Simple Extrapolation Method To Predict the Electronic Structure of Conjugated Polymers from Calculations on Oligomers

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We introduce two simple tight-binding models, which we call fragment frontier orbital extrapolations (FFOE), to extrapolate important electronic properties to the polymer limit using electronic structure calculations on only a few small oligomers. In particular, we demonstrate by comparison to explicit density functional theory calculations that for long oligomers the energies of the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), and of the first electronic excited state are accurately described as a function of number of repeat units by a simple effective Hamiltonian parametrized from electronic structure calculations on monomers, dimers and, optionally, tetramers. For the alternating copolymer materials that currently comprise some of the most efficient polymer organic photovoltaic devices one can use these simple but rigorous models to extrapolate computed properties to the polymer limit based on calculations on a small number of low-molecular-weight oligomers.