Critical assessment of the self-interaction-corrected local-density-functional method and its algorithmic implementation

We calculate the electronic structure of several atoms and small molecules by direct minimization of the self-interaction-corrected-local-density-(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 then 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 Beck-Lee-Yang-Parr functional, which we include as a representative generalized gradient approximation functional, outperforms both LDA and SIC-LDA for all ground-state properties we considered.