Topological control of singlet fission

Singlet fission is a multiple-exciton-generation process that could dramatically improve photovoltaic efficiencies or enable quantum-information processing. Because it usually occurs among distinct molecules, it relies on the energy-level alignment and aggregate structure of its host material. These dual requirements severely restrict the known singlet-fission materials (primarily acenes, rylenes, and carotenoids) to those that serendipitously adopt favorable aggregate structures and singlet/triplet energy-level alignment. Programmable DNA-scaffolded molecular networks decouple these constraints, tuning energy levels by modular chromophore selection while controlling the aggregate structure through DNA origami. However, a theoretical framework is needed to optimize the design. We introduce a topological framework based on simplicial complexes and Hodge theory that captures a fundamental feature of singlet fission: that the singlet states reside on vertices while triplet-pair states reside on edges, making singlet fission an inherently vertex-to-edge conversion. This insight shifts the focus from pair-interactions to collective network arrangements, whose control is a strength of DNA nanotechnology. We apply this framework to five lattice structures (linear, square, honeycomb, Kagomé, and Lieb) parameterized with reported pentacene, diketopyrrolopyrrole, and perylene diimide values. The lattice structure multiplies the singlet-fission efficiency, with the Kagomé lattice providing approximately a 2× enhancement. Three features explain this advantage: triangular 2-simplices with correlated multi-channel pathways, the highest edge/vertex ratio among all lattices studied, and flatband exciton localization near fission-active motifs. These predictions are testable by 2D electronic spectroscopy on DNA-scaffolded chromophore networks.