Energy Transfer between Localized Electronic States –From Non-Adiabatic to Adiabatic Hopping Limits–

A thermally-activated transition rate W between two localized electronic states is given which bridges the adiabatic limit, where the two states are mixed well at the activated lattice configuration, and the non-adiabatic limit, where they are not even there. Frequency dispersion of lattice vibrations is fully incorporated which is important to assure irreversibility of the system. Basic quantities are the interaction. energy J between the two states and the average amplitude D and velocity \(v̄\) of thermal fluctuations of the energy difference between adiabatic potentials associated with these states. The semiclassical condition \(D{}ω̄\) is assumed with \(ω̄{≡}v̄/D\). The pre-exponential factor of W is given as a function of \(γ{≡}π J²/(̄)\) which determines the adiabatic limit for γ≫1 and the non-adiabatic limit for γ≪1. The attempt frequency in W is given by \(ω̄/2π\) which is written as an average of various normal-mode frequencies.