Self-interaction-corrected

Perdew J P and Zunger A 1981 Self-interaction correction to density-functional approximations for many-electron systems Phys. Rev. B 23 5048... 

Svane A and Gunnarsson Q 1990 Transition-metal oxides in the self-interaction-corrected density-functional formalism Phys. Rev. Lett. 65 1148... 

Szotek Z, Temmerman W M and Winter H 1993 Application of the self-interaction correction to transition-metal oxides Phys. Rev. B 47 4029... 

Perdew J P and A Zunger 1981. Self-Interaction Correction to Density-Functional Approximations for Many-Electron Systems. Physical Review B23 5048-5079. 

Encl[p] is the non-classical contribution to the electron-electron interaction containing all the effects of self-interaction correction, exchange and Coulomb correlation described previously. It will come as no surprise that finding explicit expressions for the yet unknown functionals, i. e. T[p] and Encl[p], represents the major challenge in density functional theory and a large fraction of this book will be devoted to that problem. 

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. 

Csonka, G. I., Johnson, B. G., 1998, Inclusion of Exact Exchange for Self-Interaction Corrected H, Density Functional Potential Energy Surface , Theor. Chem. Acc., 99, 158. 

Goedecker, S., Umrigar, C. J., 1997, Critical Assessment of the Self-Interaction-Corrected-Local-Density-Func-tional Method and its Algorithmic Implementation , Phys. Rev. A., 55, 1765. 

Johnson, B. G., Gonzales, C. A., Gill, P. M. W., Pople, J. A., 1994, A Density Functional Study of the Simplest Hydrogen Abstraction Reaction. Effect of Self-Interaction Correction , Chem. Phys. Lett., 221, 100. 

One obvious drawback of the LDA-based band theory is that the self-interaction term in the Coulomb interaction is not completely canceled out by the approximate self-exchange term, particularly in the case of a tightly bound electron system. Next, the discrepancy is believed to be due to the DFT which is a ground-state theory, because we have to treat quasi-particle states in the calculation of CPs. To correct these drawbacks the so-called self-interaction correction (SIC) [6] and GW-approximation (GWA) [7] are introduced in the calculations of CPs and the full-potential linearized APW (FLAPW) method [8] is employed to find out the effects. No established formula is known to take into account the SIC. 

Kubo, Y., Sakurai, Y., Tanaka, Y., Nakamura, T., Kawata, H. and Shiotani, N. (1997) Effects of self-interaction correction on Compton profiles of diamond and silicon, J. Phys. Soc. Jpn., 66, Till 2780. 

Heaton, R.A., Harrison, J.G. and Lin, C.C. (1983) Self-interaction correction for density-functional theory of electronic energy bands of solids, Phys. Rev., B28, 5992-6007. 

Hamada, N. and Ohnishi, S. (1986) Self-interaction correction to the local-density approximation in the calculation of the energy band gaps of semiconductors based on the full-potential linearized augmented-plane-wave method, Phys. Rev., B34,9042-9044. 

Norman, M.R. (1984) Application ofa screened self-interaction correction to transition metals copper and zinc, Phys. Rev., B29, 2956-2962. 

While the LSD exchange-correlation hole is accurate for small interelec-tronic separations (Sect. 2.3), it is less satisfactory at large separations, as discussed in Sect. 2.5. For example, consider the hole for an electron which has wandered out into the classically-forbidden tail region around an atom (or molecule). The exact hole remains localized around the nucleus, and in Sect. 2.5 we give explicit results for its limiting form as the electron moves far away [19]. The LSD hole, however, becomes more and more diffuse as the density at the electron s position gets smaller, and so is quite incorrect. The weighted density approximation (WDA) and the self-interaction correction (SIC) both yield more accurate (but not exact) descriptions of this phenomenon. 

Successful density functional approximations such as the PW91 GGA or the self-interaction correction (SIC) [57] to LSD recover [19] LSD values for the on-top hole density and cusp. The weighted density approximation (WDA) [41,42], which recovers the LSD exchange hole density but not the LSD correlation hole density [19] in the limit u -> 0, needs improvement in this respect. 

OPM approach, the Krieger-Li-Iafrate approach and the Perdew-Zunger self-interaction-correction (SIC) method [87] however yield correct neutral fragments. 

DPT schemes, which allow to calculate the electron affinities of atoms are based on the exact [59,60] and generalized (local) [61,62] exchange self-interaction-corrected (SIC) density functionals, treating the correlation separately in some approximation. Having better asymptotic behavior than GGA s, like in the improved SIC-LSD methods, one should obtain more... 

Patchkovskii et al.91 analyzed the effect of the self-interaction correction on the calculation of spin-spin couplings in the DFT framework. When introducing such a correction, they observed an overall worsening of the total calculated coupling due to an exaggerated change in the FC term. However, the PSO contribution seems to achieve an important improvement, suggesting that self-interaction corrections could be important in molecules where this last contribution is dominant. 

A number of different methods have been proposed to introduce a self-interaction correction into the Kohn-Sham formalism (Perdew and Zunger 1981 KUmmel and Perdew 2003 Grafenstein, Kraka, and Cremer 2004). This correction is particularly useful in situations with odd numbers of electrons distributed over more than one atom, e.g., in transition-state structures (Patchkovskii and Ziegler 2002). Unfortunately, the correction introduces an additional level of self-consistency into the KS SCF process because it depends on the KS orbitals, and it tends to be difficult and time-consuming to converge the relevant equations. However, future developments in non-local correlation functionals may be able to correct for self-interaction error in a more efficient manner. 

---