Some Formal Results in a Theory of Molecular Rearrangements: Photoisomerism

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Abstract
Photoisomerism in the stilbene molecule is considered as a prototype of the general rearrangement reactions induced by absorption of light. The relevant experimental background is briefly reviewed, and the molecule is idealized in terms of a model describing a singlet vibronic level interacting (through the spin–orbit perturbation) with a nearly degenerate triplet state, which is in turn coupled (by vibronic interactions) to an isoenergetic set of closely spaced vibrational levels belonging to a lower triplet. A Green's function formalism is used to determine the time development of the system after it has been prepared in the initial state reached directly by optical excitation. The radiative and nonradiative processes are shown to proceed independently of one another in the statistical limit, and the over‐all decay of the excited state is found to be exponential. The fluorescence quantum yield and radiative lifetime depend explicitly on the (solvent‐specific) energy difference between the discrete singlet and triplet, and they are parameterized by the level density and coupling matrix elements of the zero‐order states. Finally, our formal treatment is reconciled with simple kinetic descriptions, and it is suggested how this approach can be applied to still more general photochemical reactions.