The effect of heteroatomic substitutions on the band gap of polyacetylene and polyparaphenylene derivatives

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Abstract
The electronic structures of polyparaphenylene (PPP), polyacetylene (PA), and their derivatives with small energy gaps have been studied by the Hückel and MNDO crystal orbital methods. The effect of nuclear relaxation and heteroatomic substitution on the energy gaps (Eg) have been taken into account by compelete geometry optimization using periodic boundary conditions as opposed to earlier cluster based calculations. Calculations were done on the following polyacetylene derivatives: polypyrrole (PPy), polythiophene (PT), polyisothianaphthene (PITN), poly (5,5’-bithiophene methenyl) (PBTM, 11, X=S, R=H, m1=m2=1), and poly (5,5’-bipyrrole methenyl) (PBPM, 11, X=NH, R=H, m1=m2=1). Energetics and band gaps for the two isomeric forms, the quinoid and aromatic structures of PPy and PT, are discussed and critically compared with previous calculations. Perturbational molecular orbital theory is invoked to explain the narrower Eg for PITN, PBTM, and PBPM, relative to that of PA. Calculations for PPP derivatives {m-polybenzo[b]thiophene (PBT,5b), polybenzo[b,f]thieno[3,4-c]thiophene (PBTT, 5a, X=S), and polybenzo[b,f]pyrrolo[3,4-c]pyrrole (PBPP, 5a, X=NH)} show that the Eg of some of these polymers is substantially smaller than that of PPP. Comments on ways to stabilize structures with desired small energy gaps are made. A correlation of the Eg with heteroatom perturbation and geometrical relaxation is given. It is found that Eg is controlled not by aromatic vs quinoid contributions, but by the geometrical and heteroatomic effects on the frontier orbitals of the polymer.