A first-principles calculation to determine the electronic properties of trans-polyacetylene using Hedin's $\mathrm{GW}$ approximation for the self-energy is described. To our knowledge this work is the first application of the $\mathrm{GW}$ method to a quasi-one-dimensional system. The zeroth-order approximation is used to initialize the calculation with the self-energy described by the Hartree-Fock exchange interaction. To include electron exchange and correlation beyond Hartree Fock, the first-order ($\mathrm{GW}$) approximation for the self-energy is adopted. Now the self-energy is energy dependent and is described by the single-particle Green's function ($G$) and the screened Coulomb interaction ($W$). For screening the Coulomb potential the complete wave number and frequency-dependent dielectric response tensor, within the random phase approximation, is employed. The $\mathrm{GW}$ calculation is carried to self-consistency. By implementing the $\mathrm{GWA}$, the Hartree-Fock minimum band gap is reduced by 68% and falls within the experimentally observed range. The optical reflectance and electron-energy-loss function, calculated with local field and lifetime effects, are presented and compared with experiment.

• Received 14 August 1995

DOI:https://doi.org/10.1103/PhysRevB.53.3662