Kohn–Sham Method

Abstract

To begin the topic of DFT, this chapter overviews how the Kohn–Sham method was developed historically and then introduces various extensions of this method. The Thomas–Fermi method, which is the first form of DFT, is first explained, focusing on the local density approximation of kinetic and exchange energy density functionals, in Sect.4.1. Then, the Hohenberg–Kohn theorem, which is the basic theory of DFT, is reviewed, with a mention of the constrained search formulation used to solve the V -representability problem, in Sect. 4.2. The Kohn–Sham method based on this theorem is introduced, along with the corresponding computational methods, in Sect. 4.3. As the extension of the Kohn–Sham method to include general functionals, the generalized Kohn–Sham method is surveyed in Sect. 4.4. The constrained search method, which directly constructs a Kohn–Sham potential from the electron density, is explained, and as a consequence of this method, it is clarified why the Kohn–Sham method can accurately reproduce chemical behavior in Sect. 4.5. Finally, the time-dependent and coupled-perturbed Kohn–Sham methods are reviewed as methods with which to apply the Kohn–Sham method to calculations of photoexcitation spectra and response properties, respectively, in Sects. 4.6 and 4.7.