Relationship between band gap and bond length alternation in organic conjugated polymers

We describe calculations of the evolution of the band gap as a function of geometry in conjugated polymers based on aromatic rings: polyparaphenylene, polypyrrole, polythiophene. Our results demonstrate that the gap decreases as a function of increasing quinoid character of the backbone and is thus not minimal in the case of zero bond length alternation, in contrast to the situation found in polyacetylene-like compounds. We stress the consequences of these results for the understanding of the effects of doping and for the design of new organic polymers with small gaps.