Systematic study of origin of the bandgaps of methine-linked conjugated cyclic polymers

A systematic study was performed to elucidate the origin of the bandgaps of various methine-linked conjugated cyclic polymers in connection with their chemical structures using the equation of Eg = ΔEδr + ΔE1–4 + ΔEel. Modified extended Hückel band calculations were carried out to estimate electronic properties of the polymers using the geometrical parameters optimized with the AM1 method. It is found that the contributions from the C1-C4 interactions (ΔE1–4) and the electronic effect (ΔEel) of the bridging groups become negligible due to the alternating aromatic and quinonoid sequence of the polymers. Poly(heteroarylene methines) are estimated to possess small bandgaps in the range of 1.1–1.2 eV due to their small bond-length alternations (Δr) as suggested by Kertesz and Lee (J. Chem. Phys., 91 (1987) 2690). In poly (fulvenylene methine), poly (oxocyclopentadienylene methine) (POPM) and poly (thiocyclopentadienylene methine) (PTPM), despite the relatively large Δr values similar to that of trans-polyacetylene, the bandgaps are still small (1.0–1.3 eV) since the π* orbitals of the bridging groups stabilize the lowest unoccupied crystal orbitals of the conjugated carbon backbones more than the highest occupied crystal orbitals near the Fermi level. Investigation of the relative stabilities of the aromatic versus quinonoid forms of the parent homopolymers, however, casts doubt whether or not poly(heteroarylene methines), POPM and PTPM, are chemically stable in the ground states.