Interaction of vibrational fundamental and combination states of ethylene in 3 $\mu$m region

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Ohio State University

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Formalism of symmetry groups has been developed and applied to expand the vibrational-rotational Hamiltonian and operator of dipole moment of ethylene into a power series of annihilation and creation operators as well as angular momentum operatores. This approach allows to characterize every term of the series by its specific order in which the operators appear. The first analysis of the 3 $\mu$m spectra reveals the strong coupling between $\nu_{9}$, $\nu_{11}$, $\nu_{2} + \nu_{12}$ and $2 - \nu_{10} + \nu_{12}$ yielding shifts of about $0.01 cm^{-1}$ for some low J and K lines of $C_{2}H_{4}$. We find that significant shifts are due to perturbations of $\nu_{9}$ rotational-vibrational levels via $3^{rd}$ order b-type Coriolis interaction with the $\nu_{3} + \nu_{8} + \nu_{12}$ rotational levels A prominent borrowing of transition dipole moment is predicted for some otherwise dark rovibrational lines of the $\nu_{3}+\nu_{8}+\nu_{12}$ band. These satellite lines have been found and assigned in low temperature spectra of ethylene recorded by the F-center laser spectrometer in a jet and afterwords in room temperature spectra recorded earlier by the difference-frequency laser spectrometer [1] and recently by the FTIR spectrometer in the Giessen group. The fitting of interaction parameters with the mentioned perturbations leads to a standerd deviation of 2 $10^{3}$ $cm^{-1}$, for low $J$ lines of ethylene. The leading coupling parameters in the pentade $\nu_{9}$ $\nu_{11}$, $\nu_{2} + \nu_{12}$; $2- \nu_{10} + \nu_{12}$ and $\nu_{3} + \nu_{8} + \nu_{12}$ are shown in the table The last parameter approximately describes, too the perturbations between $\nu_{9}$+$\nu_{10}$ and $\nu_{3}$+$\nu_{8}$+2-$\nu_{10}$, observed in the hot bands spectra [1] A.S. Pine Tunable Laser Survey of Molecular Air Pollutants, Final Report NSF/ASRA/DAR 78-24562,MIT, Lexington, Mass, (1980)


Author Institution: General Physics Institute RAS; Department of Molecular and Laser Physics, Catholic University of Nijmegen