A constrained variational approach to the designing of low transport band gap materials: A multiobjective random mutation hill climbing method

Neutral polythiophene (PT) and polyselenophene (PSe) are semiconductors with band gaps of about 2 eV. We have proposed and implemented a constrained variational method in which total energy of neutral PT or PSe oligomers is minimized under the constraint that the band gap measured by HOMO-LUMO energy difference is also a minimum in each case. The constrained (bimodal) minimization has been carried out by an adaptive random mutation hill climbing method within the basic framework of Su-Schrieffer-Heeger type of model. We show that the "band-gap constrained minimization" automatically creates electron deficient quinoid regions (QR) in the PT or PSe chains, embedded in aromatic regions (ARs), on both sides. We have investigated how the number and distribution of such QRs can reduce the band gap. Band gap constrained electronic structure calculations thus provide designing clues for low transport band gap materials based on molecular chromophores.