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

$^{a}$ 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 UniversityAn 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