Time evolution of fluorescence and strong nonadiabatic effects

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Abstract
In this paper we study the spontaneous emission of systems with intersecting potential energy curves and strong nonadiabatic effects from first principles. Within the dipole approximation for the spontaneous emission process and a two‐state description of the vibronic coupling system we derive expressions for the transition operator and the intensity of fluorescence which are virtually exact in the small molecule limit. The concept of a radiative damping matrix is introduced and formulated as an operator in vibrational space. Apart from energy prefactors, the probability of photon emission is found to be governed by the probability of occupying the upper of the vibronically interacting electronic states. It follows that the usual autocorrelation function is no longer an appropriate measure of the fluorescence in systems with strong nonadiabatic effects. As an application we study the Ã→X̃ internal conversion in C2H+4 for broadband excitation and find an ultrafast nonradiative decay (decay time ≊3 fs).