First-principles calculation of the three-dimensional band structure of poly(phenylene vinylene)

We have carried out a local-density-functional calculation of the three-dimensional (3D) band structure of the conducting polymer poly(phenylene vinylene) (PPV). The motivation was to investigate the effects of interchain coupling. The major effects are due to coupling of carbons in the rings to their closest neighbors, hydrogens on rings in adjacent chains. Among the effects of this coupling are splitting by up to 0.4 eV at various points of the Brillouin zone of the double degeneracy that would exist if the two chains in the unit cell were uncoupled; loss of electron-hole symmetry; the band edge at a point in the Brillouin zone off the chain direction; and a band gap smaller by 0.2 eV than that obtained from 1D calculations. The calculation results in a ratio of the transfer integral ${\mathit{t}}_{\mathrm{\perp }}$ perpendicular to the chains to ${\mathit{t}}_{\mathrm{\parallel }}$, parallel to the chains, ≃0.03. This value is too large to permit the existence of polarons in a perfect PPV crystal. Nevertheless, there is evidence for the existence of polarons in PPV crystals currently available. The large value of ${\mathit{t}}_{\mathrm{\perp }}$/${\mathit{t}}_{\mathrm{{\rm N}}}$ means that polaron existence must be due to defects, such as inclusions of precursor polymer. This would result in the polarons having a wide range of properties, i.e., extent on the chain and energy levels.