Correlaction Effects on the Band Gap of Conducting Polymers

By applying the projection technique to the computation of excitation energies, we study the correlation effects on the band gap of conducting polymers. In the presence of an additional electron or hole, the correlation induces a polarization cloud around the addi- tional particle, which forms a polaron. For the excitation energy of a polaron,there is a competition between a {\it loss} of the correla- tion energy in the ground state and a {\it gain} of polarization energy. For the Hubbard interaction, the {\it loss} of correlation energy is dominant and correlations increase the band gap.However,for long-range interactions, the {\it gain} of polarization energy is dominant and correlations decrease the band gap. Screening the long- range interaction suppresses the {\it gain}of the polarization energy so that correlations again increase the band gap.A small dimerization is always favorable to the correlation effects. For {\it trans}-poly- acetylene, we obtain the on-site repulsion $U=4.4$eV and the nearest- neighbor interaction $V=0.8$ eV. The screening of $\pi$ electrons due to the polarizability of $\sigma$ electrons is quite strong. ** to be published in Phys. Rev. B