Internal Rotation and the Breakdown of the Adiabatic Approximation: Many-Phonon Radiationless Transitions

In this paper we consider the role of hindered internal rotation in the breakdown of the Born–Oppenheimer approximation. The intramolecular coupling matrix elements are derived in a form which allows the theory of many-phonon radiationless transitions to be extended to include torsional motion. It is shown that the strongly coupled degree of freedom (that mode whose equilibrium positions differ greatly in the initial and final electronic states) can be separated out from the remaining vibrations in the general rate expressions. We treat, in particular, a model of photoisomerism in which the adiabatic potential curves describing the zero-order states have certain simplifying features. We are able to derive in this case a simple rule governing the distribution of electronic energy amongst the internal modes in the radiationless deactivation of the lowest (twisted) triplet. In marked contrast to the usual situation encountered in the literature, this intersystem mixing with the ground state is predicted, under certain conditions, to show a negligible isotope effect.