TIGHT-BINDING THEORY OF INTERCHAIN COUPLING IN DOPED POLYACETYLENE

Although many properties of polyacetylene, (CH)x, can be qualitatively understood with a one-dimensional model, a three-dimensional model is necessary for understanding others, and for a quantitative description in any case. We formulate here a tight-binding model of three-dimensional interactions in undoped and alkali-metal-doped polyacetylene using the structures determined by x-ray diffraction. In the calculation of interchain coupling, all pi orbitals on the chains are included, not just those directly opposite each other and their nearest neighbors. The coupling strength for each pair is calculated from a semiempirical relation due to Harrison, and extrapolated, again semiempirically, beyond typical interatomic spacings. It is found that the interchain coupling is energy dependent, being much stronger at the valence-band minimum than at higher energies. The calculations show that, if the Coulomb potential of the ions were absent, the potassium-doping levels required to give rise to metallic (CH)x would be greater than 15%, thus much greater than the experimental value. Dispersion relations perpendicular to the chain are derived for undoped, sodium-doped, and potassium-doped (CH)x in the "metallic" regime by means of an approximate treatment of interchain coupling. Corrections are calculated to the density of states versus energy for chain-chain coupling and doping ion-chain coupling. The ion-chain coupling is found to be of the same order of magnitude as chain-chain coupling because the larger orbital overlap between carbon atoms and doping ions than between interchain carbons is balanced out by the energy difference between these orbitals.