Knowledge Bank

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 $S2O$ molecules. The fluorescence accompanying selective excitation of single rovibronic lines in the $202301$ and $2ov(\nu =0-3)$ bands of the intense $C~\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A\prime \leftarrow \mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A\prime (\pi \ast \leftarrow \pi )$ absorption system were dispersed under moderate spectral resolution $(5-10cm-1)$. Ground state vibrational levels possessing as much as 20 quanta of excitation in the $v2S-S$ stretching mode and residing up to $\sim 13000cm-1$ above the vibrationless $X~\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A\prime$ zero-point energy have been observed and assigned. Detailed analyses of $S2O$ vibrational energies within the $X~$ and $C~$ 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 $S2O$ vibrational dynamics suggests that the $X~\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A\prime$ surface is substantially more ``local'' in nature than the $C~\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A\prime$ 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 $C~\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}A\prime$ equilibrium geometry inferred from previous studies under the assumption of an unchanged S-O bond length upon $C~\leftarrow X~$ excitation.