The Dushinsky effect and sum rules for vibronic transitions in polyatomic molecules

A method is presented for analyzing, in terms of sum rules, the intensity distribution among the vibronic bands in electronic spectra of polyatomic molecules, taking into account the rotation of the excited-state normal coordinates relative to those of the ground state (the Dushinsky effect). In the harmonic oscillator approximation, a quantitative criterion for the occurrence of the Dushinsky effect is obtained. The existence of this effect leads to non-product formulas for probabilities of the joint excitation of different vibrational modes. Expressions are obtained for the mean number of quanta excited in a given mode, and for its standard deviation, as well as for the correlation coefficients. The proposed method does not require a complete vibrational analysis of the spectrum of interest. As an example, the calculation of the correlation coefficient for the 3700-Å band system of the absorption spectrum of SO₂ is given.