The vibronically-resolved emission spectrum of disulfur monoxide (S2O): An algebraic calculation and quantitative interpretation of Franck–Condon transition intensities

Abstract

Emission spectra obtained from jet-cooled disulfur monoxide (S 2 O) molecules have been interpreted by means of a novel Lie algebraic formalism that makes possible the facile evaluation of multidimensional Franck-Condon factors. Fluorescence accompanying selective excitation of isolated vibronic bands in the S 2 O C 1 AЈ-X 1 AЈ(*-) absorption system has been dispersed under moderate spectral resolution, allowing assignment of ground state levels possessing up to 20 quanta of vibration in the 2 S-S stretching mode ͓E vib (X )р13 900 cm Ϫ1 ͔. Aside from providing a rigorous and economical description for the inherently anharmonic nature of highly-excited polyatomic species, our algebraic approach enables quantitative information on molecular wavefunctions to be extracted directly from spectroscopic data. The emerging picture of S 2 O vibrational dynamics suggests that the X 1 AЈ potential surface is substantially more ''local'' in character than the C 1 AЈ manifold. While the observed pattern of X 1 AЈ vibrational energies could be reproduced well through use of model Hamiltonians that include only diagonal anharmonicities in the local algebraic basis, successful treatment of the C 1 AЈ state necessitated explicit incorporation of off-diagonal anharmonicities that lead to pervasive mixing of local vibrational character. This disparate behavior is manifest strongly in measured C -X transition strengths, thereby allowing detailed investigations of Franck-Condon intensities to discern the underlying dynamics. Structural parameters deduced from algebraic analyses are in good accord with previous predictions of the change in S 2 O geometry accompanying *-excitation.

A quantitative study of non-Condon effects in the S2O C̃→X̃ emission spectrum

“…Building upon Lie algebraic techniques, our method incorporates vibrational anharmonicity from the onset and provides a computationally efficient means for extracting dynamical and structural information from experimental data. 5 Our previously reported Franck-Condon analyses of S 2 O C 1 AЈ -X 1 AЈ(*Ϫ) emission spectra reproduced experimental intensities accurately for ground state features possessing up to ϳ10 quanta of excitation in the 2 S-S stretching mode. Theoretical predictions systematically overestimated the strength of vibronic bands terminating on higher-lying vibrational levels of the X 1 AЈ potential surface.…”

“…As described in our earlier investigations, 5 the Lie algebraic approach affords a systematic means for expanding molecular eigenstates in terms of a ''local oscillator'' basis thereby allowing matrix elements such as those defined by Eqs. ͑1͒ and ͑2͒ to be formulated as simplified products of one-dimensional integrals.…”

“…12 In the non-Condon case (␤ 0), Eq. ͑3͒ can be used to investigate anharmonic oscillators ͑e.g., Morse͒ by exploiting the same perturbative corrections introduced in our previous work, 4,5 ␣ϭ␣ 0 ͑ 1Ϫv ͒, ␣Јϭ␣ 0 Ј͑1ϪЈvЈ͒, first-order corrections to the width ͑i.e., concavity͒ and coordinate origin, respectively, for the harmonic oscillators embodied in Eq. ͑3͒, thereby allowing the ensuing calculation of transition matrix elements to reproduce the classical turning points of a true Morse potential.…”

“…The evaluation of requisite transition matrix elements is accomplished in a manner very similar to that introduced previously, 5 except that all overlap integrals between the two electronic configurations ͑for S 2 O, X 1 AЈ and…”

“…1 Although this approach has been exploited extensively in traditional optical spectroscopy 2 as well as in many other areas, 3 the calculation of multidimensional Franck-Condon factors has remained a difficult and computationally intensive task, with most reports published to date based upon an harmonic treatment of nuclear dynamics. Recently, we have introduced a method to analyze Franck-Condon transition intensities in polyatomic molecules quantitatively and have applied it to the interpretation of vibronically-resolved emission 4,5 and absorption 6 spectra for the triatomic disulfur monoxide (S 2 O) species. Building upon Lie algebraic techniques, our method incorporates vibrational anharmonicity from the onset and provides a computationally efficient means for extracting dynamical and structural information from experimental data.…”