The structure of the density-potential mapping. Part I: Standard density-functional theory

TL;DR

This paper critically examines the foundational role of the Hohenberg-Kohn theorem in density-functional theory, suggesting it is a consequence of a broader mathematical framework rather than its basis, with implications for generalized DFTs.

Contribution

It clarifies the conceptual status of the Hohenberg-Kohn theorem within DFT and discusses extensions including magnetic fields, challenging traditional views.

Findings

Hohenberg-Kohn theorem is a consequence, not the basis, of DFT.

Provides evidence for a more comprehensive mathematical framework.

Implications for constructing generalized DFTs.

Abstract

The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. Part I of this review aims at clarifying the status of the Hohenberg-Kohn theorem within DFT and Part II at different extensions of the theory that include magnetic fields. We collect evidence that the Hohenberg-Kohn theorem does not so much form the basis of DFT, but is rather the consequence of a more comprehensive mathematical framework. Such results are especially useful when it comes to the construction of generalized DFTs.