Finite-Size Correction in Many-Body Electronic Structure Calculations

Abstract

Finite-size (FS) effects are a major source of error in many-body (MB) electronic structure calculations of extended systems. A method is presented to correct for such errors. We show that MB FS effects can be effectively included in a modified local density approximation calculation. A parametrization for the FS exchange-correlation functional is obtained. The method is simple and gives post-processing corrections that can be applied to any MB results. Applications to a model insulator (P2 in a supercell), to semiconducting Si, and to metallic Na show that the method delivers greatly improved FS corrections.PACS numbers: 02.70. Ss, 71.15.Nc, Realistic many-body (MB) calculations for extended systems are needed to accurately treat systems where the otherwise successful density functional theory (DFT) approach fails. Examples range from strongly correlated materials, such as high-temperature superconductors, to systems with moderate correlation, for instance where accurate treatments of bond-stretching or bond-breaking are required. DFT or Hartree Fock (HF), which are effectively independent-particle methods, routinely exploit Bloch's theorem in calculations for extended systems. In crystalline materials, the cost of the calculations depends only on the number of atoms in the periodic cell, and the macroscopic limit is achieved by a quadrature in the Brillouin zone, using a finite number of k-points. MB methods, by contrast, cannot avail themselves of this simplification. Instead calculations must be performed using increasingly larger simulation cells (supercells). Because the Coulomb interactions are long-ranged, finite-size (FS) effects tend to persist to large system sizes, making reliable extrapolations impractical. The resulting FS errors in state-of-the-art MB quantum simulations often can be more significant than statistical and other systematic errors. Reducing FS errors is thus a key to broader applications of MB methods in real materials, and the subject has drawn considerable attention [1,2].In this paper, we introduce an external correction method, which is designed to approximately include FS corrections in modified DFT calculations with finite-size functionals. The method is simple, and provides postprocessing corrections applicable to any previously obtained MB results. Conceptually, it gives a consistent framework for relating FS effects in MB and DFT calculations, which is important if the two methods are to be seamlessly interfaced to bridge length scales. The correction method is applied to a model insulator (P 2 in a supercell), to semiconducting bulk Si, and to Na metal. We find that it consistently removes most of the FS errors, leading to rapid convergence of the MB results to the infinite system.We write the N -electron MB Hamiltonian in a supercell as (Rydberg atomic units are used throughout):where the ionic potential on i can be local or non-local, and r i is an electron position. The Coulomb interaction V FS between electrons depends on the supercell size and shape, due to modificatio...

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