ABSTRACT
Until now we have been trying to solve the many-body problem by approximating the many-body wave function such as in Hartree or Hartree-Fock (H-F) methods. Since the many-body wave function involves the coordinates of all the electrons, it is a function of 3N variables, where N is the number of electrons. Obviously, such an approach is complex and numerically very demanding. It would be much simpler if the electronic system could be described in terms of electron density n r( )
, which is a function
of only three variables (e.g., x, y, z). A firm and exact theoretical foundation for such description was provided by Hohenberg and Kohn in 1964 and is known as the density functional theory (DFT). We shall see that in the local density approximation (LDA) it is as simple as the Hartree theory but gives much better results than that given by the H-F theory. The reason is that even the simplest version of the theory includes both exchange and correlations, fairly accurately, while the H-F equation includes exchange exactly but neglects correlations completely. Owing to its simplicity, most of the electronic structure calculations on materials are done using the DFT, and it has made a big impact in understanding the atoms, molecules, atomic clusters, and solids. Recognizing this achievement Walter Kohn (Figure 3.1), who played the leading role in the development of DFT, was awarded the Nobel Prize in 1998.
