Hohenberg-Kohn Theorem for Coulomb Type Systems

TL;DR

This paper provides a rigorous proof of the Hohenberg-Kohn theorem specifically for Coulomb systems, addressing gaps and inaccuracies in previous proofs to strengthen the theoretical foundation of density functional theory.

Contribution

It restates and rigorously proves the Hohenberg-Kohn theorem for Coulomb systems using the Fundamental Theorem of Algebra, improving the mathematical foundation of DFT.

Findings

Established a complete and rigorous proof of the Hohenberg-Kohn theorem for Coulomb systems.

Clarified the conditions under which the theorem holds for many-electron Coulomb systems.

Enhanced the theoretical basis for density functional theory applications.

Abstract

Density functional theory (DFT) has become a basic tool for the study of electronic structure of matter, in which the Hohenberg-Kohn theorem plays a fundamental role in the development of DFT. Unfortunately, the existing proofs are incomplete even incorrect; besides, the statement of the Hohenberg-Kohn theorem for many-electron Coulomb systems is not perfect. In this paper, we shall restate the Hohenberg-Kohn theorem for Coulomb type systems and present a rigorous proof by using the Fundamental Theorem of Algebra.