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A new quantum chemical descriptor, quinoid stabilization energy (QSE), is established for the computational design of narrow-bandgap polymers. QSE was constructed based on the energy change of homodesmotic reactions of a dimethylated monomer with oligoacetylene. It can be uniquely defined for heterocyclic and polycyclic monomers, unlike the arbitrary conventional descriptors based on bond length alternation. Density functional theory (DFT) calculations revealed a relationship between QSE and the bandgap of polymers. According to the relationships obtained for 268 homopolymers and 179 alternating copolymers selected from many different families, narrow-bandgap polymers can be designed with QSE = 0, which indicates the intermediate state between aromatic and quinoid forms. Copolymers having QSE = 0 can be achieved by combining a quinoidal monomer with an aromatic one. The main advantage of this approach of designing narrow-bandgap polymers is that it requires only information of the monomers and their linking site. Using this approach, we propose a new candidate of narrow-bandgap alternate copolymers constructed by two monomer units that are both usually categorized as acceptors. The proposed copolymer has a calculated bandgap of 0.76 eV, indicating a potentially high air stability. Since QSE as a simple descriptor is highly compatible with machine learning, this approach should accelerate the development of ultra-narrow-bandgap polymers.

Development of a quantum chemical descriptor expressing aromatic/quinoidal character for designing narrow-bandgap π-conjugated polymers