Necessary and sufficient conditions for the N-representability of density functionals
- Department of Chemistry, McMaster University, Hamilton, Ontario, Canada L8S 4M1 (Canada)
- Division of Research Computing, Information Technology Services, University of North Carolina, Chapel Hill, North Carolina 27599-3455 (United States)
It is well known that variational optimization of the energy using approximate density functionals can give results below the true ground-state energy. This can be attributed to the fact that many approximate density functionals are not N-representable. This paper presents a general method for deriving N-representability conditions in density-functional theory and presents specific results for the kinetic energy, the electron-electron interaction energy, the Hohenberg-Kohn functional, and the exchange-correlation energy functional. The method can be extended to energy densities, and specific results are presented for two different choices of the kinetic-energy density. Max-min variational principles for minimizing the energy subject to N-representability constraints are presented. Some constraints on exchange-correlation density functionals are among our secondary findings. In particular, we construct an exact meta-generalized-gradient-approximation (meta-GGA) functional using a Legendre transform and use this expression to show that (a) meta-GGAs should be convex functionals of the kinetic-energy density and (b) the sum of the Coulomb energy and the meta-GGA exchange-correlation energy should be a convex functional of the electron density.
- OSTI ID:
- 20982113
- Journal Information:
- Physical Review. A, Vol. 75, Issue 2; Other Information: DOI: 10.1103/PhysRevA.75.022514; (c) 2007 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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