Perdew-Zunger scheme

Of course, this self-correction error is not limited to one electron systems, where it can be identified most easily, but applies to all systems. Perdew and Zunger, 1981, suggested a self-interaction corrected (SIC) form of approximate functionals in which they explicitly enforced equation (6-34) by substracting out the unphysical self-interaction terms. Without going into any detail, we just note that the resulting one-electron equations for the SIC orbitals are problematic. Unlike the regular Kohn-Sham scheme, the SIC-KS equations do not share the same potential for all orbitals. Rather, the potential is orbital dependent which introduces a lot of practical complications. As a consequence, there are hardly any implementations of the Perdew-Zunger scheme for self-interaction correction. 

Note that, within this approximation, the nuclear KS potential depends on the state it acts on. This is analogous to the SIC scheme of Perdew and Zunger... 

At present the most frequently used parameterization for exchange and correlation are those of Perdew and Zunger [40] or Vosko, Wilk and Nusalr [41]. These two functionals which are based on the Monte Carlo simulations by Ceperly and Adler [42] give rather similar results. There are deficiencies in the LDA schemes which are due to the wrong asymptotic behaviour of the exchange and correlation potential since it falls off exponentially and not as... 

Perdew and Zunger (PZ) have listed a number of inadequacies of the LSD approximation which they attributed primarily to the spurious selfinteraction terms. They then proposed an orbital self-interaction correction scheme. The list of LSD failures given by PZ is ... 

Besides, self-interaction correction (SIC) is one of the most popular correction schemes. Perdew and Zunger suggested a scheme for the application of SIC to occupied orbitals where the self-interaction components of the Coulomb and exchange energies are simply subtracted from the total exchange-correlation energy [81]... 

Eqs. (44) and (45) were stressed in the self-interaction correction scheme of Perdew and Zunger [77]. 

---