Knowledge Bank

Torsional splittings in the torsional hot band $v9+v4$ of $C2H6$ have been measured in the P and R branch sub-bands from $R15$ to $P16$. Every transition is split into a non-degenerate and a doubly degenerate component with appittings generally near $0.086cm-1$. Individual splittings vary between extrcames of $0.235cm-1$ and $-.079cm-1$ (splitting is of opposite phase). The detailed behavior of the splitting is deseribed quantitively by the $zeroth$ order torsional Hamiltonian for $\nu 9$. $HTOR(9)=AP\gamma 2+V62(9)(1-\cos 6\gamma ).$ together with the xy Coriolis Interaction $operator(1)$ $HCOR-2B\zeta 4,9xy[(2A)1/2P\gamma (J-Q9++J+Q9-)-(2A)-1/2\sin 6\gamma 6(J-P9++J+P9-)]$ 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 $zeroth$ order splitting $(0.086cm-1)$ and the Coriolis interaction constant ($\zeta 4,9xy$) 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 $ethane(1)$.