The geometrical and electronic properties of a negatively charged soliton in trans-polyacetylene are calculated at the ab initio Hartree-Fock level. The optimized geometry of a system including a sodium counterion is compared with that of a negatively charged soliton with no counterion present. It is shown that in the presence of the dopant, the characteristics width of the soliton is reduced by a factor of 2.5. For higher doping levels, a single counterion does not represent the dopant potential accurately. Instead, the situation of high doping concentration is represented by a cluster of three polymer chains, carrying one solition each and surrounding a channel of three sodium ions. In our calculations, only one of these chains is treated quantum mechanically. Theother two chains are represented by an array of point charges located at the carbon sites of these chains. When the electrostatic interaction with these point charges is taken into account, as well as the full interaction with the sodium ions, the soliton width is increased as compared to the case of the soliton interacting with a single counterion. Due to the attractive potential of soliton-counterion complexes on neighboring chains, additional geometrical distortions in the soliton geometry occur. This effect must be considered when discussing the transition into a metallic state for highly doped trans-polyacetylene. © 1991.
Fredriksson, C., & Stafström, S. (1991). Ab initio calculations of trans-polyacetylene clusters including sodium counterions. Synthetic Metals, 44(1), 65–74. https://doi.org/10.1016/0379-6779(91)91858-8