Exciton coherence times and diffusion constants in molecular crystals from exciton-phonon coupling with an ab initio GW-BSE approach*

Predictive theories of exciton dynamics are of growing importance as increasingly complex materials, with strong electron-hole interactions, are used in device physics applications. For instance, in organic photovoltaics, an important part of energy conversion processes involves the diffusion of a photo-excited exciton to donor-acceptor interfaces where charge separation can occur. To quantitatively understand exciton dynamics, a microscopic theory of exciton-phonon interactions is required. Here, we describe an ab initio framework for computing exciton-phonon matrix elements, using density functional perturbation theory in conjunction with many-body perturbation theory within the GW plus Bethe-Salpeter equation (BSE) approach. We apply this formalism to crystalline tetracene, a prototypical organic semiconductor with strong electron-hole interactions. We compare and contrast how low-lying spin singlet and triplet excitons couple to the phonon field. We perturbatively compute phonon-limited exciton coherence times throughout the Brillioun zone and report exciton diffusion constants, evaluated using the relaxation time approximation. In all cases, we compare with experimental measurements, where available.