Arbitrary Choice of Basic Variables in Density Functional Theory. II. Illustrative Applications

TL;DR

This paper demonstrates how choosing different basic variables in density functional theory can lead to various well-known and new single-particle equations, enhancing the flexibility and applicability of the theory.

Contribution

It applies a recent general theory to derive multiple single-particle equations by selecting different basic variables, including the occupation matrix and density of states.

Findings

Derivation of the LDA+U-like equation from occupation matrix choice

Recovery of the Hartree-Fock-Kohn-Sham equation via exchange energy as a basic variable

Modification of energy-band structures near the Fermi level through density of states-based variables

Abstract

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.