Two transferable physical parameters are incorporated into the Su-Schrieffer-Heeger Hamiltonian to model conducting polymers beyond polyacetylene: the parameter γ scales the electron-phonon coupling strength in aromatic rings and the other parameter ε specifies the heterogeneous core charges. This generic Hamiltonian predicts the fundamental band gaps of polythiophene, polypyrrole, polyfuran, poly-(p-phenylene), poly-(p-phenylene vinylene), and polyacenes, and their oligomers of all lengths, with an accuracy exceeding time-dependent density functional theory. Its computational costs for moderate-length polymer chains are more than eight orders of magnitude lower than first-principles approaches.

In bulk heterojunction photovoltaic systems both the open-circuit voltage as well as the short-circuit current, and hence the power conversion efficiency, are dependent on the optical bandgap of the electron-donor material. While first-principles methods are computationally intensive, simpler model Hamiltonian approaches typically suffer from one or more flaws: inability to optimize the geometries for their own input; absence of general, transferable parameters; and poor performance for non-planar systems. We introduce a set of new and revised parameters for the adapted Su-Schrieffer-Heeger (aSSH) Hamiltonian, which is capable of optimizing geometries, along with rules for applying them to any -conjugated system containing C, N, O, or S, including non-planar systems. The predicted optical bandgaps show excellent agreement to UV-vis spectroscopy data points from literature, with a coefficient of determination , a mean error of −0.05 eV, and a mean absolute deviation of 0.16 eV. We use the model to gain insights from PEDOT, fused thiophene polymers, poly-isothianaphthene, copolymers, and pentacene as sources of design rules in the search for low bandgap materials. Using the model as an in-silico design tool, a copolymer of benzodithiophenes along with a small-molecule derivative of pentacene are proposed as optimal donor materials for organic photovoltaics.

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