title: Locality of correlation in density functional theory.
abstract: The Hohenberg-Kohn density functional was long ago shown to reduce to the Thomas-Fermi (TF) approximation in the non-relativistic semiclassical (or large-Z) limit for all matter, i.e., the kinetic energy becomes local. Exchange also becomes local in this limit. Numerical data on the correlation energy of atoms support the conjecture that this is also true for correlation, but much less relevant to atoms. We illustrate how expansions around a large particle number are equivalent to local density approximations and their strong relevance to density functional approximations. Analyzing highly accurate atomic correlation energies, we show that EC → -AC ZlnZ + BCZ as Z → ∞, where Z is the atomic number, AC is known, and we estimate BC to be about 37 mhartree. The local density approximation yields AC exactly, but a very incorrect value for BC, showing that the local approximation is less relevant for the correlation alone. This limit is a benchmark for the non-empirical construction of density functional approximations. We conjecture that, beyond atoms, the leading correction to the local density approximation in the large-Z limit generally takes this form, but with BC a functional of the TF density for the system. The implications for the construction of approximate density functionals are discussed.
authors: Department of Chemistry, University of California, Irvine, California 92697, USA.
authors: Kieron
authors: K
authors: Burke
authors: Department of Physics and Astronomy, Ball State University, Muncie, Indiana 47306, USA.
authors: Antonio
authors: A
authors: Cancio
authors: Qld Micro- and Nanotechnology Centre, Griffith University, Nathan, Qld 4111, Australia.
authors: Tim
authors: T
authors: Gould
authors: CNR-Istituto di Nanoscienze, Via Campi 213A, I-41125 Modena, Italy.
authors: Stefano
authors: S
authors: Pittalis