Quasiparticle energy-band structures in semiconducting polymers: Correlation effects on the band gap in polyacetylene

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Abstract
Single- and many-particle effects contributing to the formation of energy-band gaps in semiconducting polymers are investigated using exact-exchange Hartree-Fock (HF) theory and Toyozawa's electronic-polaron model. The electron correlation is calculated by Møller-Plesset perturbation theory including explicitly all significant matrix elements in second order. Their efficient calculation is facilitated by the use of optimally localized Wannier functions. The importance of both short- and long-range contributions, of extended atomic basis sets, and of the use of the full virtual space is exhibited in the case of trans-polyacetylene (PA) as a model system. Correlation effects are shown to reduce the single-particle energy-band gap first by diminishing the bond alternation in PA. On the other hand, due to the self-energy corrections, the HF energy-band states are transformed to quasiparticle (electronic-polaron) states, the valence band is shifted upward, and the conduction band is shifted downward. The original HF energy-band gap of 5 eV is reduced to 3 eV at an estimated level of 70-75% of valence-shell correlation. Its extrapolated value for full correlation is found to be 2.5 eV. The remaining 0.5-eV difference between theory and experiment is assigned to phonon-polaron and relaxation effects.