Electronic and lattice structures in potassium-doped stage-1 polyacetylene II. Effects of incommensurate arrangement of dopants and revaluation of the Thomas-Fermi potential

Effects of incommensurate arrangements of dopants to carbon atoms are investigated in K-doped stage-1 polyacetylene ((CH)x). Owing to the large size of the valence orbitals of K, the dense nature of the interchain transfers (ICTs) via dopants is not so much affected by the dopantsʹ arrangement though their patterns change site by site. The Thomas-Fermi potential calculated following Davisʹ method is necessary to give correct interchain Coulomb (ICC) and dopant Coulomb (DC) potentials. The DC potentials are always alternating because of the zigzag nature of (CH)x chains though some approximate ones have phase changes or intensity modulations due to incommensurate arrangements of dopants. Hartree-Fock calculations show that the ground state is CDW bipolaron lattices owing to the continually alternating nature of the DC potentials. They are ordered in-phase on each chain, owing to the ICC potentials with similar values at the nearest and next-nearest sites in a chain. ICTs little affect intrachain states owing to their dense nature. The system has a gap between the bipolaron band and the conduction band. Electron correlation seems to be essential to obtain a metallic (CH)x.