Calculation of Franck–Condon Factors for Radiationless Transitions Based on Selective Excitation of Single Vibronic Levels

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Abstract
A theoretical framework is developed for a comparative study of rate constants of radiationless transitions originating from single vibronic levels in the manifold of the initial state. It is shown that in large molecules these rate constants show a characteristic relationship. Specifically, their ratios can be interpreted in terms of effective vibrational quantum numbers for the contribution of the oscillators excited in the initial state to the over-all Franck–Condon factor of the radiationless transition. The analysis is applied to recent data on singlet–triplet intersystem crossing in benzene and the contributions of two normal modes are calculated.