A Simple Kinetic Model for Singlet Fission: A Role of Electronic and Entropic Contributions to Macroscopic Rates

A simple three-state model for the dynamics of the singlet fission (SF) process is developed. The model facilitates the analysis of the relative significance of different factors, such as electronic energies, couplings, and the entropic contributions. The entropic contributions to the rates are important; they drive the SF process in endoergic cases (such as tetracene). The anticipated magnitude of entropic contributions is illustrated by simple calculations. By considering a series of three acenes (tetracene, pentacene, and hexacene), we explained the experimentally observed 3 orders of magnitude difference in the rate of SF in tetracene and pentacene and predicted that the rate in hexacene will be slightly faster than in pentacene. This trend is driven by the increased thermodynamic drive for SF (Gibbs free energy difference of the initial excitonic state and two separated triplets). The model also explains experimentally observed fast SF in 5,12-diphenyltetracene. Consistently with the experimental observations, the model predicts weak temperature dependence of the multiexciton formation rate in tetracene as well as a reduced rate of this step in solutions and in isolated dimers.