Excitonic Hamiltonian for Singlet Fission: Beyond a Dimer Model

The importance of singlet fission as a fundamental process with a variety of implications in energy harvesting cannot be overstated. The challenge is to characterize the energy states of these large singlet fission molecular aggregates that participate in the process. Large dimensionality and essential multiconfiguration nature of the electronic states of interest combine to make accurate ab initio calculations prohibitively difficult. We present a spin-resolved tight-binding excitonic model for singlet fission that can be parametrized on the basis of ab initio calculations on monomers and dimers of molecules and is highly suitable for the study of aggregates. This excitonic model is then used to solve for the energetics of large aggregates. This coarse-grained model is demonstrated specifically on the pentacene crystal, where we evaluated the spectra and density of states. We show the natural emergence of bands of states in some cases and characterize them. Through an analysis of the participation ratio of the eigenstates, we gain crucial insight into the extent of their multireference character. This method is useful in understanding not just the structure of these extended aggregates but also as a cornerstone for incorporation of vibronic features and simulation of the singlet fission dynamics at a quantum-classical or semiclassical level.