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 X̃ state has attracted considerable attention because it grants Franck–Condon access to local bending vibrational levels of the X̃ 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 X̃ 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 X̃ 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 vx and vy quantum 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.