Twisting of conjugated oligomers and polymers: case study of oligo- and polythiophene.

Interring twisting (change in the dihedral angle between conjugated rings) of polythiophene was studied theoretically using periodic boundary conditions (PBC) at the B3LYP/6-31G(d) level. We find that the band gap of polymers is strongly dependent on the interring twist angle; yet twisting requires very little energy. A twist of 30 degrees increases the band gap by 0.75 eV in polythiophene, while requiring only 0.41 kcal mol(-1) per monomer unit. Such a small energetic value is of the order of crystal packing or van der Waals forces. These results are compared with calculations performed on model oligomers. Sexithiophene, its radical cations, and its dication are optimized at 0-180 degrees end-to-end twist angles (which correspond to 0-36 degrees interring dihedral angles) using the B3LYP/6-31G(d) method. The theoretical results suggest that the HOMO-LUMO gap, ionization potential, and charge distribution of oligomers are strongly dependent on twisting, whereas, similar to the case of polythiophene, twisting of neutral oligothiophenes costs very little energy. In the case of the radical cation, the lowest energy transition is shifted to a longer wavelength region on twisting, while the second-lowest energy transition is shifted to a shorter wavelength region. This implies that twisted, doped conducting polymers (modeled here by an oligomer radical cation), in contrast to planar, doped polymers, should be transparent within a certain optical window (in the far-visible region, at approximately 1.5 eV). This observation is explained on the basis of changes in the shape and overlap of the frontier molecular orbitals.