Functional Mode Singlet Fission Theory

Abstract

Singlet fission is a multiple exciton generation process that splits a singlet exciton (S0S1) into a correlated triplet pair (T1T1), 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 T1T1, the diabatic product state. In a subsequent step, linear response time-dependent density functional theory is utilized to formulate the S0S1 diabatic reactant state. Functional mode analysis is then applied to a thermalized ensemble of diabatic energy gaps to ascertain the reaction coordinate for the S0S1 → T1T1 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 charge-transfer (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.