Dynamics of molecules using semigroup techniques: Vibrational line shapes in exciton models of mixed valency

The vibrational line shapes expected for a case of ’’excitation mixed valency’’ (defined, in analogy, to ordinary electronic mixed valency, as one exciton moving between two equivalent electronic sites) is studied using a semigroup formalism to include relaxation effects. We include the quadratic electron-vibration coupling, corresponding to frequency changes. The results demonstrate the line narrowing expected in the rapid exchange limit, but also show that similar behavior may be caused by rapid electronic excitation. The simple model is readily extended to include transfer rates and ordinary (electronic) mixed valency. The relaxation process introduced a new time scale into the problem; when this becomes of the order of other relevant time scales (transfer, vibration, barrier residence) interesting line shape phenomena may be observed.