Indranath Mukhopadhyay

Torsion-rotation analysis of OH stretch overtone-torsion combination bands in methanol

We report rotationally resolved spectra of jet-cooled methanol for the OH stretch overtones, 2v(1) and 3v(1), and for the torsional combinations, 2v(1)+v(12), 2v(1)+2v(12), 3v(1)+v(12), and 3v(1)+2v(12). The spectra are obtained by direct excitation from the vibrational ground state with an infrared laser pulse. Population in the resulting upper state levels is detected by infrared laser assisted photofragment spectroscopy (IRLAPS). Global fits of the spectra to the Herbst Hamiltonian yield the torsional and rotational parameters, including F, rho, V-3, and V-6, for each OH stretch excited state. For each quantum of OH stretch excitation, we find that the torsional barrier height V-3 increases by 40.9 +/-1.9 cm(-1) and the torsional inertial F decreases by 0.89 +/-0.02 cm(-1). With reference to ab initio calculations, we explain the increase in V-3 in terms of changes in the electronic structure of methanol as the OH bond is elongated. For Deltav(12)=1 we observe only transitions with DeltaK=+/-1, and for Deltav(12)=2 we observe only DeltaK=0. We present a Franck-Condon model to explain these apparent selection rules and the overall pattern of intensity

Correlation problems and a correlation-free torsion-rotation Hamiltonian for a molecule with an internal rotor

To develop a correlation-free reduced form of torsion-rotation Hamiltonian that is suitable for analyzing observed spectra for methanol and its isotopic species, the origin of various classes of correlation problems often encountered in fitting the molecular constants to experimental data are analyzed for a molecule with an internal rotation. It is shown that the correlation problems can be completely eliminated by considering either the data set or the reduction of the Hamiltonian together with practical considerations, where an appropriate definition of order of magnitude plays an important role. For a molecule with C3v(M) symmetry such as methanol and its isotopic species, it is found that some terms which are included in the traditional or a reduced Hamiltonian given so far should not be used simultaneously. For example, the traditional terms k5Pa2(1−cos 3γ) and k6Pa{Pγ,1−cos 3γ} should not be used simultaneously as adjustable ones and one of three traditional terms k6Pa{Pγ,1−cos 3γ}, k7{Pγ2,1−cos 3γ}...

The calculation of molecular parameters for a molecule with an internal rotor

A derivation for the formulas to calculate centrifugal distortion constants, based on a recent formulation [Duan and Takagi, Phys. Lett. A (1995)] of centrifugal distortion effects for a molecule containing a threefold symmetric internal rotor, is presented. Some constants which are independent of the barrier derivatives, especially the constants representing interactions between torsion and rotation, are given in terms of molecular structural parameters and force constants. These calculated constants are helpful in the reduction of the Hamiltonian and in the analysis of observed transitions. The derived formulas are applied to numerical calculations of the centrifugal distortion constants of methanol. It is shown that most of the calculated constants are in good agreement with those obtained from the fitting to experimental data.

Vibration–torsion–rotation analysis of the ν12 band of CH3CD3

A Fourier transform spectrum of the lowest frequency degenerate fundamental of CH3CD3 (v12=1←0) near 680 cm−1 has been measured in order to investigate the vibration–torsion–rotation effects in a symmetric top. The spectrum was recorded at an instrumental resolution of 0.0024 cm−1 using a modified Bomem spectrometer. The temperature and pressure of the sample were 130 K and 0.4 Torr, respectively. Although the intrinsic tunneling splittings in each (J′←J″) multiplet are the order of 0.002 cm−1 or smaller, the splittings typically observed for an intermediate J″ of 10 are two to three orders of magnitude larger. These splittings are caused primarily by the Coriolis interaction between the torsional stack of levels v6=0,1,2,… for v12=1 and the corresponding stack for v12=0. The shift of each upper level (v12=1, l; J, v6=0, K, σ) is seen to be a sensitive function of (l;K,σ), where σ labels the torsional sublevels. Because of near degeneracies between the upper level and its interaction partner with (v12=0, ...

HIGH RESOLUTION SPECTROSCOPY OF CH3OD INVOLVING THE GROUND AND FIRST EXCITED TORSIONAL STATES IN THE VIBRATIONAL GROUND STATE

Abstract In this work, the reduced eighth order Hamiltonian parameters of CH3OD have been determined using the high resolution Fourier transform far-infrared (FIR) assigned transitions in the ground and first excited torsional states. The data set consisted of 2348 FIR transitions with the rotational angular momentum J

Observation and analysis of high-J o1−e1 inter-state transitions in CH2DOH

We report the observation and assignments of several series of transitions in CH2DOH, including a new and intense series of Q-branch c-type transitions between the e1 and o1 torsional substates through high values of the rotational quantum number J. Other transitions assigned are c-type R-branch and P-branch transitions between these two substates and a-type lines within the e1 and o1 substates. The assignments were facilitated by initial analysis of the strong Q-branch series, as recorded by the fast scan submillimeter spectroscopy technique (FASSST). The assigned lines of CH2DOH include the first inter-state transitions in the sub-millimeter-wave region and the first to possess high J-values. The completeness of the data generated by FASSST and the success of a simple power series analysis suggest that many parts of the spectrum of CH2DOH may be far more tractable than previously believed. The data should be useful in the development of a full Hamiltonian and in the assignment of astronomical emission f...

Quantum dynamics of methanol: Hamiltonian, representation and intensity considerations

Abstract Employing a body-fixed axis system and Jacobi coordinates, a model for the vibration–torsion–rotation Hamiltonian of the CH 3 OH molecule with large-amplitude internal motions has been derived. This Hamiltonian is expressed in terms of Jacobi coordinates and is partitioned in the form H A + H B + H int , where H A and H B are the rovibrational Hamiltonians of methyl group CH 3 and asymmetric rotor OH, and H int represents their interactions. The resulting Hamiltonian is used to carry out a pure quantum mechanical calculation for this kind of molecule or to construct the potential surface using observed data. The detailed discussion of the Hamiltonian is presented for the model with a rigid methyl group and a rigid OH, which describes five lower frequency vibrational modes and pure rotation in the molecule. We discuss the advantages of body-fixed Jacobi form of the Hamiltonian and solution strategies for practical programming. The properties of labels of the energy states, potential function and dipole moments are investigated according to the molecular symmetry group G 6 of methanol. Finally, the developed formulation is used to calculate the energy levels of CO-stretching–torsion–rotation for lower rotational excitation ( J ⩽5). Comparison of the calculated results with experimental ones is presented.

On the physical interpretation of torsion–rotational parameters for CH3OD isotopomers

Abstract Using the formulation (Phys. Lett. A 207 (1995) 203) of the centrifugal distortion effects in terms of the potential parameters for a molecule that contains a threefold symmetric internal rotor, molecular parameters have been determined for the 12 C and 13 C isotopomers of CH 3 OD with O-16, 17 and 18. The calculated parameters, especially the constants that represent interactions between torsion and rotation, are used to interpret the relationships among the terms in the reduced Hamiltonian and in the analysis of the observed torsion–rotational spectrum. Molecular parameters are calculated from several potential energy functions for methanol isotopomers to check the quality of these potentials. The dependence of torsion–rotational parameters on the mass of atom and the geometric parameters are addressed by comparisons of calculated values for various isotopomers of CH 3 OD. The parameters are compared with the parameters that were obtained from several global fits to experimental spectrum data. The good agreement between the calculated torsion–rotational parameters and those derived from the global fits demonstrates that the derived formulae provide a useful tool for understanding the physical origins of the Hamiltonian parameters and the dependence of torsion–rotational parameters on fundamental molecular parameters.

Analysis of torsion-rotational transitions in the first three torsional states of CH3OD

Abstract In the framework of systematic analysis and fitting of transition frequencies of methanol isotopomers with a reduced torsion-rotational Hamiltonian that is obtained from the one-large-amplitude internal rotation model, 1126 Fourier transform far-infrared (FIR) transitions involving the second excited torsional level ( v t =2) have been added to the data set of Duan and McCoy [J. Mol. Spectros. 199 (2000) 302] to achieve a global fit of the observed high resolution microwave (MW), millimeter wave (MMW) and Fourier transform FIR spectra for CH 3 OD. The CH 3 OD data set contains 460 MW and MMW transitions and 3474 Fourier transform FIR transitions with v t ⩽2 and J ⩽21. The MW and MMW transitions have been fit with a root-mean-square (rms) deviation of 0.12 MHz, whereas FIR transitions have a rms deviation of 0.00026 cm −1 . These deviations are approximately equal to the experimental uncertainties, indicating that the MW, MMW and FIR spectral transitions have been fit to an accuracy approaching the experimental uncertainties and the reduced torsion-rotational Hamiltonian model is capable of accurately describing CH 3 OD energy levels up through the second excited torsional level. The success of the fit demonstrates that the increased general asymmetry in CH 3 OD can be taken care adequately by the reduced Hamiltonian model.

High resolution spectroscopy in the second excited torsional state of CH3OD and the atlas of the Fourier transform spectrum in the range 20–205 cm−1

Abstract In this work, the reduced eighth order Hamiltonian that has been used for the determination of the molecular parameters—using the high resolution Fourier transform far-infrared (FIR) assigned transitions in the ground and first excited torsional states of CH3OD—has been applied to assign and refine the model for the second excited torsional state. The data set consisted of 1220 FIR transitions with the rotational angular momentum J