Vibrational Properties of Excitons in Molecular Crystals

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Abstract
A general theory is developed for the interaction of exctions with molecular vibrations in pure and impure molecular crystals. A study is made of a model Hamiltonian which describes the interaction of Frenkel excitons with harmonic oscillators, with particular attention paid to the case in which exciton bandwidth is fairly narrow. Equations of motion for molecular excitons are obtained in the form of Dyson equations using the method of double‐time Green's function. By solving the Dyson equations, it is shown that the vibrational energies of excitons in pure and impure molecular crystals, which can be classified into zero‐phonon and one‐phonon energies, are very different for different combinations of the energies of molecular vibrations and the exciton bandwidth. For example, a series of vibronic exciton bands is obtained for a pure crystal when the energies of phonons are larger than the exciton bandwidth while for an impure crystal, under certain circumstances, molecular vibrations can induce a delocalization of exciton impurity states in the opposite case. A study is then made of the role of phonons in the exciton energy transfer in a pure molecular crystal. It is shown that the effect of exciton—phonon interactions is to reduce the exciton bandwidth from free exciton value while there can exist a phonon‐assisted energy transfer with emission or absorption of a single phonon, which has a long‐range oscillatory interaction form similar to the Ruderman—Kittel interaction. A brief discussion is also given of the transfer of energy associated with an exciton impurity state to host molecules.

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