Arbitrary choice of basic variables in density functional theory: Formalism

The Hohenberg-Kohn theorem of the density functional theory ~DFT! is extended by modifying the Levy constrained-search formulation. The theorem allows us to choose arbitrary physical quantities as basic variables which determine the ground-state properties of the system. Moreover, the theorem establishes a minimum principle with respect to variations in chosen basic variables as well as with respect to variations in the density. By using this theorem, self-consistent single-particle equations are derived. N single-particle orbitals introduced reproduce not only the electron density but also arbitrary physical quantities which are chosen as basic variables. The validity of the theory is confirmed by examples where the spin density or paramagnetic current density is chosen as one of basic variables. The resulting single-particle equations coincide with the KohnSham equations of the spin-density functional theory or current-density functional theory, respectively. By choosing basic variables appropriate to the system, the present theory can describe the ground-state properties more efficiently than the conventional DFT.