Bright state decay rate

The excited vibrational states can be considered as quasi-eigenstates [41]. As can be seen in the simplified scheme of Figure 2.2, these states are a result of the relatively strong coupling between a zero-order bright state (ZOBS), namely i >, with several zero-order dark states (ZODS), l > [48], that are further weakly coupled to the bath states that include a dense manifold of nearly equally coupled levels with a finite decay rate. 

This two-state quantum beat example is identical to the doorway mediated non-radiative decay problem frequently encountered in polyatomic molecule Intramolecular Vibrational Redistribution (IVR), Inter-System Crossing (ISC), Internal Conversion (IC), and compound anticrossings. There is a single, narrow bright state. It couples to a single, broad, and dark doorway state. The width of the doorway state is determined by the rate of its Fermi Golden Rule decay into a quasi-continuum of dark states. 

Excited dimers, with the energy placed initially in monomer vibrational modes, decay via one of three mechanisms (1) direct vibrational predissociation (VP) at a rate kyp in which the energy from the bright state is transferred directly to the van der Waals bond followed by rapid dissociation (2) sequential IVR (rate = kj r) in which the energy becomes equilibrated among the dimer normal modes including the van der Waals modes, followed by statistical dissociation of the equilibrated complex via the rate k and (3) a combination of IVR and VP in which the two-proceed in a parallel fashion ... 

Figure 7.4 The lifetime for non-radiative decay of different low vibrational states in the first excited singlet state of benzene (Si = B2u) plotted against the vibrational energy. The vibrational states of Si are identified by the number of quanta, shown as superscripts, in the C-C bend, mode 6, symmetric stretch, mode 1, and out-of-plane bend, mode 16. The rates are measured from the rate of disappearance of the bright state (which determines the sum of radiative and non-radiative rates) and the quantum yield of fluorescence [adapted from K. G. Spears and S. A. Rice,...

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