Electronic structure of conducting polymers: Limitations of oligomer extrapolation approximations and effects of heteroatoms

Density-functional methods are used to analyze the scaling of discrete oligomeric pi-electron conducting molecules towards idealized isolated polymer chains, treated in periodic boundary conditions. The band gaps of a series of conjugated oligomers of incrementally increasing lengths exactly fit a nearly-free-electron molecular-orbital picture and exhibit a smooth deviation from the classical empirical "1/N" trend for long oligomers and infinite polymers. The calculations also show a smooth convergence of bond lengths. The full band structures and densities of states of a polyacetylene, polypyrrole, polyfuran, and polythiophene show that band crossing, localized bands, and other effects cannot be accurately determined from simple extrapolation of oligomer electronic structures. Systematic comparisons of the electronic structure variations of the polymers investigated indicate that the electron affinity, rather than the electronegativity of the heteroatom or the bond-length alternation of the conjugated backbone, significantly affects the band gap of the resulting polymer as indicated by the presence of heteroatom states in the partial density of states of the conduction band, requiring revision of previous semiempirical analyses. Consequences for doping processes are also studied, along with a comparison of valence bandwidths, conduction bandwidths, and carrier effective masses as a function of heteroatom.