THEORY OF PURE ROTATIONAL TRANSITIONS IN $C_{2}H_{6}$
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Date
1979
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Ohio State University
Abstract
The pure rotational spectrum of ethane is considered to be forbidden, since the point group of the molecule in its equilibrium position, $D_{3d}$, contains a center of symmetry. However, in the non-rigid molecules, belonging to the symmetry group $G^{+}_{36},$ torsion-vibration-rotation interaction induce an effective dipole moment of the form $\mu_{\omega} - \mu^{T}_{\omega} J_{\omega} P_{\gamma}(\omega = 0, \pm 1)$ where $J_{\omega}$ and $P_{\gamma}$ are components of the rotational and tensional angular momentum, respectively, and $\mu^{T}_{\omega}$ are coupling constants that obey the relation $\mu^{T}_{1} - \mu^{T}_{-1} + \mu^{T}_{0}$. This effective dipole moment operator gives rise to pure rotational transitions in doubly degenerate tensional states, with the selection rules $\Delta J = 0, \pm 1$ and $\Delta K = 0$. The same operator is also responsible for the pure torsionAL torsion-rotation transitions discussed $previously^{1,2}$. Expression for the integrated intensities of pure rotational transitions will be presented. Based on the estimate $\mu^{T}_{1} + \mu^{T}_{0} - 10^{-4}D$, derived from the observed torsion and fundamental $band^{1}$, the line strengths for low J transitions in the microwave region were calculated to be of the order of $10^{-11} cm^{-2} atm^{-1}$. Such lines can be observed in the laboratory with the state of the art microwave spectrometers. Estimated transition intensities in the infrared region are of the order of $10^{-8} cm^{-2} atm^{-1}$ and are considered too weak to be observed in the laboratory with conventional far infrared instrumentation.
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$^{1}$D. F. Eggers, JR., J. Chem, Phys, 48, 1393 (1967). $^{2}$D. F. Eggers, JR., R. C. Lord and Wickstrom, J. Mol. Spectrosc., 59, 63 (1976).
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