Self-interaction correction method

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. 

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. 

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. 

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... 

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. 

Finally, in careful comparative studies of the molecular electron densities generated by HF, correlated ab initio, and pure, self-interaction corrected, and hybrid DFT calculations, Cremer et al have made a very interesting observation [72, 73]. They found that the pure DFT generated densities differed from those obtained with accurate ab initio methods in a particular way, and that both hybrid, and self-interaction corrected DFT methods, yielded densities closer to the correct ones. Based on this observation, they suggested that mixing in of exact exchange in hybrid functionals serves as a proxy for the self-interaction correction. 

J. VandeVondele and M. Sprik (2005) A molecular dynamics study of the hydroxyl radical in solution applying self-interaction corrected density functional methods. Phys. Chew,. Chew,. Phys. 7, p. 1363... 

The computation of A from Eq. (19) often meets convergence problem [36], Hence, it has been considered to be preferable to calculate electronegativity as the negative of the highest occupied orbital energy in the Xu method with or without spin polarization [47 49] and with self-interaction correction [50]. Electron affinity (A) can be obtained from the following relation ... 

Several previous workers [14, 75-77] have examined various procedures, called self-interaction-corrected (SIC) DFT methods, aimed at remedying this deficiency. One possible approach involves merely subtracting out the Coulomb and XC energies corresponding to the single-particle densities, i.e. a correction term of the form... 

A different approach to treat correlation effects which are not well described within the LSDA consists in incorporating self-interaction corrections (SIC) [111-114] in electron structure methods for solids, Svane et al. [115-120]. In the Hartree-Fock (HF) theory the electron-electron interactions are usually divided into two contributions, the Coulomb term and the exchange term although they both are Coulomb interactions. The separation though, is convenient because simplifications of self-consistent-field calculations can be obtained by including in both terms the interaction of the electron itself. In the HF theory this has no influence on the solutions because these selfinteractions in the Coulomb and exchange terms exactly cancel each other. However, when the exchange term is treated... 

Another disadvantage of the LDA is that the Hartree Coulomb potential includes interactions of each electron with itself, and the spurious term is not cancelled exactly by the LDA self-exchange energy, in contrast to the HF method (see A1.3I. where the self-interaction is cancelled exactly. Perdew and Zunger proposed methods to evaluate the self-interaction correction (SIC) for any energy density functional [40]. However, full SIC calculations for solids are extremely complicated (see, for example [41. 42 and 43]). As an alternative to the very expensive GW calculations, Pollmann et al have developed a pseudopotential built with self-interaction and relaxation corrections (SIRC) [44]. 

In other words, the existence of the so-called Self-Interaction-Correction (SIC) makes the method reminiscent of the Hartree (product) wavefunction rather than the Hartree-Fock (determinant) case. 

Description of core orbitals is investigated by estimating core-excitation energies of carbon monoxide, computed by the self-interaction corrected (SIC)-ASCF and SIC-TDDFT methods. First, the formulations of SIC-ASCF and SIC-TDDFT are briefly introduced, and subsequently numerical analysis is demonstrated. 

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