SIMPLIFIED CARTESIAN BASIS MODEL FOR INTRAPOLYAD EMISSION INTENSITIES IN THE A_X BENT-TO-LINEAR TRANSITION OF ACETYLENE

The acetylene emission spectrum from the textit{trans}-bent electronically excited $mathrm{tilde{A}}$ state to the linear ground electronic $mathrm{tilde{X}}$ state has attracted considerable attention because it grants Franck-Condon access to local bending vibrational levels of the $mathrm{tilde{X}}$ state with large-amplitude motion along the acetylene $rightleftharpoons$ vinylidene isomerization coordinate. For emission from the ground vibrational level of the $mathrm{tilde{A}}$ state, there is a simplifying set of Franck-Condon propensity rules that gives rise to emph{only one} zero-order bright state per conserved vibrational polyad of the $mathrm{tilde{X}}$ state. Unfortunately, when the upper level involves excitation in the highly admixed textit{ungerade} bending modes, $nu_4'$ and $nu_6'$, the simplifying Franck-Condon propensity rule breaks down---so long as the usual polar basis (with $v$ and $l$ quantum numbers) is used to describe the degenerate bending vibrations of the $mathrm{tilde{X}}$ state---and the intrapolyad intensities result from complicated interference patterns between many zero-order bright states. We show that when the degenerate bending levels are instead treated in the Cartesian two-dimensional harmonic oscillator basis (with $v_x$ and $v_y$ quantum numbers), the propensity for emph{only one} zero-order bright state (in the Cartesian basis) is emph{restored}, and the intrapolyad intensities are simple to model, so long as corrections are made for anharmonic interactions. As a result of $transrightleftharpoons cis$ isomerization in the $mathrm{tilde{A}}$ state, intrapolyad emission patterns from overtones of $nu_4'$ and $nu_6'$ evolve as quanta of textit{trans} bend ($nu_3'$) are added, so the emission intensities are not only relevant to the ground-state acetylene $rightleftharpoons$ vinylidene isomerization---they are also a direct reporter of isomerization in the electronically-excited state