Noncrossing theorem for the ground ensembles of systems with noninteger particle numbers

Journal Article · Tue Aug 15 04:00:00 EDT 2006 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.74.022506· OSTI ID:20853055

Sagvolden, Espen ^[1]

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1. Department of Physics and Quantum Theory Group, Tulane University, New Orleans, Louisiana 70118 (United States)

That the external potential v{sub ext}(r-vector) of a system of electrons is determined uniquely by the ground-state density is one of the central statements of the first Hohenberg-Kohn theorem. It is known that the validity of this statement extends to densities n(r-vector) with noninteger particle number [i.e., n(r-vector) integrates to a number that is not an integer] if the functional derivative of T{sub s}[n(r-vector)]+U[n(r-vector)]+E{sub xc}[n(r-vector)] exists or (without relying on the existence of functional derivatives) if the ground-state energy is a strictly convex function of the particle number. In the present article, a proof that relies neither on the existence of the above functional derivative nor on the strict convexity of the ground-state energy is presented. The fact that the density determines the external potential leads to a noncrossing theorem for ground-state densities. The noncrossing theorem produces knowledge as to what the integer-particle-number ground-state densities of a system cannot be. The noncrossing theorem produces inequalities that the functional derivatives of the exchange-correlation energy functional E{sub xc}[n(r-vector)] and the noninteracting kinetic energy functional T{sub s}[n(r-vector)] must fulfill.

• OSTI ID: 20853055
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 2 Vol. 74; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
DENSITY
ELECTRON CORRELATION
ELECTRONS
ENERGY-LEVEL DENSITY
GROUND STATES
KINETIC ENERGY
POTENTIALS
VECTORS