Density function method Kohn-Sham orbital

Density Functional Theory (DFT) has become the method of choice for the study of the electronic structure of solids. Advances in computer technology have made possible the development of DFT-based codes providing a detailed ab initio description of the electronic structme of complex materials. Following the two celebrated papers by Hohenberg and Kohn and Kohn and Sham, a wide variety of approaches have been developed and turned into very efficient computational tools. These approaches differ in the way they represent the density, potential, and Kohn-Sham orbitals. Essentially DFT approaches can be classified in two main groups all electron methods and pseudopotential methods. 

A popular alternative is to employ density functional theory (DFT) methods. Kohn-Sham (KS) orbital energies in the ground state are a more reliable predictor of the ion state ordering than Koopmans theorem. There are good theoretical reasons for interpreting them as approximate vertical IE." For transition metal compounds AE methods, the DFT equivalent... 

In practical calculations, the electronic density is still calculated from wave functions, using a method originally devised by Kohn and Sham [6]. These so-called Kohn-Sham orbitals correspond to a virtual system of noninteracting electrons, similar to Hartree-Fock methods. Even though these Kohn-Sham orbitals have no clear physical meaning, they may still be quite useful in interpreting the results from a DFT calculation in terms of molecular orbital theory. 

Density functional techniques are, in principle, based on minimization of energy as a functional of the electron density p(r). In practice the density is represented in terms of Kohn-Sham orbitals, and therefore the implementation takes the same broad form [Equation (2)] as Schrodinger based methods. We will forgo extensive discussion of specific forms of [ ] until Section 2 below, and consider simple examples to illustrate the use simulated annealing here. 

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