Effects of the Hubbard interaction and electrostatic pinning in polyacetylene

The discrete model for the coupled electron-phonon system in polyacetylene has been extended to include the electronic effects of electrostatic pinning and the Hubbard interaction in the unrestricted Hartree-Fock approximation. To fit experimental structural data, the Hamiltonian also includes the lattice kinetic energy and the coupling of several vibrational degrees of freedom. This model is then used to self-consistently determine the electronic eigenstates and the structural configuration for an odd-membered ring. The electronic states from this equilibrium configuration are then used to calculate the charge and spin density, optical absorption, and the single-electron loop corrections to the dynamical matrix. The resulting vibrational modes are examined and used in conjunction with the self-consistent electronic states to calculate the infrared-absorption spectra. Assuming that the pinning arises from an oppositely charged soliton on an adjacent chain leads to a pinning frequency of ≊500 ${\mathrm{cm}}^{\mathrm{-}1}$, in excellent agreement with observed results. A value for the Hubbard interaction of 4 eV leads to an excellent fit for the rest of the infrared spectra and the optical absorption for both a charged and a neutral soliton.