Solitons and polarons in polyacetylene: Self-consistent-field calculations of the effect of neutral and charged defects on molecular geometry

Semiempirical self-consistent-field calculations are carried out on various polyenes with emphasis on defect configurations designed to simulate soliton and polaron excitations in polyacetylene. For defect-free polyenes, the calculated bond-length alternation ($\Delta r=0.106\mathrm{}$ Å) is in close agreement with generally accepted values for polyacetylene. Solitons and polarons are simulated on polyene radicals, ions, and radical ions by the introduction of appropriate symmetries and by charging; these are viewed as neutral (radical) and charged (cation and anion) defects in the polyene structure. The equilibrium geometries and charge distributions of varying-length polyenes and defect-containing polyenes are calculated. The extent of disruption of the bond-length alternation pattern of the carbon backbone is predicted to be about half as large as previously thought for neutral defects (solitons) and even smaller for anionic defects. Positively charged solitons are of larger extent. These results are consistent with known conductivity—doping-level relationships. A spatially damped charge-density wave is associated with the charged solitons and a spin-density wave with the neutrals; in both cases the wave extends farther than the lattice kink itself. Polarons and bipolarons, studied as soliton-antisoliton pairs (radical cations and radical anions) on the same model molecule, are also found to exhibit charge-density-wave solutions. The bipolaron is shown to be unstable to the formation of a like-charge soliton-antisoliton pair. Strong interchain coupling is expected as a result of the large dipole moments associated with the unique form of the lattice polarization due to the damped charge-density wave in charged solitons and polarons.