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One of the most frequently used method that incorporates self-interaction correction was proposed by Perdew and Zunger [133]. Definitely improved results can be obtained by this method. For a review see [143]. Another method, that goes beyond the local density approximation is the weighted density approximation (WDA) [144]. The gist of this approximation, which leads to nonlocal energy functional, is a more careful transcription of the exchange-correlation hole of the homogeneous electron gas to the case of an inhomogeneous system.
131] found that the calculated one-electron and total energies were very close to that of the Hartree—Fock method. Norman and Koelling [132] combined the optimized effective potential method with the technique of including self-interaction correction proposed by Perdew and Zunger [133]. The optimized effective potential method was generalized for the spin polarized case by Krieger et al. [49]. Krieger et al. [49] introduced an approximate OPM method. Recently, an alternative derivation to the KLI method was proposed [134].
Nagy / Physics Reports 298 (1998) 1—79 As we have already seen the excitation energy is not simply the difference of the one-electron energies. The extra term jE /jw" U is generally not zero. At certain values of w it gives a significant L contribution. The function jE /jw" U for atoms B, C, O, Mg, Si, S, and P has an almost linear L dependence on w. On the other hand, for the atoms F, Cl and Na there is a value w"w , where it disappears. It means that at w the excitation energy can be simply given by the difference !