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.
We present a computational pair density ͑PD͒ functional theory using multiple Slater determinants in constructing the PD. Compared to the effective initial scheme ͓M. Higuchi and K. Higuchi, Phys. Rev. B 78, 125101 ͑2008͔͒, the search region for the ground-state PD is substantially extended within the set of N-representable PDs. The merit of the present scheme is to guarantee the resultant PD to be N-representable and to describe correlation effects beyond the effective initial scheme, which enables us to tackle with the development of the approximate form of the kinetic energy functional. We derive two restrictive conditions on the kinetic energy functional. With the aid of these restrictive conditions, we also propose several types of approximate functionals of the kinetic energy. To check the abilities and limitations of the present scheme including such approximate functionals, actual calculations are performed for the neutral neon atom. The results show that the present scheme provides the N-representable and correlated PDs, though it would have some limitations. What we need to do first for improvement of the computational PD functional theory is that the development of the approximate functional of the kinetic energy is further advanced along the present scheme.
We present a pair density ͑PD͒ functional scheme utilizing the noninteracting reference system. In order to check to what extent this scheme can express the correlation effects, actual calculations are performed for the neutral neon atom. It is shown that this scheme reproduces about 20% of the correlation energy through use of noninteracting single determinants with an approximate correlating kinetic energy functional. Thus, since it obviously provides the N-representable and correlated PD, this scheme can be positioned as an effective initial theory in the field of the PD functional theory, just like the position of the Hartree-Fock approximation in the field of the wave function theory.
The coupling-constant expression and virial relation for the exchange-correlation energy functional of the extended-constrained search theory ͓M. Higuchi and K. Higuchi, Phys. Rev. B 69, 035113 ͑2004͔͒ are derived. These provide the guideline for developing and testing the approximate form of the exchange-correlation energy functional.
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