ABSTRACT
A number of attempts have been made to go bey_ond the LDA. Among the most successful of these are the LDA+U (Anisimov, Zaanen, and Andersen 1991, Anisimov et al. 1993, Lichtenstein, Zaanen, and Anisimov 1995) and the self-interaction correction (SIC) method (Cowan 1967, Lindgren 1971, Zunger, Perdew, and Oliver 1980, Perdew and Zunger 1981, Svane and Gunnarsson 1990, Szotek, Temmerman, and Winter 1993, Arai and Fujiwara 1995) described in the other contributions to this book. Another popular approach is the generalized gradient approximation (GOA) (see e.g. Perdew, Burke, and Emzerhof 1997 and references therein for a recent development, Becke 1988, 1992, 1996, Svendsen and von Barth 1996, Springer, Svendsen, and von Barth 1996) which was initiated by the work ofLangreth and Mehl (1983). While in general gradient corrections give a significant improvement in the total energy (Causa and Zupan 1994, Philipsen and Baerends 1996, Dal Corso 1996) there is almost no major improvement for quasiparticle energies (Dufek et al. 1994 ). A recent approach of improving the LDA is the optimized effective potential method (Kotani 1995, Bylander and Kleinman 1995a,b, Kotani and Akai 1996) where the exchange energy is calculated exactly and a local exchange potential is obtained by taking a functional derivative of the exchange energy with respect to the density. The correlation energy can be approximated by the LDA value. The original idea of this method is due to Talman and Shadwick (1976) in their work on atoms as a restricted minimum search of the Hartree-Fock total energy within local potentials, i.e. the orbitals are restricted to be solutions to single-particle Hamiltonians with local potentials. Another recent attempt is a generalized Kohn-Sham scheme (Seidl et al. 1996) with a non-local exchange-correlation potential.
