A numerical Poisson solver with improved radial solutions for a self-consistent locally scaled self-interaction correction method

Abstract

The universal applicability of density functional approximations is limited by the self-interaction error made by these functionals. Recently, a novel one-electron self-interaction-correction (SIC) method that uses an iso-orbital indicator to apply the SIC at each point in space by scaling the exchange-correlation and Coulomb energy densities was proposed. The LSIC method is exact for the one-electron densities, and unlike the well-known Perdew-Zunger SIC (PZSIC) method recovers the uniform electron gas limit of the uncorrected density functional approximation and reduces to PZSIC method as a special case when the isoorbital indicator is set to unity. Here, we present a numerical scheme that we have adopted to evaluate the Coulomb potential of the electron density scaled by the iso-orbital indicator required for the self-consistent LSIC calculations. After analyzing the behavior of the finite difference method and the green function solution to the radial part of the Poisson equation, we adopt a hybrid approach that uses the FDM method for the Coulomb potential due to the monopole and the GF for all higher order terms. The performance of the resultant hybrid method is assessed using a variety of systems. The results show improved accuracy compared to earlier numerical schemes. We also find that, even with a generic set of radial grid parameters, accurate energy differences can be obtained using a numerical Coulomb solver in standard density functional studies.