A critical assessment of the Self-Interaction Corrected Local Density Functional method and its algorithmic implementation

TL;DR

This paper evaluates the Self-Interaction Corrected LDA functional's performance in atomic and molecular calculations, deriving a new gradient expression, and compares its accuracy to LDA and GGA functionals.

Contribution

It provides a corrected gradient expression for SIC-LDA and assesses its computational performance and accuracy relative to other density functionals.

Findings

SIC-LDA improves total energies, ionization energies, and charge densities over LDA for atoms.

SIC-LDA performs worse than LDA in predicting molecular bond lengths and reaction energies.

GGA functional BLYP outperforms both LDA and SIC-LDA across all tested properties.

Abstract

We calculate the electronic structure of several atoms and small molecules by direct minimization of the Self-Interaction Corrected Local Density Approximation (SIC-LDA) functional. To do this we first derive an expression for the gradient of this functional under the constraint that the orbitals be orthogonal and show that previously given expressions do not correctly incorporate this constraint. In our atomic calculations the SIC-LDA yields total energies, ionization energies and charge densities that are superior to results obtained with the Local Density Approximation (LDA). However, for molecules SIC-LDA gives bond lengths and reaction energies that are inferior to those obtained from LDA. The nonlocal BLYP functional, which we include as a representative GGA functional, outperforms both LDA and SIC-LDA for all ground state properties we considered.