Preliminaries and Notation

First of all, a few words on the scope of this review seem to be appropriate. For simplicity, all explicit formulae in this chapter will be given for spin-saturated systems only. Of course, the complete formalism can be extended to spin-density functional theory (SDFT) and all numerical results for spin-polarized systems given in this paper were obtained by SDFT calculations. In addition, the discussion is restricted to the nonrelativistic formalism - for its relativistic form see Chap. 3. The concept of implicit functionals has also 

In order to introduce the notation, the basic relations of DFT are now summarized, starting with the KS equations [5], 

Throughout this chapter f k and always denote the KS orbitals and eigenvalues, respectively. As usual, the total KS potential is given by the sum of the external (nuclear) potential r ext, the Hartree potential wh and the xc-potential v c- 

The density is obtained by summing up the energetically lowest KS states, 

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