Torsion Rotation Interactions Research Articles

An Analysis of Higher Order Vibration–Torsion–Rotation Interactions and Spectra for a Molecule with an Internal Rotor

Motivated by attempts to answer the questions (i) if the same order of magnitude is really appropriate for the torsional angular momentum termsP2γand the rotational angular momentum termP2(orP2a), (ii) how to systematically analyze various higher order interaction effects, especially the torsional effects, and (iii) if a reduced Hamiltonian can be used to fit observed spectroscopic data to an accuracy approaching experimental uncertainties over a significant range of quantum states, a detailed discussion is presented on the order of magnitude of a Hamiltonian termHmlnfor molecules with an internal rotation. A new scheme of the ordering by magnitude is proposed to analyze the vibration–torsion–rotation (VTR) interactions, in which the importance of the torsional problem is emphasized. The contact transformation technique is applied to the VTR Hamiltonian, which makes it possible to analyze clearly various higher order VTR interactions and their effects in the VTR spectra of the molecule. The resulting formulas are applicable to analyze observed spectra. A reduced torsion–rotation Hamiltonian for the molecule withC3v(M) symmetry is given in the new ordering scheme. As an application, a total of 568 microwave lines withvt≤ 3,J≤ 42 andK≤ 8 for CH318OH have been fitted to 64 molecular constants by using the reduced Hamiltonian with a root mean square (rms) of 0.262 MHz, where theAandEsubstates are treated simultaneously. About 35 newly assigned lines are added to our former fitting data (M. Ikeda, Y. B. Duan, S. Tsunekawa, and K. Takagi,ApJS,117, 249 (1998)).

Analysis of Rotational Transitions in Excited Vibrational States of Propionitrile (C2H5CN)

We have observed rotational transitions of propionitrile (C2H5CN) in the 8–200 GHz region and assigned 208 transitions withJ≤ 16 andKa≤ 2 in the first excited state of torsional vibration, 244 transitions withJ≤ 16 andKa≤ 2 in the first excited state of CCN in-plane bending vibration, and 374 transitions withJ≤ 16 andKa≤ 4 in the first excited state of CCN out-of-plane bending vibration. We simultaneously analyzed these transitions in the three excited vibrational states, combining with the previously reported transitions in the ground vibrational state, on the basis of a Hamiltonian including CCN-bending vibration–torsion–rotation interactions. A total of 1560 transitions were fitted with 0.95-MHz 1ς standard deviation, and molecular constants were determined.

Class II maser candidates in substituted methanol: CH3OD, 13CH3OH, CH318OH and CH3SH

We investigate the possibility of interstellar masers in transitions of the methanol isotopomers CH3OD, 13CH3OH and CH318OH, and of CH3SH. The model used, in which masers are pumped through the first and second torsionally excited states by IR radiation, has accounted successfully for the Class II masers in main species methanol, 12CH316OH. Several potential maser candidates are identified for CH3OD, their detectability depending on the enrichment of this species in star-forming regions. In 13CH3OH and CH318OH the best maser candidates are direct counterparts of the well-known 6.7- and 12.2-GHz methanol masers, but the lower interstellar abundance of these substituted species means that the expected brightness is greatly reduced. The maser candidates in CH3SH are also weak. By comparing these species we find that the large b-component of the dipole moment in methanol plays a significant role in its propensity to form masers, as does the strong torsion–rotation interaction due to the light hydroxyl frame. Thus the exceptional brightness of interstellar methanol masers is due to a favourable combination of molecular properties as well as high interstellar abundance.

Nonlinear dynamics of torsion–rotation interactions: A model study of toluene

The internal rotation, or torsion, of a methyl group has been implicated in the acceleration of intramolecular vibrational redistribution (IVR) in numerous experimental studies. In the present work, we investigate its interaction with overall molecular rotation. To isolate the effects of torsion–rotation coupling, a simple two-degree-of-freedom model, including only torsion and three-dimensional rotation, is constructed and its dynamics at j=45 for several energies are studied. Investigation of other values of angular momentum indicate that the results reported are largely independent of j. Two primary effects are observed: (i) a shifting of the stable and unstable axes of rotation due to free methyl torsion, and (ii) a limited degree of weakly chaotic dynamics for trajectories whose torsional energy is near the top of its barrier. Chaos is first observed at the lowest energy at which torsion can surmount its barrier, but then disappears from the system at higher energies. Model toluene exhibits only narrow, high-order nonlinear resonances due to the frequency disparity between torsion and rotation, and these resonances are reduced in number by “selection rules” that arise in part from the symmetry of the Hamiltonian. These observations are analyzed in depth and simple, but quantitative, models are proposed to explain the magnitude of the rotational axis shift, the limited extent of chaos, and the resonance selection rules.

The Third and Fourth Torsional States of Acetaldehyde

A least-squares fit is presented of 1105 far-infrared and 2860 microwave transitions in acetaldehyde, which sample rotational levels in all torsional states below the lowest-frequency small-amplitude vibration ν10. Four-fifths of these transitions, involving torsional states below the barrier (vt≤ 2), were treated in an earlier publication; here the theoretical model is further tested by extending the data set to include thevt= 3 and 4 states above the barrier. The new data set includes (i) 224vt= 3 ← 2 far-infrared transitions, (ii) Nizhny Novgorod RAD-2a-type andb-type submillimeter transitions invt= 2, which make more precise ΔK= ±1 intervals in this last torsional state below the barrier, (iii) RAD-3a-type submillimeter transitions invt= 3 and 4, and (iv) microwave and submillimeter measurements or remeasurements from NIST and Lille of transitions withvt≤ 4. The global fit, which uses an improved version of the computer program previously applied to thevt≤ 2 data, gave a weighted overall standard deviation of 1.21 with 55 adjusted and 2 fixed parameters. Residuals from the fit were close to experimental uncertainties for the infrared wavenumber measurements and for microwave and submillimeter frequency measurements below the barrier, but some residuals reached several MHz or more for frequency measurements involving levels near ν10. We have attempted to achieve a qualitative understanding of the numerical results by presenting a general overview of internal rotation energy levels above the barrier and a theoretical discussion of torsion–rotation interactions among these levels.

Higher-order effects in the vibration–torsion–rotation spectra of a molecule with an internal rotor

The sequential contact transformation technique is applied to the vibrational–torsional–rotational Hamiltonian for molecules containing a threefold symmetric internal rotor, which makes it possible to analyze various higher-order vibration–torsion–rotation interactions and their effects in the vibration–torsion–rotation spectra of the molecule. The formalism for the calculation of Hamiltonian coefficients is developed in terms of the fundamental molecular parameters. The resulting formulas are applicable to analyze the molecular structure. The theory presented is applied to the calculation of the quartic and sixtic centrifugal distortion constants of the molecule.

Torsion-vibration interaction in H 2O 2: First high-resolution observation of ν3

High-resolution Fourier transform spectra recorded between 450 and 1050 cm −1 have been used to obtain an extensive analysis of several vibration-torsion-rotation bands of H 2O 2 leading to a precise and extended set of torsion-rotation levels in both the ground and the ν 3 vibrational states of this molecule. In particular, the first observation of the ( n, τ) = (0, 1) and (0, 3) torsional states of the v 3 = 1 vibrational state is reported. The centers of these two torsional bands are 865.939 and 877.934 cm −1, respectively. In addition to the observation of ν 3, new results concerning the ( n, τ) torsional states of the ground state up to n = 3 are presented. All the observed levels have been reproduced with the aid of a Hamiltonian which takes into account the torsion-rotation interactions within a given vibrational state, the staggering due to the cis-barrier, and the strong Coriolis-type interaction which couples the levels of the ground state with those of the v 3 = 1 state. Indeed it is impossible to treat the ground state levels without this interaction, which has been considered here for the first time.

Torsion–rotation interactions in a two-top molecule: High resolution S1←S electronic spectrum of 2,3-dimethylnaphthalene

A rotationally resolved fluorescence excitation spectrum of the O00 band in the S1←S0 transition of 2,3-dimethylnaphthalene has been obtained using a cw laser/molecular beam spectrometer. More than 3000 lines were observed, each exhibiting a width of about 3 MHz. Despite the proximity of the two methyl groups, the observed rotational structure can be interpreted satisfactorily using an uncoupled rotor model. However, extensive torsion–rotation interactions are observed. Accurate measurements of these perturbations are used to determine the effective threefold hindering potentials in both electronic states, V3(S0)=652 cm−1 and V3(S1)=391 cm−1, respectively. Rotor–rotor couplings do influence these barriers as well as the patterns of lines observed in the rotationally resolved spectra of higher vibronic bands.

Internal rotation in low barrier, heavy-top molecules: Calculation of energy levels

A computer program has been written for the calculation of the energy levels for internal rotation in a low barrier heavy-top molecule, such as CF3NO2. Molecules of this type are expected to exhibit microwave spectra of intermediate barrier type because the presence of a heavy internal-top increases the reduced barrier height. The necessary treatment is based on the simplest IAM of an asymmetric top molecule, i.e., where the internal rotation axis co-incides with one of the principal axes. The energy matrix can be factorized into the eigenstates of the torsion and torsion-rotation interaction Hamiltonian. This factorization greatly facilitates the calculation of high-J levels and the application of a least-squares fitting technique to observed microwave spectra. The output of the program gives the torsional eigenvalues and eigenfunctions, the rotational levels and eigenfunctions, transition frequencies together with relative intensities and first-order Stark coefficients. This program can be applied to all ranges of barrier height especially for an intermediate barrier case.

ChemInform Abstract: INFRARED ABSORPTION INTENSITIES OF TORSION‐ROTATION TRANSITIONS OF MOLECULES WITH SYMMETRIC INTERNAL ROTOR

The infrared absorption intensities of torsion-rotation transitions were theoretically derived on the basis of torsion-rotation interactions of molecules with symmetric internal rotor. The theoretical intensities depend upon molecular structure parameters and molecular dipole moment. Implications of the present theory are discussed on absolute intensities, orientations of dipole transition moment, band types (A, B, or C), and deuteration effects on absorption intensities of methyl torsional transitions. For propylene oxide and propylene sulfide, the far infrared spectra of the gaseous state were measured, and the experimental absorption intensities of methyl torsional vibrations were compared with theoretical intensities.

Infrared Absorption Intensities of Torsion–Rotation Transitions of Molecules with Symmetric Internal Rotor

Abstract The infrared absorption intensities of torsion-rotation transitions were theoretically derived on the basis of torsion-rotation interactions of molecules with symmetric internal rotor. The theoretical intensities depend upon molecular structure parameters and molecular dipole moment. Implications of the present theory are discussed on absolute intensities, orientations of dipole transition moment, band types (A, B, or C), and deuteration effects on absorption intensities of methyl torsional transitions. For propylene oxide and propylene sulfide, the far infrared spectra of the gaseous state were measured, and the experimental absorption intensities of methyl torsional vibrations were compared with theoretical intensities.

Microwave Spectra of Molecules of Astrophysical Interest: III. Methanol

The available data on the microwave spectrum of methanol are critically reviewed for information applicable to radio astronomy. Molecular data such as moments and product of inertia, torsional potential constants, centrifugal distortion and torsion-rotation interaction constants, dipole moment, and structural parameters are tabulated. Observed rotational transitions are presented for the astronomically interesting isotopic forms of methanol when available. Detailed centrifugal distortion and torsion-rotation interaction calculations have been carried out for the most abundant isotopic form of methanol. Transitions are tabulated for the frequency range from 500 MHz to 200 GHz. Measured transition error limits have been reproduced from the original literature. References are given for all data included.

Barriers to Internal Rotation in Asymmetric Molecules: 3-Fluoropropene

The potential function hindering internal rotation in 3-fluoropropene has been determined using microwave and far-infrared spectroscopic data. It is given by the six potential constants in cm−1 (calories/mole): V1 = − 247 ± 30(− 707), V2 = 185 ± 25(530), V3 = 857 ± 15(2449), V4 = 188 ± 25(538), V5 = 7 ± 5(20), V6 = − 93 ± 10(− 265). From these the cis–gauche and gauche–trans–gauche barrier heights were determined to be 1090 + 75 − 25 cm−1 and 520 ± 40 cm−1, respectively. The spectra were interpreted using a one-dimensional model in which the only internal motion is the rotation about the bond connecting the top (–CH2F) to the frame (H2C=CH–); the various parameters in the Hamiltonian which was derived using the theory of internal rotation in asymmetric molecules developed by Quade and Lin were determined numerically and expressed as Fourier expansions in the internal coordinate α. In addition, the general theory was rederived and extended to include the case where neither the top nor the frame has a plane of symmetry. The large torsion–rotation interaction terms were reduced numerically by means of a Van Vleck transformation. The angle dependence of the reduced moment of inertia for the torsion was removed by a nonlinear coordinate transformation which yields a new Hamiltonian giving the same energy spectrum as the old but having a constant kinetic energy and a modified potential function. Finally, our potential is compared with that which was calcuated from the electrostatic model of Lowe and Parr.