Second‐order many‐body perturbation‐theory calculations in extended systems

Explicit expressions for electron correlation at the second‐order many‐body perturbation‐theory [MBPT(2)] level are presented and implemented for the total energy per unit cell and for the band structure of extended systems. In the latter case, a formula is presented for a direct evaluation of the band gap rather than obtaining it as a difference of two large numbers. Application is made to alternating trans‐polyacetylene. We assess the convergence of MBPT(2) with the number of unit cells (N) included in the lattice summations, the number of k‐points (K) taken for the integrals over k in the first Brillouin zone, and the cutoff threshold (10−C) for the two‐electron integrals. The MBPT(2) correlation correction to the band structure converges very slowly with N and demands a large K while the MBPT(2) correction to the total energy per unit cell converges much faster with N and needs a much smaller K. Neither MBPT(2) correction is sensitive to the cutoff of the two‐electron atomic orbital integrals, 10−C, w...

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