Interaction of vibrational fundamental and combination states of ethylene in 3 μm region

\underline{Boris G. Sartakov}, General Physics Institute RAS, Vavilov str. 38, 117942, Moscow, Russia; Jos Oomens and Jörg Reuss, Department of Molecular and Laser Physics, Catholic University of Nijmegen Toernooiveld 1, 6525ED Nijmegen, The Netherlands.

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 operators. 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 μm spectra reveals the strong coupling between ν_{9}, ν_{11}, ν_{2} + ν_{12} and 2 · ν_{10} + ν_{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 ν_{9} rotational-vibrational levels via 3^{rd} order b-type Coriolis interaction with the ν_{3} + ν_{8} + ν_{12} rotational levels. A prominent borrowing of transition dipole moment is predicted for some otherwise dark rovibrational lines of the ν_{3} +ν_{8} +ν_{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 afterwards 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 standard deviation of 2 · 10^{−3} cm^{−1}, for low J lines of ethylene. The leading coupling parameters in the pentade ν_{9}, ν_{11}, ν_{2} + ν_{12}, 2 · ν_{10} + ν_{12} and ν_{3} + ν_{8} + ν_{12} are shown in the table

States  Type  Value (cm^{−1})
ν_{11} and ν_{2} + ν_{12}  cubic anharmonicity  45.459(2)
ν_{2} + ν_{12} and 2 · ν_{10} + ν_{12} cubic anharmonicity  -10.721(2)
ν_{9} and ν_{11}  1^{st} order Coriolis interaction -0.130(3)
ν_{9} and ν_{3} + ν_{8} + ν_{12}  3^{st} order Coriolis interaction -0.022(8)

The last parameter approximately describes, too, the perturbations between ν_{9}+ν_{10} and ν_{3}+ν_{8}+2·ν_{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)