  The Hohenberg-Kohn theorem of the density functional theory is extended by
modifying the Levy constrained-search formulation. The new theorem allows us to
choose arbitrary physical quantities as the basic variables which determine the
ground-state properties of the system. Moreover, the theorem establishes a
minimum principle with respect to variations in the chosen basic variables as
well as with respect to variations in the density. By using this theorem, the
self-consistent single-particle equations are derived. N single-particle
orbitals introduced reproduce the basic variables. The validity of the theory
is confirmed by the examples where the spin-density or paramagnetic
current-density is chosen as one of the basic variables. The resulting
single-particle equations coincide with the Kohn-Sham equations of the
spin-density functional theory (SDFT) or current-density functional theory
(CDFT), respectively. By choosing basic variables appropriate to the system,
the present theory can describe the ground-state properties more efficiently
than the conventional DFT.
