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

\underline{THOMAS MÜLLER}, PATRICK DUPRÉ^{a}, and PATRICK H. VACCARO, Department of Chemistry, Yale University, 225 Prospect Street, New Haven, CT 06520; FRANCISCO PEREZ-BERNAL^{b} and FRANCESCO IACHELLO, Center for Theoretical Physics, Yale University, New Haven, CT 06520.

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 jetcooled S_{2}O molecules. The fluorescence accompanying selective excitation of single rovibronic lines in the 2_{0}^{2}3_{0}^{1} and 2_{o}^{v} (v=0-3) bands of the intense C̃ ^{1}A′ ← X̃ ^{1}A′ (π^{∗} ←π) 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 ν_{2} S-S stretching mode and residing up to ∼13000 cm^{−1}above the vibrationless X̃ ^{1}A′ zero-point energy have been observed and assigned. Detailed analyses of S_{2}O vibrational energies within the X̃ and C̃ 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 X̃ ^{1}A′ surface is substantially more ”local” in nature than the C̃ ^{1}A′ state, with the latter exhibiting significant mixing of vibrational character among the ν_{1} (S-O stretching), ν_{2} (S-S stretching) and (to a lesser extent) ν_{3} (bending) degrees of freedom. Structural parameters deduced from algebraic analyses largely confirm the C̃ ^{1}A′ equilibrium geometry inferred from previous studies under the assumption of an unchanged S-O bond length upon C̃ ← X̃ excitation.

aPermanent address: High Magnetic Field Laboratory, CNRS, BP 166, 38042 Grenoble, Cedex 9 (France)

bPermanent address: Facultad de Fisica, Universidad de Sevilla, Apartado Postal 1065, 41080 Sevilla (Spain)