TORSIONAL SPLITTINGS IN $v_{9}^{+}v_{4}$ OF $C_{2}H_{6}$

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Ohio State University

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Torsional splittings in the torsional hot band $v_{9}^{+}v_{4}$ of $C_{2}H_{6}$ have been measured in the P and R branch sub-bands from $R_{15}$ to $P_{16}$. Every transition is split into a non-degenerate and a doubly degenerate component with appittings generally near $0.086 cm^{-1}$. Individual splittings vary between extrcames of $0.235 cm^{-1}$ and $-.079 cm^{-1}$ (splitting is of opposite phase). The detailed behavior of the splitting is deseribed quantitively by the $zero^{th}$ order torsional Hamiltonian for $\nu_{9}$. $H_{TOR}^{(9)} = A P^{2}_{\gamma}+ V_{\frac{6}{2}}^{(9)} (1 - \cos 6\gamma).$ together with the xy Coriolis Interaction $operator^{(1)}$ $H_{COR}-2B\zeta^{xy}_{4,9}[(2A)^{1/2}P_{\gamma}(J_{-} Q_{9+}+J_{+}Q_{9-})-(2A)^{-1/2}\frac{\sin 6\gamma}{6}(J_{-}P_{9+}+ J_{+}P_{9-})]$ connecting $\nu_{9}+\nu_{4}$ and the excited torsional states $2\nu_{h}, 3\nu_{h}, 4\nu_{h}, 5\nu_{h}$, and $6\nu_{h}$. Of these, interactions with the nearaby $4\nu_{h}$ and $5\nu_{h}$ states contribute very significantly to the splittings. Interactions of $\nu_{9}+\nu_{4}$ with $n\nu_{h}$ (n=odd) are nominally forbidden (g + u) in the high barrier limit, corresponding to a rigid molecule. Such interactions are not strictly forbidden, however, but are allowed only in doubly degenerate torsional states, with matrix elements which increase rapidly with torsional quantum number. The $zero^{th}$ order splitting $(0.086 cm^{-1})$ and the Coriolis interaction constant ($\zeta^{xy}_{4,9}$) and torsional matrix elements consistent with the spectra are predicted extremely well by the coefficients determined from the analysis of splittings in the $\nu_{9}$ band of $ethane^{(1)}$.


$^{1}$ J. Susskind, D. Reuter, D. E. Jennings, S. J. Daunt, W. E. Blass, and G. W. Halsey, J. Chem. Phys., 77, 2728 (1982)
Author Institution: NASA GSFC.; Molecular Spectrosocopy Laboratory, Dept. of Physics and Astronomy, University of Tennessee, Knoxville. TN 37996