A General Minimum Principle for Correlated Densities in Quantum Many-Particle Systems

Abstract

It is shown that interacting many-particle quantum systems can be described in terms of fully correlated n-particle densities, which determine uniquely the potential acting on the system and satisfy a minimum principle with respect to the ground-state energy. This leads to a generalization of ordinary density functional theory in terms of n-particle densities which allows the direct and selfconsistent treatment of correlation effects within electronic structure methods for atoms, molecules, and solids. [S0031-9007 (96)01364-6] PACS numbers: 71.15.Mb, 31.10.+ z, 31.15.Ew

A proposal of the approximate scheme for calculating the pair density

“…Ziesche first proposed the PD functional theory using the natural spin geminals [6,7]. Another scheme was offered by Gonis with taking the two-particle densities as basic variables [8,9]. Nagy generalized Gonis's theory to the PD functional theory, which has the auxiliary equation of a two-particle problem [10,11].…”

A restrictive condition on approximate forms of the kinetic energy functional of the pair density functional theory

“…After the PD functional theory was proposed by Ziesche [1], a lot of works have been done so far [2][3][4][5][6][7][8][9][10][11][12][13][14]. One of the key points to develop the PD functional theory is how approximate forms of the kinetic energy functional are described by using the PD.…”

Scaling method for the pair-density-functional theory in combination with energy functionals satisfying the virial theorem: Checking the validity via atomic-structure calculations

“…The inequality (17) means that E[γ (2) 0, λ ] may take a minimum value at the PD that belongs toC 1 ∩ C 2 , whereC 1 denotes the complementary set of C 1 . If we add to the search region the set of PDs that belong toC 1 ∩ C 2 , i.e., we retake C 1 ∪ C 2 as the search region of PDs, then the variationally best PD within C 1 ∪ C 2 can be obtained from…”