Conjugated polymers: A systematic investigation of their electronic and geometric properties using density functional theory and semi-empirical methods

Abstract

Ten conjugated polymers (polypyrrole, polyfuran, polythiophene, polyborole, polycyclopentadiene, polysilole, polyphosphole, polycyclopentadienethione, polycyclopentadieneone, poly(p-phenylene)) have been investigated using density functional theory (DFT) and semi-empirical method. BP86-30% HF hybrid functional with CEP-31G* basis set combined with the quadratic regression provides bandgaps of polymers that are consistent with their optical experiment bandgaps. The higher contribution of quinoid character in polymer results in lower bandgap, and this observation is supported by shorter carbon – carbon bondlength of inter-rings of polymer with prefered quinoid character. The averaged crystal orbital overlap population (COOP) between carbon – carbon of inter-rings shows that polymer with higher orbital overlap population leads to lower bandgap. The resonance energies of polymers calculated using natural bond orbital method (NBO) show two opposite observations: very low bandgap polymer (≤0.19 eV) has highest resonance energy; however, with polymer having bandgap larger than 1 eV, higher resonance energy results in higher bandgap. This observation is due to the fact that resonance energy may be associated with electron delocalization over entire polymer backbone or within the rings. Band structures of polymers typically present direct bandgap at gamma point, and lower bandgap polymers do not essentially show higher carrier mobility.