Model calculation of the temperature dependence of triplet exciton E.S.R. line shapes for local exciton phonon interaction

Abstract

The E.S.R. line shape of a triplet exciton moving in a coupled coherent and incoherent manner within a pair of differently oriented molecules is calculated. The hamiltonian describing the model includes the excitation energies of the identical, but differently oriented molecules, the interaction matrix element describing the coherent exciton transfer, the Zeeman energy, and the fine-structure terms of the molecules. Furthermore it contains the phonons which are treated quantum mechanically and their linear and local interaction with the exciton. Using a unitary transformation of the hamiltonian, the exciton-phonon interaction is transformed into a phonon modulated exciton transfer operator. Considering now the phonons a heat bath, with the help of the transformed hamiltonian the Liouville equation for the reduced density operator is derived, which contains only triplet exciton degrees of freedom. The eigenvalues and eigenvectors of the reduced density matrix are calculated numerically using parameters characteristic for naphthalene. From linear response theory the E.S.R. line shape is determined using the eigensolutions of the Liouville equation. These calculations show that in the high temperature limit a localization of the exciton either at molecule A or molecule B occurs for all values of the exciton-phonon interaction. The E.S.R. line shape is also discussed in regions where level anticrossings occur.