expansion for rotation-vibration spectra is achieved. Vibrational spectra of diatomic molecules can be described by the q-deformed anhannonic oscillator, having the symmetry Uq(2)>Oq(2). An alternative de- scription is obtained in terms of the quantum algebra SUq(1,1). In both cases the energy formula obtained is equivalent to an expansion in terms of powers of (v+½) , where ν is the vibrational quantum number, while in the classical ST(1,1) case only the first two powers appear. In all cases the improved description of the empirical data is obtained with q being a phase (and not a real number). Further applications of quantum algebraic symmetries in nuclei and molecules are discussed.

Influence of the Coriolis effect on the properties of scattering resonances in symmetric and asymmetric isotopomers of ozone.

Scattering resonances above dissociation threshold are computed for four isotopically substituted ozone species: 16O18O16O, 16O16O18O, 18O16O18O and 16O18O18O, using a variational method with accurate treatment of the rotation-vibration coupling terms (Coriolis effect) for all values of the total angular momentum J from 0 to 4. To make these calculations numerically affordable, a new approach was developed which employs one vibrational basis set optimized for a typical rotational excitation (J,Λ), to run coupled rotation-vibration calculations at several desired values of J. In order to quantify the effect of Coriolis coupling, new data are contrasted with those computed using the symmetric-top rotor approximation, where the rotation-vibration coupling terms are neglected. It is found that, overall, the major properties of scattering resonances (such as their lifetimes, the number of these states, and their cumulative partition function Q) are all influenced by the Coriolis effect and this influence grows as the angular momentum J is raised. However, it is found that the four isotopically substituted ozone molecules are affected roughly equally by the Coriolis coupling. When the ratio η of partition functions for asymmetric over symmetric ozone molecules is computed, the Coriolis effect largely cancels, and this cancelation seems to occur for all values of J. Therefore, it does not seem grounded to attribute any appreciable mass-independent symmetry-driven isotopic fractionation to the Coriolis coupling effect.

High-Resolution Molecular Spectroscopy at the Institute of Atmospheric Optics: Current Status of Theoretical and Experimental Research

Results of high-resolution molecular spectroscopy researches carried out at V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences (IAO SB RAS) during the last five years are briefly reviewed. We consider theoretical problems of vibrational-rotational spectra of basic molecules of atmospheric gases, spectral line profiles, problems of the atmospheric continuum absorption, and databases of molecular spectral characteristics in the gas phase. In the section of experimental researches, the main attention is paid to the Fourier spectroscopy results obtained with laser diodes as radiation sources, as well as with the Fourier spectrometer coupled to a multipass 30-meter cell with computer control of the optical path length under variations of gas temperature and pressure.

Toward Elimination of Discrepancies between Theory and Experiment: Anharmonic Rotational-Vibrational Spectrum of Water in Solid Noble Gas Matrices.

Rotational–vibrational spectroscopy of water in solid noble gas matrices has been studied for many decades. Despite that, discrepancies persist in the literature about the assignment of specific bands. We tackle the involved rotational–vibrational spectrum of the water isotopologues H216O, HD16O, and D216O with an unprecedented combination of experimental high-resolution matrix isolation infrared (MI-IR) spectroscopy and computational anharmonic vibrational spectroscopy by vibrational configuration interaction (VCI) on high-level ab initio potential energy surfaces. With VCI, the average deviation to gas-phase experiments is reduced from >100 to ≈1 cm–1 when compared to harmonic vibrational spectra. Discrepancies between MI-IR and VCI spectra are identified as matrix effects rather than missing anharmonicity in the theoretical approach. Matrix effects are small in Ne (≈1.5 cm–1) and a bit larger in Ar (≈10 cm–1). Controversial assignments in Ne MI-IR spectra are resolved, for example, concerning the ν3 triad in HDO. We identify new transitions, for example, the ν2 101 ← 110 transition in D2O and H2O or the ν3 000 ← 101 transition in D2O, and reassign bands, for example, the band at 3718.9 cm–1 that is newly assigned as the 110 ← 111 transition. The identification and solution of discrepancies for a well-studied benchmark system such as water prove the importance of an iterative and one-hand combination of theory and experiment in the field of high-resolution infrared spectroscopy of single molecules. As the computational costs involved in the VCI approach are reasonably low, such combined experimental/theoretical studies can be extended to molecules larger than triatomics.

Analysis of Methods of Investigation of the Vibration–Rotation Spectrum of Monomers and Dimers of Sulphur Hexafluoride Isotopes

The stability of the system of sulphur hexafluoride dimer SF6 under the action of external laser radiation has been estimated using ab initio quantum-chemical calculations of the vibration–rotation spectrum of SF6 monomers as well as homo- and heterodimers. It is noted that for simple CO molecule as an example, the most widely used method of calculations based on the Hessian matrix approach cannot serve as a reliable instrument in quantitative calculations of some molecular systems. As a potential analog, we have tested the algorithm for obtaining the vibration–rotation spectrum based on molecular dynamics data.

Infrared Emission from Photodissociation of Methyl Formate [HC(O)OCH3] at 248 and 193 nm: Absence of Roaming Signature.

Following photodissociation at 248 nm of gaseous methyl formate (HC(O)OCH3, 0.73 Torr) and Ar (0.14 Torr), temporally resolved vibration-rotational emission spectra of highly internally excited CO (ν ≤ 11, J ≤ 27) in the 1850-2250 cm-1 region were recorded with a step-scan Fourier-transform spectrometer. The vibration-rotational distribution of CO is almost Boltzmann, with a nascent average rotational energy (ER0) of 3 ± 1 kJ mol-1 and a vibrational energy (EV0) of 76 ± 9 kJ mol-1. With 3 Torr of Ar added to the system, the average vibrational energy was decreased to EV0 = 61 ± 7 kJ mol-1. We observed no distinct evidence of a bimodal rotational distribution for ν = 1 and 2, as reported previously [Lombardi et al., J. Phys. Chem. A 2016, 129, 5155], as evidence of a roaming mechanism. The vibrational distribution with a temperature of ∼13000 ± 1000 K, however, agrees satisfactorily with trajectory calculations of these authors, who took into account conical intersections from the S1 state. Highly internally excited CH3OH that is expected to be produced from a roaming mechanism was unobserved. Following photodissociation at 193 nm of gaseous HC(O)OCH3 (0.42 Torr) and Ar (0.09 Torr), vibration-rotational emission spectra of CO (ν ≤ 4, J ≤ 38) and CO2 (with two components of varied internal distributions) were observed, indicating that new channels are open. Quantum-chemical calculations, computed at varied levels of theory, on the ground electronic potential-energy schemes provide a possible explanation for some of our observations. At 193 nm, the CO2 was produced from secondary dissociation of the products HC(O)O and CH3OCO, and CO was produced primarily from secondary dissociation of the product HCO produced on the S1 surface or the decomposition to CH3OH + CO on the S0 surface.

Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3

In the present work, we report a detailed description of the symmetry properties of the eight-atomic molecule ethane, with the aim of facilitating the variational calculations of rotation-vibration spectra of ethane and related molecules. Ethane consists of two methyl groups CH 3 where the internal rotation (torsion) of one CH 3 group relative to the other is of large amplitude and involves tunnelling between multiple minima of the potential energy function. The molecular symmetry group of ethane is the 36-element group G 36 , but the construction of symmetrised basis functions is most conveniently done in terms of the 72-element extended molecular symmetry group G 36 (EM). This group can subsequently be used in the construction of block-diagonal matrix representations of the ro-vibrational Hamiltonian for ethane. The derived transformation matrices associated with G 36 (EM) have been implemented in the variational nuclear motion program TROVE (Theoretical ROVibrational Energies). TROVE variational calculations are used as a practical example of a G 36 (EM) symmetry adaptation for large systems with a non-rigid, torsional degree of freedom. We present the derivation of irreducible transformation matrices for all 36 (72) operations of G 36 (M) (G 36 (EM)) and also describe algorithms for a numerical construction of these matrices based on a set of four (five) generators. The methodology presented is illustrated on the construction of the symmetry-adapted representations both of the potential energy function of ethane and of the rotation, torsion and vibration basis set functions.

Accurate all-electron calculation on the vibrational and rotational spectra of ground states for O2 and its ions**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403300), the National Natural Science Foundation of China (Grant Nos. 91750104, 11574114, and 11874177), and the Natural Science Foundation of Jilin Province, China (Grant No. 20160101332JC).

The potential energy curves, spectroscopic constants, and low-lying vibration–rotation levels of ground-state O2 and its cation and anion were calculated with the explicitly correlated multireference configuration interaction method. The zeroth-order reference wavefunction was treated with the complete active space multiconfigurational self-consistent field method, in which the active space was carefully selected, and an additional molecular orbital was added into the full valence active space. The electron correlation of the 1s core in the oxygen atom was considered in the computations. The Davidson correction on molecular energy was considered to account for higher electron excitation. The relativistic effects, including the scalar relativistic effect and spin–orbit coupling, were considered in the computation of potential energy curves. These physical effects on the spectroscopic constants were examined. The low-lying levels of vibration–rotation spectra of O2 and its ions were determined based on the computed potential energy curves. Comparisons with available experiments were made and excellent agreement was obtained for the vibrational and rotational parameters. The spectroscopic constants and vibration–rotation spectrum of , which is sparse in experiments, were provided. Our study will shed some light on further theoretical and experimental studies on these simple but important molecular systems.

Evidence for Triangular D_{3h}^{'} Symmetry in ^{13}C.

We derive the rotation-vibration spectrum of a 3α+1 neutron(proton) configuration with triangular D_{3h} symmetry by exploiting the properties of the double group D_{3h}^{'} and show evidence for this symmetry to occur in the rotation-vibration spectra of ^{13}C. Our results, based on purely symmetry considerations, provide benchmarks for microscopic calculations of the cluster structure of light nuclei.

High-resolution spectral analysis of hybrid A/B-type band of 1,3-butadiene at 6.2 μm using an EC-QCL coupled with cavity ring-down spectroscopy

The fine rotational-vibrational spectra of long-chain molecules like 1,3-butadiene are very closely spaced and highly overlapped. Such investigations require high-sensitive techniques to avoid overlapping and adequate resolution to observe their fine structure spectra. In this work, we have utilized a high-resolution external cavity-quantum cascade laser at ∼6.2 μm coupled with high-sensitive cavity ring-down spectroscopy (CRDS) to determine the fine ro-vibrational spectra of 1,3-butadiene in the gas phase. We experimentally probed the hybrid A/B-type band at 1596.412 cm−1 and also calculated relevant spectroscopic parameters of 1,3-butadiene using Gaussian 16 and subsequently simulated the spectra using PGOPHER simulation. Finally, we selected a unique interference-free spectral region within the 1,3-butadiene spectrum, and performed detailed ro-vibrational study of 3 spectral lines in this region. These results are a great advance over the earlier works and provide a spectroscopic window that may enable selective and high-sensitive sensing of 1,3-butadiene in the future.

Discovery of New Lines in the R9 Multiplet of the 2v_{3} Band of ^{12}CH_{4}.

We present the first results for resolving methane (CH_{4}) line transition frequencies down to the kilohertz level for overlapping lines using comb-linked cavity ring-down spectroscopy, while most available laboratory measurements, having resolution at the megahertz level, cannot separate merged lines. To demonstrate the technique, Lamb-dip spectra and linear-absorption spectra were used to identify overlapped lines of vibration-rotation spectra in the R9 multiplet of the 2v_{3} band. Three new weak lines were found for the first time. The experimental methods are extensible to other important bands of CH_{4} and many other gas-phase molecules, and should provide a more detailed understanding of molecular structure and line parameters for future high-precision studies.

The FELion cryogenic ion trap beam line at the FELIX free-electron laser laboratory: infrared signatures of primary alcohol cations.

The combination of a 4 K 22-pole ion trap instrument, FELion, with the widely tunable free electron lasers at the FELIX Laboratory is described in detail. It allows for wide-range infrared vibrational spectroscopy of molecular ions. In this study, the apparatus is used for infrared vibrational predissociation (IR-PD) measurements of the simple alcohol cations of methanol and ethanol as well as their protonated forms. Spectra are taken by tagging the cold molecular ions with He atoms. The infrared spectrum of protonated methanol is recorded for the first time, and the wavelength coverage for all other species is substantially extended. The bands of all spectra are analysed by comparison to ab initio calculation results at different levels of theory. Vibrational bands of different isomers and conformers (rotamers) are discussed and identified in the experimental spectra. Besides the measurement of IR-PD spectra, the method of infrared multiple photon dissociation IR-MPD is applied for some cases. Spectral narrowing due to the cold environment is observed and rotational band contours are simulated. This will help in identifying more complex species using the IR-MPD method in future measurements. Overall the IR-PD spectra reveal more bands than are observed for the IR-MPD spectra. In particular, many new bands are observed in the fingerprint region. Depletion saturation of the finite number of trapped ions is observed for the IR-PD spectra of the ethanol cation and the presence of only one isomeric species is concluded. This special feature of ion trapping spectroscopy may be used in future studies for addressing specific isomers or cleaning the ion cloud from specific isomers or conformers. In addition, the results of this study can be used as a basis to obtain high-resolution infrared vibrational and THz rotational spectra of alcohol ions in order to detect them in space.