Axiomatic formulations of the Hohenberg-Kohn functional
- Department of Chemistry, McMaster University, Hamilton, Ontario, Canada L8S 4M1 (Canada)
Properties of the Hohenberg-Kohn functional are considered. In particular, the Hohenberg-Kohn functional should (a) give correct results in the variational principle and should be (b) continuous, (c) convex, and (d) size consistent. All of these properties are satisfied by the Legendre-transform functional (equivalently, the density matrix constrained search functional) and, moreover, this is the only functional that possesses all these properties. Not only that, but the Legendre-transform functional is determined uniquely by requiring (a) (b), and either (c) or (d). This shows how an 'axiomatic' approach to constructing the Hohenberg-Kohn functional leads naturally to the Legendre-transform functional. Among all functionals consistent with the variational principle, the Legendre-transform functional is the smallest. One corollary to this approach is a simple proof of the equivalence of the Legendre-transform and density-matrix constrained search functionals. For completeness, the Appendix shows that ensemble-v-representable densities lie dense in the set of N-representable densities.
- OSTI ID:
- 20786703
- Journal Information:
- Physical Review. A, Vol. 73, Issue 1; Other Information: DOI: 10.1103/PhysRevA.73.012513; (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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