# DUSCHINSKY MIXING BETWEEN FOUR NON-TOTALLY SYMMETRIC NORMAL COORDINATES IN THE $\mathrm{S}_{1}$--$\mathrm{S}_{0}$ VIBRONIC STRUCTURE OF PHENYLVINYLACETYLENE: A QUANTITATIVE ANALYSIS

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 Title: DUSCHINSKY MIXING BETWEEN FOUR NON-TOTALLY SYMMETRIC NORMAL COORDINATES IN THE $\mathrm{S}_{1}$--$\mathrm{S}_{0}$ VIBRONIC STRUCTURE OF PHENYLVINYLACETYLENE: A QUANTITATIVE ANALYSIS Creators: Muller, Christian W.; Liu, Ching-Ping; Newby, Josh J.; Zwier, Timothy S. Issue Date: 2008 Abstract: Phenylvinylacetylene is one of the $\mathrm{C}_{10}\mathrm{H}_{8}$ isomers that is a likely initial adduct formed by radical-molecule reactions of importance in combustion processes$^{1}$. \begin{wrapfigure}[9]{l}{5.5cm} Due to its longer conjugated side chain compared to that of its parent styrene, \mbox{PVA} can support Duschinsky mixing among several low-frequency out-of-plane coordinates, increasing the complexity of this mixing relative to that of styrene. We have studied the fluorescence excitation spectrum and several single vibronic level fluorescence~(\mbox{SVLF}) spectra of the $\mathrm{S}_{1}$\,$\leftarrow$\,$\mathrm{S}_{0}$ transition of~\mbox{PVA} cooled in a supersonic jet. Visual inspection of four hot-band \mbox{SVLF} spectra and seven normal \mbox{SVLF} spectra provided evidence for mixing between the lowest non-totally symmetric vibrational coordinates~($\nu_{45}$, $\nu_{46}$, $\nu_{47}$, and~$\nu_{48}$). The intensities of nearly 280~overtone and combination transitions of these normal modes in the eleven \mbox{SVLF} spectra and the fluorescence excitation spectrum were quantitatively analyzed in order to determine the amount of Duschinsky mixing between the four vibrational coordinates. Four-dimensional Franck-Condon overlap integrals were calculated based on recursion relations between harmonic oscillator wavefunctions derived using the standard generating function approach$^{2}$. The calculated intensities were fit to experimental intensities in an automated fitting procedure in which an unweighted least-squares sum was minimized using a patternsearch algorithm to find the optimized Duschinsky rotation angles. The results of the Duschinsky analysis will be discussed in light of the $\pi$--$\pi^{\ast}$ transition involved in the electronic excitation. \vspace*{0.2cm} (1) A.~G.~Robinson, P.~R.~Winter and T.~S.~Zwier, \textit{J. Phys. Chem.~A}, \textbf{2002}, \textit{106}, 5789.\\ (2) P.~T.~Ruhoff, \textit{Chem. Phys.}, \textbf{1994}, \textit{186}, 355. URI: http://hdl.handle.net/1811/33243 Other Identifiers: 2008-TG-05