Arbitrary choice of basic variables in density functional theory . II . Illustrative applications

Our recent extended constrained-search theory @M. Higuchi and K. Higuchi, Phys. Rev. B 69, 035113 ~2004!# enables us to choose arbitrary quantities as the basic variables of density functional theory. In this paper, we apply it to several cases. In the case in which the occupation matrix of localized orbitals is chosen as a basic variable, we can obtain the single-particle equation which is equivalent to that of the LDA1U method. The theory also leads to the Hartree-Fock-Kohn-Sham equation by letting the exchange energy be a basic variable. Furthermore, if the quantity associated with the density of states near the Fermi level is chosen as a basic variable, the resulting single-particle equation includes the additional potential which could mainly modify the energy-band structures near the Fermi level.