Biexciton Hamiltonian for the correlated triplet pair states in singlet fission: Revealing the contest between triplet-triplet exchange and triplet-triplet energy transfer coupling

The correlated triplet pair state 1(TT) is a key intermediate in the singlet fission process, and understanding the mechanism by which it separates into two independent triplet states is critical for leveraging singlet fission for improving solar cell efficiency. This separation mechanism is dominated by two key interactions: (i) the exchange interaction (K) between the triplets which leads to the spin splitting of the biexciton state into 1(TT),3(TT) and 5(TT) states, and (ii) the triplet-triplet energy transfer integral (t) which enables the formation of the spatially separated (but still spin entangled) state 1(T...T). In this work, we use simple ab inito calculations to compute the triplet-triplet exchange (K) and triplet-triplet energy transfer coupling (t). For a model 1D system, we show how these parameters affect the biexciton energy manifold using a steady state approximation. Our key findings reveal a new condition for successful correlated triplet pair state dissociation. If the K to t ratio is comparable to or less than one, biexction dissociation is favored for large chromophore assemblies. Additionally, for smaller chromophore assemblies, the biexciton exchange interaction needs to be negligible compared to the triplet energy transfer for favourable dissociation. We also explore the effect of chromophore packing to reveal geometries where the triplet energy transfer integral is significantly larger compared to the triplet-triplet exchange.