Simplified cartesian basis model for intrapolyad emission intensities in the bent-to-linear electronic transition of acetylene

The acetylene emission spectrum from the trans-bent electronically excited à state to the linear ground electronic X state has attracted considerable attention because it grants Franck-Condon access to local bending vibrational levels of the X state with large-amplitude motion along the acetylene vinylidene isomerization coordinate. For emission from the ground vibrational level of the à state, there is a simplifying set of Franck-Condon propensity rules that gives rise to only one zero-order bright state per conserved vibrational polyad of the X state. Unfortunately, when the upper level involves excitation in the highly admixed ungerade bending modes, ν4^′ and ν6^′, the simplifying Franck-Condon propensity rule breaks down-as long as the usual polar basis (with v and l quantum numbers) is used to describe the degenerate bending vibrations of the X state-and the intrapolyad intensities result from complicated interference patterns between many zero-order bright states. In this article, we show that, when the degenerate bending levels are instead treated in the Cartesian two-dimensional harmonic oscillator basis (with v_xand v_yquantum numbers), the propensity for only one zero-order bright state (in the Cartesian basis) is restored, and the intrapolyad intensities are simple to model, as long as corrections are made for anharmonic interactions. As a result of trans cis isomerization in the à state, intrapolyad emission patterns from overtones of ν4^′ and ν6^′ evolve as quanta of trans bend (ν3^′) are added, so the emission intensities are not only relevant to the ground-state acetylene vinylidene isomerization, they are also a direct reporter of isomerization in the electronically excited state.