Radiationless Transitions: A Semiclassical Model

Radiationless transitions of a solute molecule embedded in a crystalline solvent are treated in close analogy to radiative transitions. A semiclassical interaction Hamiltonian employing empirically determined coupling constants connects solute particles to a force field amplitude set up by the phonons of the solvent. By relating this amplitude to phonon energy density an Einstein B coefficient is derived. Debye's formula for the phonon energy density combined with thermodynamic arguments yield Einstein A coefficients. It is shown that the theory (1) explains the fast rates of radiationless transitions, (2) provides for temperature dependence, (3) has a cutoff frequency for radiationless transition, (4) provides for the Franck—Condon principle, and (5) explains the lack of selection rules. A value is derived for the empirical coupling constants.