Singlet fission is a multiple exciton generation process that splits a singlet exciton (S 0 S 1 ) into a correlated triplet pair (T 1 T 1 ), affording a route to overcome the long-standing Shockley−Queisser thermodynamic limit for solar energy conversion. A new theory, based on multiconfiguration-constrained density functional theory and functional mode analysis, has been developed to model intermolecular singlet fission in organic photovoltaics. Specifically, constrained density functional theory is first employed to construct molecular orbitals for the six spin configurations comprising T 1 T 1 , the diabatic product state. In a subsequent step, linear response time-dependent density functional theory is utilized to formulate the S 0 S 1 diabatic reactant state. Functional mode analysis is then applied to a thermalized ensemble of diabatic energy gaps to ascertain the reaction coordinate for the S 0 S 1 → T 1 T 1 transition. If singlet fission is assumed to follow a direct route, its rate may be evaluated using a modified Jortner formula within strong vibronic coupling regime. In contrast, second-order perturbation theory must be adopted to treat alternate pathways that are mediated by a chargetransfer (CT) intermediate. As shown through numerical simulations of single crystal tetracene, our theory reveals the direct mechanism to be the primary transition path, with an experimentally consistent singlet fission rate of 0.02 ps −1 . CT pathways are effectively blocked due to a substantially diminished vibrational resonance among participating states. Our results have broad applicability, as only trivial alterations are needed to enable our new theory to model vibrationally modulated singlet fission using time-delayed pulse sequences.
We have applied our functional mode framework for singlet fission to pentacene, a prototypical organic material for multiple exciton generation. It was found that singlet fission in pentacene occurs predominantly through a coherent process mediated by a virtual charge-transfer (CT) intermediate, which lies slightly above the photoexcited S1S0 state. This energetic near-degeneracy facilitates a substantial vibronic superposition, leading to a rapid transition rate of 25.1 ps–1. By contrast, the direct S1S0 → T1T1 path constitutes a much more sluggish route with a rate of 2.6 ps–1, largely due to the weak diabatic coupling between participant states. These data collectively afford an experimentally consistent rate of 27.7 ps–1 for the entire singlet fission process. The presence of this low-lying CT intermediate suggests that enhanced electronic coupling between S1S0 and T1T1 states may collude with coherent vibrational mixing to expedite the formation of triplet pairs. The knowledge gleaned from our investigations heralds a new approach to charge transfer-mediated singlet fission, a rapidly growing research field that holds great promise to circumvent the Shockley–Queisser thermodynamic limit for solar energy conversion.
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