Solitons, polarons, and excitons in polyacetylene: Step-potential model for electron-phonon coupling inπ-electron systems

Abstract

The bond lengths in π-electron systems, determined by electron-phonon coupling, are calculated by using a simple step-potential model. The geometry of a system is obtained by finding the self-consistency between bond length and π-electron density in the middle of each bond. The model has no free parameter and leads to a satisfactory description of unsaturated hydrocarbon chains and rings and of defect states in trans-polyacetylene (kinks, polarons, bipolarons, and excitons). For defect-free trans-polyacetylene, the calculated bond-length alternation of 0.08 Å is in close agreement with x-ray data and gives a band gap of 1.34 eV. Kinks in odd-numbered systems show hyperbolic-tangent defect geometry and have an extent of 12–18 sites, depending on the charge. Proceeding from negatively charged to neutral to positively charged kinks, the intergap state shifts towards the conduction band. Polarons created from the ground state by adding or subtracting one electron are bound and have an extent of 20–24 sites, depending on the charge. Bipolarons created from the ground state by adding or subtracting two electrons are not bound and convert, by electron-phonon coupling, to a kink ($K^{\pm }$) and an antikink (K${¯}^{\pm }$) pair with equal charge. Excitons created by excitation of the ground state are not bound and convert to a neutral $K^0$K${¯}^0$ pair.