Supercell representation of localized defects: A method for calculating band-gap states in conjugated polymers.

Abstract

A method for calculating single-particle energy levels and wave functions associated with polaron and bipolaron defects in \ensuremath{\pi}-conjugated polymers is developed. The method is based in the valence-effective-Hamiltonian technique and utilizes a Green's-function method for calculating the defect energy levels. A dual representation of the defect wave functions in a local basis set as well as in the Bloch states of the host polymer is used. The potential of a single defect on the polymer chain is augmented to form a superperiodic defect potential without loss of accuracy. This so-called supercell representation allows us to calculate the defect energy levels and their corresponding wave functions exactly for a given basis set. The method is applied to polaron and bipolaron defects in polythiophene, defects that previously have been studied by means of cluster type of calculations. We show that a single polaron or bipolaron defect in an infinite system gives rise to exactly two energy levels within the energy band gap around the Fermi level. This result is in agreement with the results of calculations on finite systems. Quantitatively, the energies of the electronic transitions involving the defect levels are in close agreement with experimental optical-absorption data.