Implementation of an approximate self-energy correction scheme in the orthogonalized linear combination of atomic orbitals method of band-structure calculations

Based on the Sterne-Inkson model for the self-energy correction to the single-particle energy in the local-density approximation (LDA), we have implemented an approximate energy-dependent and k-dependent GW correction scheme to the orthogonalized linear combination of atomic orbital-based local-density calculation for insulators. In contrast to the approach of Jenkins, Srivastava, and Inkson, we evaluate the on-site exchange integrals using the LDA Bloch functions throughout the Brillouin zone. By using a k-weighted band gap Eg and a plasmon frequency ωₚ determined by valence-electron density for the estimation of the dielectric constant, our approach retains the first-principles nature for the single-particle energy correction. Test calculations on semiconductors such as diamond, Si, Ge, GaAs, GaP, and ZnSe show good results with the GW-corrected gap values generally within 10% of the experimental values. It is shown that an accurate and well-converged LDA result is very important for the correct self-energy correction, and its convergence with respect to the number of k points needed in the computation is much slower than that in the LDA calculation.