# ALGEBRAIC APPROACH FOR THE CALCULATION OF POLYATOMIC FRANCK-CONDON FACTORS: APPLICATION TO THE VIBRONICALLY-RESOLVED EMISSION SPECTRUM OF $S_{2}O$

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 Title: ALGEBRAIC APPROACH FOR THE CALCULATION OF POLYATOMIC FRANCK-CONDON FACTORS: APPLICATION TO THE VIBRONICALLY-RESOLVED EMISSION SPECTRUM OF $S_{2}O$ Creators: Müller, Thomas; Dupré, Patrick; Vaccaro, P. H.; Pérez-Bernal, F.; Iachello, F. Issue Date: 1998 Publisher: Ohio State University Abstract: An algebraic theory, based upon expansion of the molecular Hamiltonian in terms of bosonic creation and annihilation operators, has been used to extract detailed vibrational information from vibronically-resolved emission spectra of jet-cooled $S_{2}O$ molecules. The fluorescence accompanying selective excitation of single rovibronic lines in the $2^{2}_{0}3^{1}_{0}$ and $2^{v}_{o} (\nu=0-3)$ bands of the intense $\tilde{C} {^{1}}A^{\prime} \leftarrow {^{1}}A^{\prime}(\pi^{\ast} \leftarrow \pi)$ absorption system were dispersed under moderate spectral resolution $(5-10 cm^{-1})$. Ground state vibrational levels possessing as much as 20 quanta of excitation in the $v_{2} S-S$ stretching mode and residing up to $\sim 13000 cm^{-1}$ above the vibrationless $\tilde{X} {^{1}}A^{\prime}$ zero-point energy have been observed and assigned. Detailed analyses of $S_{2}O$ vibrational energies within the $\tilde{X}$ and $\tilde{C}$ manifolds, as well as their interconnecting vibronic resonances, have been performed through a $U(2)$ based algebraic treatment. Although computationally no more intensive than a Dunham-like expansion, this approach offers the ability to extract multidimensional wavefunctions and related vibrational information. in particular, Franck-Condon factors and vibronic transition amplitudes can be evaluated efficiently without recourse to arduous numerical calculations. The emerging picture of $S_{2}O$ vibrational dynamics suggests that the $\tilde{X} {^{1}}A^{\prime}$ surface is substantially more local'' in nature than the $\tilde{C} {^{1}}A^{\prime}$ state, with the latter exhibiting significant mixing of vibrational character among the $\nu_{1}$ (S-O stretching), $\nu_{2}$ (S-S stretching) and (to a lesser extent) $\nu_{3}$ (bending) degrees of freedom. Structural parameters deduced from algebraic analyses largely confirm the $\tilde{C} {^{1}}A^{\prime}$ equilibrium geometry inferred from previous studies under the assumption of an unchanged S-O bond length upon $\tilde{C} \leftarrow \tilde{X}$ excitation. Description: $^{a}$ Permanent address: High Magnetic Field Laboratory, CNRS, BP 166, 38042 Grenoble, Cedex 9 (France) $^{b}$ Permanent address: Fac*** de Fisica, universi*** de Sevilla, Apartado Pos*** 1065, 41080 Sevilla (Spain) Author Institution: Department of Chemistry, Yale University; Center for Theoretical Physics, Yale University URI: http://hdl.handle.net/1811/19007 Other Identifiers: 1998-TB-06