The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory

Ryan Pederson; Kieron Burke

doi:10.1063/5.0172058

The difference between molecules and materials: Reassessing the role of exact conditions in density functional theory

J Chem Phys. 2023 Dec 7;159(21):214113. doi: 10.1063/5.0172058.

Authors

Ryan Pederson¹, Kieron Burke^{1

2}

Affiliations

¹ Department of Physics and Astronomy, University of California, Irvine, California 92697, USA.
² Department of Chemistry, University of California, Irvine, California 92697, USA.

PMID: 38054515
DOI: 10.1063/5.0172058

Abstract

Exact conditions have long been used to guide the construction of density functional approximations. However, hundreds of empirical-based approximations tailored for chemistry are in use, of which many neglect these conditions in their design. We analyze well-known conditions and revive several obscure ones. Two crucial distinctions are drawn: that between necessary and sufficient conditions and that between all electronic densities and the subset of realistic Coulombic ground states. Simple search algorithms find that many empirical approximations satisfy many exact conditions for realistic densities and non-empirical approximations satisfy even more conditions than those enforced in their construction. The role of exact conditions in developing approximations is revisited.