Pair density functional theory utilizing the noninteracting reference system: An effective initial theory

Abstract

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.

Excited-state pair-density-functional theory

“…One can try to use or generalize the ground-state approximate functionals. Higuchi and Higuchi developed a method to approximate the ground-state kinetic energy functional [58][59][60]. As their method is based on the constrained search technique, it can be extended to excited states.…”

“…They use representable pair densities with a restriction of the searching area to the set of single Slater determinants. The kinetic energy functional T s gained by this procedure is, of course, different from the exact one and Higuchi and Higuchi [58][59][60][61] proposed several approximate forms for the difference T . Their technique can be extended to excited states by a further restriction of the searching area to those single Slater determinants that are orthogonal to the first i − 1 states.…”

“…Finally, one has to find adequate approximation for the difference T . Probably, one of the approximate forms proposed by Higuchi and Higuchi [58][59][60] will work for excited states, too. That will be the subject of further research.…”

Coupling-constant expression and exact relations for the kinetic-energy functional in pair-density-functional theory

“…However, the necessary and sufficient conditions for the N -representability of the PD have not yet been known in a practical form. We have recently attempted to utilize as the search region of PDs the set of PDs that come from some kind of antisymmetric wave functions [20][21][22][23][24]. More recently, we have proposed an efficient method to extend the search region within the set of N-representable PDs [25].…”

“…(2) means that integrals are performed over the volume . In the previous scheme [20,22,23], the noninteracting reference system is introduced so as to reproduce the variationally best PD within the set of PDs that are constructed from the single Slater determinants (SDs). The Hamiltonian of the noninteracting reference system is given byĤ…”