  Our recent theory (Ref. 1) enables us to choose arbitrary quantities as the
basic variables of the density functional theory. In this paper we apply it to
several cases. In the case where 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 LDA+U 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.
