Theoretical Calculations of Band Gaps in the Aromatic Structures of Polythieno[3,4-b]benzene and Polythieno[3,4-b]pyrazine

Band gaps in polythiophene ( T ) and the related polymers with a fused benzene ring ( TB, polythieno[3,4- b ]benzene) or a fused pyrazine ring ( TN, polythieno[3,4- b ]pyrazine) have been computed using a variety of methods. Geometries of oligomers up to octamers (AM1) and up to tetramers (B3LYP/6-31G*) have been optimized, while excitation energies have been computed using ZINDO (INDO/S), configuration interaction singles (CIS), and time-dependent density functional theory (TDDFT). Band gaps have been extrapolated from excitation energies. T oligomers are found to have nonplanar geometries, though the planar form is only slightly less stable. TB oligomers are found to be nonplanar due to steric repulsion between a hydrogen on the fused benzene ring and the thiophene sulfur, while TN oligomers are predicted to be planar. As a result, the band gap in the TN polymer is predicted to be smaller than in the TB polymer. The aromatic/quinoid character of the TB oligomer units is discussed. Extrapolation of DFT HOMO−LUMO energies also gives reasonable band gap predictions.