Electronic Structures and Optical Absorption of N-Type Conducting Polymers at Different Doping Levels

Theoretical understanding of the electronic structure and optical transitions in n-doped conducting polymers is still controversial for polaronic and bipolaronic states and is completely missing for the case of a high doping level. In the present paper, the electronic structure and optical properties of the archetypical n-doped conducting polymer, double-stranded benzimidazo-benzophenanthroline ladder (BBL), are studied using the density functional theory (DFT) and the time dependent DFT method. We find that a polaronic state in the BBL chain is a spin-resolved doublet where the spin degeneracy is lifted. The ground state of two electrons corresponds to a triplet polaron pair, which is in stark contrast to a commonly accepted picture where two electrons are postulated to form a spinless bipolaron. The total spin gradually increases until the reduction level reaches c(red) = 100% (i.e., one electron per monomer unit). With further increase of the reduction level, the total spin decreases until it becomes 0 for the reduction level c(red) = 200%. The calculated results reproduce the experimentally observed spin signal without any phenomenological parameters. A detailed analysis of the evolution of the electronic structure of BBL and its absorption spectra with increase in reduction level is presented. The calculated UV-vis-NIR spectra are compared with the available experimental results. The electronic structure and optical absorption for different reduction levels presented here are generic to a wide class of conducting polymers, which is illustrated by the corresponding calculations for another archetypical conducting polymer, poly(3,4-ethylenedioxythiophene) (best known as PEDOT).