Self-interaction correction to density-functional approximations for many-electron systems

@article{Perdew1981SelfinteractionCT,
  title={Self-interaction correction to density-functional approximations for many-electron systems},
  author={John P. Perdew and Alex Zunger},
  journal={Physical Review B},
  year={1981},
  volume={23},
  pages={5048-5079}
}
exchange and correlation, are not. We present two related methods for the self-interaction correction (SIC) of any density functional for the energy; correction of the self-consistent one-electron potenial follows naturally from the variational principle. Both methods are sanctioned by the Hohenberg-Kohn theorem, Although the first method introduces an orbital-dependent single-particle potential, the second involves a local potential as in the Kohn-Sham scheme. We apply the first method to LSD… 
A comparison of self-interaction-corrected local correlation energy functionals
A new selfinteraction-corrected local correlation energy functional is constructed to conform with the exact limiting behaviour in both one-electron systems and N-electron systems (N to infinity )
Two avenues to self-interaction correction within Kohn—Sham theory: unitary invariance is the shortcut
The most widely used density functionals for the exchange-correlation energy are inexact for one-electron systems. Their self-interaction errors can be severe in some applications. The problem is not
Exchange parameters from approximate self-interaction correction scheme.
TLDR
Although ASIC performs reasonably well for systems where the magnetism originates from half-filled bands, it suffers from similar problems than those of local density approximation for other situations, and the exchange constants are still overestimated.
Implementation and reassessment of the Perdew-Zunger self-interaction correction
Density functional theory (DFT) using semi-local functional approximations can describe many chemical properties to high accuracy, but in some cases large and even qualitative errors emerge. Some of
Atomic-orbital-based approximate self-interaction correction scheme for molecules and solids
We present an atomic-orbital-based approximate scheme for self-interaction correction (SIC) to the local-density approximation (LDA) of density-functional theory. The method, based on the idea of
Self-interaction corrections in density functional theory.
TLDR
Self-interaction corrections for Kohn-Sham density functional theory are reviewed for their physical meanings, formulations, and applications and it is shown that the self-interactions error has a serious effect on the states of core electrons, but it has a smaller than expected effect on valence electrons.
Dimensionality dependence of the self-interaction correction in the local-density approximation to density functional theory
In the terminology of the review article 1 of Walter Kohn on condensed matter physics, the so-called Wigner lattice 2,3 is governed by the radical effect of the electron-electron interaction vr= e 2
DRIVING OUT THE SELF-INTERACTION ERROR
Simple density functional [1–4] for the exchange-correlation energy typically work well for many-electron systems, but fail to be exact for one-electron systems. This lecture reviews the
...
...