The damping of one-dimensional triplet-state excitons by acoustic phonons

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Abstract
A theory for the rate of decay of triplet-state excitons by their interaction with acoustic phonons is developed under the assumption that only the equilibrium internuclear distance between molecules is changed when one of them is excited. The decay rate is found to be proportional to the square of the gradient of the exchange energy |·J/·r|2. A procedure for obtaining ·J/·r is outlined, and numerical results are presented for two benzene molecules in a geometry similar to that of the phenyl rings of adjacent molecules in crystalline 1,2,4,5-tetrachlorobenzene. The calculated exchange interaction energy |J|=16·7 cm-1 is an order of magnitude larger than the exciton frequency bandwidth Δv=1·3 cm-1 recently reported by Francis and Harris, while the calculated exciton decay rate ∼1011 s-1, being comparable to Δv, is much too large to be compatible with the observations. A postulated Franck-Condon reduction of |J| arising from an intramolecular lattice distortion bound to the exciton is necessary to reconcile these theoretical results with the experiment.