Correction of finite size errors in many-body electronic structure calculations

Abstract

PAGE Electronic structure calculations using simulation cells for extended systems typically incorporate periodic boundary conditions as an attempt to mimic the real system with a practically infinite number of particles. Periodic boundary conditions introduce unphysical constraints that give rise to finite-size errors. In mean-field type calculations, the infinite size limit is achieved by simple quadrature in the Brillouin zone using a finite number of k-points. Many-body electronic structure calculations with explicit two-particle interactions cannot avail themselves of this simplification. Direct extrapolation is computationally costly while size correction with less accurate methods is frequently not sufficiently accurate. The Hartree-Fock method neglects the correlation energy, while the conventional density functional theory (DFT) uses the infinite-size limit of the exchange correlation function. Here we present a new finite-size exchange correlation function designed to be used in DFT calculations to give more accurate estimates of the finite-size errors. Applications of the method are presented, including the P2 molecule, fcc silicon, bcc sodium and BiScO3 perovskite. The method is shown to deliver rapidly convergent sizecorrections. Dedicated to my mother Heryawaty and the memory of my father Johnny Kwee.