Coupled coherent and incoherent motion of triplet excitons: Influence on the ESR line shape of pairs of differently oriented molecules

Abstract

The ESR line shape of triplet excitons, moving in a coupled coherent and incoherent manner within a pair of differently oriented molecules, is calculated. The dynamics of the electronic degrees of freedom is described by the Hamiltonian of the Haken-Strobl model, which consists of a time-independent part, determining the coherent exciton motion via the exchange-interaction integral $J$ between the molecules, and of a stochastically-time-dependent part. The latter part takes into account the influence of the phonons by fluctuations of the energy of the localized excitation (strength ${\ensuremath{\gamma}}_{0}$) and of the exchange-interaction integral (strength ${\ensuremath{\gamma}}_{1}$) and represents the incoherent part of the motion. The spin Hamiltonian constains the Zeeman energy of the spin in an external magnetic field and the fine-structure terms of the two differently oriented molecules. The eigensolutions of the Liouville equation for the density operator are calculated using parameter values fitting the naphthalene $\mathrm{AB}$ pair; their dependence of ${\ensuremath{\gamma}}_{0}$ and ${\ensuremath{\gamma}}_{1}$ is discussed. From linear-response theory the ESR line shape is determined using the eigensolutions of the Liouville equation. It is shown that from this model the ESR line shape is obtained not only for the cases of the completely coherent and the purely hopping motion of the exciton, as well as for the case of its complete localization on the $A$ and $B$ molecules, but also for all cases in between depending on the relative magnitude of the exchange-interaction integral $J$ and of the strengths ${\ensuremath{\gamma}}_{0}$ and ${\ensuremath{\gamma}}_{1}$ of the local and nonlocal fluctuations.