Noncrossing theorem for the ground ensembles of systems with noninteger particle numbers
- 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, Vol. 74, Issue 2; Other Information: DOI: 10.1103/PhysRevA.74.022506; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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