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

Abstract

A novel technique has been developed for the quantitative study of vibronically-resolved transition intensities in polyatomic molecules beyond the Condon approximation. Matrix elements of coordinate-dependent transition moment operators are evaluated analytically with the pertinent vibrational wave functions obtained by means of Lie algebraic methods. Experimentally-observed S 2 O C 1 AЈ -X 1 AЈ(*Ϫ) emission intensities, in conjunction with previous Franck-Condon calculations, reveal pronounced non-Condon effects for vibronic bands terminating on higher-lying vibrational levels of the ground electronic state. The transition dipole moment is examined as a function of both the S-O and S-S local stretching coordinates.

A new approach to obtain the non-Condon factors in closed form for two one-dimensional harmonic oscillators

“…When only one oscillator is considered the different results may be equivalent in computing time and precision, but when applied to highly excited polyatomic molecules it is convenient to count on compact formulas that allows to carry out the description in an efficient way. We believe that our results may be useful to describe transition intensities between two different electronic states for polyatomic molecules in the framework of a local model, not only in terms of harmonic oscillators but also to take into account anharmonicities [13,[32][33][34].…”

“…Afterwards we carry out a transformation to obtain the simplified formula (29), which involves a summation of real numbers. In the limit of equal frequencies the expression (34) reduces to the simple result (43) in terms of Laguerre polynomials where no explicit summations are involved. This procedure contrasts with the one given in [17], where an analysis in terms of hypergeometric functions was carried out.…”

“…The expression (29) has the disadvantage that it involves two cases for the calculation of the overlaps (34). This problem may be surmounted by considering only the special case x 2 > x 1 , which implies that v > 0.…”