Towards a practical pair density-functional theory for many-electron systems

Journal Article · Sun Aug 01 04:00:00 EDT 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.70.022514· OSTI ID:20645889

Furche, Filipp ^[1]

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1. Institut fuer Physikalische Chemie, Universitaet Karlsruhe, Kaiserstrasse 12, 76128 Karlsruhe (Germany)

In pair density-functional theory, the only unknown piece of the energy is the kinetic energy T as a functional of the pair density P(x{sub 1},x{sub 2}). Although T [P] has a simpler structure than the Hohenberg-Kohn functional of conventional density-functional theory, computational requirements are still moderate. In the present work, a particularly convenient model system to represent many-electron pair densities is introduced. This 'boson pair model' (BPM) approximately treats electron pairs as noninteracting bosons. The resulting explicit model for the kinetic energy T{sub 2}[P] is shown to be exact for two-electron systems and a lower bound to T [P] for more than two electrons. The one- and two-particle density matrices obtained from the BPM yield upper bounds for the corresponding many-electron quantities. This suggests a partitioning T [P]=T{sub 2}[P]+T{sub eff} [P], where only the remainder T{sub eff} [P]{>=}0 needs to be approximated. If the BPM is constrained to yield the exact ground-state pair density, a two-electron Schroedinger equation with an effective local two-particle potential results; the latter is identified as a sum of the bare Coulomb interaction and the functional derivative of T{sub eff} [P]. This self-consistent scheme to minimize the energy with respect to P is more efficient than previous procedures. Further information on the functional derivative of T{sub eff} [P] is derived from a contracted Schroedinger equation. Since T{sub eff} [P] is explicitly known in the two-electron and noninteracting (Hartree-Fock) limits, the present method provides an alternative to density-matrix functional theories, which can be exact in the same limits and are similar in computational cost.

• OSTI ID: 20645889
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 70; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
BOSONS
DENSITY FUNCTIONAL METHOD
DENSITY MATRIX
ELECTRON PAIRS
ELECTRONS
GROUND STATES
HARTREE-FOCK METHOD
INFORMATION
KINETIC ENERGY
POTENTIALS
SCHROEDINGER EQUATION