Full dimensional Franck-Condon factors for the acetylene $\tilde{\mathbf {A}}$Ã 1
A
u—$\mathbf {\tilde{X}}$X̃ $\mathbf {^1\Sigma _g^+}$Σg+1 transition. II. Vibrational overlap factors for levels involving excitation in ungerade modes
Authors: Park G. Barratt , Baraban Joshua H. , Field Robert W. 
Published: October 2014

A full-dimensional Franck-Condon calculation has been applied to the \documentclass[12pt]{minimal}\begin{document}$\tilde{\mathrm{A}}$\end{document}Ã 1Au—\documentclass[12pt]{minimal}\begin{document}$\tilde{\mathrm{X}}$\end{document}X̃ \documentclass[12pt]{minimal}\begin{document}$^1\Sigma _g^+$\end{document}Σg+1 transition in acetylene in the harmonic normal mode basis. Details of the calculation are discussed in Part I of this series. To our knowledge, this is the first full-dimensional Franck-Condon calculation on a tetra-atomic molecule undergoing a linear-to-bent geometry change. In the current work, the vibrational intensity factors for levels involving excitation in ungerade vibrational modes are evaluated. Because the Franck-Condon integral accumulates away from the linear geometry, we have been able to treat the out-of-plane component of trans bend (\documentclass[12pt]{minimal}\begin{document}$\nu _4^{\prime \prime }$\end{document}ν4′′) in the linear \documentclass[12pt]{minimal}\begin{document}$\tilde{\mathrm{X}}$\end{document}X̃ state in the rotational part of the problem, restoring the χ Euler angle and the a-axis Eckart conditions. A consequence of the Eckart conditions is that the out-of-plane component of \documentclass[12pt]{minimal}\begin{document}$\nu _4^{\prime \prime }$\end{document}ν4′′ does not participate in the vibrational overlap integral. This affects the structure of the coordinate transformation and the symmetry of the vibrational wavefunctions used in the overlap integral, and results in propensity rules involving the bending modes of the \documentclass[12pt]{minimal}\begin{document}$\tilde{\mathrm{X}}$\end{document}X̃ state that were not previously understood. We explain the origin of some of the unexpected propensities observed in IR-UV laser-induced fluorescence spectra, and we calculate emission intensities from bending levels of the \documentclass[12pt]{minimal}\begin{document}$\tilde{\mathrm{A}}$\end{document}Ã state into bending levels of the \documentclass[12pt]{minimal}\begin{document}$\tilde{\mathrm{X}}$\end{document}X̃ state, using normal bending mode and local bending mode basis sets. Our calculations also reveal Franck-Condon propensities for the Cartesian components of the cis bend (\documentclass[12pt]{minimal}\begin{document}$\nu _5^{\prime \prime }$\end{document}ν5′′), and we predict that the best \documentclass[12pt]{minimal}\begin{document}$\tilde{\mathrm{A}}$\end{document}Ã-state vibrational levels for populating \documentclass[12pt]{minimal}\begin{document}$\tilde{\mathrm{X}}$\end{document}X̃-state levels with large amplitude bending motion localized in a single C–H bond (the acetylene↔vinylidene isomerization coordinate) involve a high degree of excitation in \documentclass[12pt]{minimal}\begin{document}$\nu _6^{\prime }$\end{document}ν6′ (cis-bend). Mode \documentclass[12pt]{minimal}\begin{document}$\nu _4^{\prime }$\end{document}ν4′ (torsion) populates levels with large amplitude counter-rotational motion of the two hydrogen atoms.