Nonequilibrium vibrational population and donor-acceptor vibrations affecting rates of radiationless transitions

An analytical theory is developed for radiationless transitions in molecules characterized by nonequilibrium populations of their vibrational modes. Several changes to the standard transition-state framework follow from nonequilibrium conditions: (i) non-Arrhenius kinetics, (ii) the violation of the fluctuation-dissipation theorem (FDT), and (iii) the breakdown of the detailed balance. The violation of the FDT is reflected in the breakdown of relations between the first (Stokes shift) and second (inhomogeneous band-width) spectral moments, and of similar relations between reorganization parameters for radiationless transitions. The detailed balance between the forward and backward rates is not maintained, requiring a lower effective free energy of the reaction relative to the thermodynamic limit. The model suggests that strong control of radiationless transitions can be achieved if a nonequilibrium population of vibrations modulating the donor-acceptor distance is produced.