A Density-Genetic Algorithm Method for Computing Electronic Structures of Doped and Undoped Polythiophene Oligomers: A Modified Su–Schrieffer–Heeger Hamiltonian-Based Study

Abstract

We propose a genetic algorithm (GA)-driven density matrix method for calculating the equilibrium geometry and charge storage configurations of hole(bipolaron)-doped Polythiophene (PT) oligomers. A modified version of the Su–Schrieffer–Heeger Hamiltonian is used to describe the PT chain. A population of geometry strings are used to generate the corresponding PT-Hamiltonians which act as generators of corresponding unitary transformations which transform a single trial one-electron density matrix into a population of density matrices for different geometries. As the geometry strings evolve under the action of GA operators, the density matrices also evolve on the fitness landscape. Once the fitness reaches maximum, the optimum geometry string, the corresponding Hamiltonian, and the density matrix lead to equilibrium geometry, energy, charge distribution, band gap, Fermi energy, etc. The bipolaronic defect–induced conducting state is predicted to have a symmetric lattice-like admixture of “aromatic” and “quininoid” regions and is characterized by nonzero density of states at Fermi energy and low band gaps.

Keywords:

• Band-gap reduction in polythiophene
• Density-genetic algorithm
• Doped polythiophene
• Genetic algorithm and electronic structure
• Su–Schrieffer and Heeger's method

ACKNOWLEDGMENT

Thanks are due to the DST, Government of India, New Delhi, for a generous research grant (No. SR/S1/PC-11/2003).