Chromophore Packing and Singlet Fission Rates
Results of a theoretical examination of the effect of crystal packing on singlet fission (SF) rate are presented. For a model system (pair of ethylenes) and several known or suspected SF materials: tetracene (1), cibalackrot (2), and 1,3-diphenylisobenzofuran (3), we predict molecular pair arrangements that are especially favorable for the rate of SF. The predictions are obtained from an approximate evaluation of squares of SF eectronic matrix elements, based on a complete search of all possible pair packing geometries. This is refined by an evaluation of intermolecular contributions to the energy balance of the SF process, followed by Marcus theory evaluation of SF rates, which are used to reoptimize the best geometries. We also evaluate biexciton binding energies. Going beyond the prediction of optimal geometries, the model has been applied to a series of variously fluorinated derivatives of 3 and found to determine successfully which ones perform SF and which ones yield excimers instead. Although a consideration of molecular pairs thus appears to be a useful first step and may be sufficient in some cases, experimental evidence shows convincingly a need to consider at least three molecules at a time in the future. Evaluation of triplet yields will require an additional evaluation of rates of competing processes, especially charge separation and excimer formation.