Title: Differentiable but exact formulation of density-functional theory

The universal density functional F of density-functional theory is a complicated and ill-behaved function of the density—in particular, F is not differentiable, making many formal manipulations more complicated. While F has been well characterized in terms of convex analysis as forming a conjugate pair (E, F) with the ground-state energy E via the Hohenberg–Kohn and Lieb variation principles, F is nondifferentiable and subdifferentiable only on a small (but dense) subset of its domain. In this article, we apply a tool from convex analysis, Moreau–Yosida regularization, to construct, for any ε > 0, pairs of conjugate functionals ({sup ε}E, {sup ε}F) that converge to (E, F) pointwise everywhere as ε → 0{sup +}, and such that {sup ε}F is (Fréchet) differentiable. For technical reasons, we limit our attention to molecular electronic systems in a finite but large box. It is noteworthy that no information is lost in the Moreau–Yosida regularization: the physical ground-state energy E(v) is exactly recoverable from the regularized ground-state energy {sup ε}E(v) in a simple way. All concepts and results pertaining to the original (E, F) pair have direct counterparts in results for ({sup ε}E, {sup ε}F). The Moreau–Yosida regularization therefore allows for an exact, differentiable formulation ofmore » density-functional theory. In particular, taking advantage of the differentiability of {sup ε}F, a rigorous formulation of Kohn–Sham theory is presented that does not suffer from the noninteracting representability problem in standard Kohn–Sham theory.« less

Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo (Norway)

(United Kingdom)

Publication Date:

OSTI Identifier:

22253466

Resource Type:

Journal Article

Resource Relation:

Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 18; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:

United States

Language:

English

Subject:

74 ATOMIC AND MOLECULAR PHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY FUNCTIONAL METHOD; FUNCTIONALS; GROUND STATES