THR $\nu_{3} / \nu_{2} + \nu_{4} + \nu_{5}$ RESONANCE IN ACETYLENE

Author Institution: Molecular Physics Division, National Institute of Standards and TechnologyThe energy levels of the $\nu_{3}$ fundamental of $^{12}C_{2}H_{2}$ are accidentally perturbed by the levels of the close-lying combination band $\nu_{2}+\nu_{4}+\nu_{5}$. The interacting levels are so close that the resonance mixing causes the combination band to have very nearly the same intensity as the fundamental, and, in order to fit the observed line frequencies of either band to within the experimental uncertainties using conventional polynomial expansions in J(J+1), it is necessary to use very high-order terms in the expansions. This resonance also affects the overtone and combination levels involving quanta of $\nu_{3}$. The interaction is not a just a simple $2\times 2$ Fermi interaction, since the combination level has $\Sigma^{+}, \Sigma^{-} (\ell=0)$. and $\Delta (\ell =2)$ components. The $\Delta$ levels of the combination state are linked via Coriolis-like t-type resonance with the A levels, and this resonance, by virtue of the strong Fermi resonance, affects also the energy levels of the $\nu_{3}$ fundamental. Although this system has been studied in a number of laboratories, as yet no successful analysis has been performed to account for the observed line frequencies to within experimental uncertainty. During the course of a study of the $\Pi-\sigma$ combination bands in the $2.5 \mu m$ region and the hot bands in the $3 \mu m$ region which have a common upper state with the $2.5 \mu m$ bands, we recorded as well the $v_{3}$ and $v_{2}+v_{4}+v_{5} (\Sigma^{+})$ bands with a BOMEN spectrometer at a resolution of $0.004 cm^{-1}$. Although the A levels of the combination band have not been observed, we decided to attempt to fit the observed $\Sigma^{+}$ state line frequencies. In order to do this, an estimate of the unperturbed energies of the $\Sigma$ states as well as the B rotational constant of $\nu_{3}$ was made using the observed band centers and B values, and values of $\alpha_{2}, \alpha_{4}$ and $\alpha_{5}$ which have been determined previously. The $\Sigma^{+} - \Delta$ separation of the combination level was initially assumed to be that determined earlier in a study of the $\nu_{4}+\nu_{5}$ band system. A non-linear least-squares fitting program was used to determine the best estimate of the constants of the unperturbed bands. A 9 parameter fit yielded an experimentally limited standard deviation of $0.00036 cm^{-1}$. The unperturbed frequency of $\nu_{3}$ is $3288.7175(38) cm^{-1}$ and the Fermi interaction constant obtained is $6.46097(10) cm^{-1}$. The spectroscopic constants of the combination bands and hot bands studied will also be reported