On the Necessary Conditions for the Validity of the Hohenberg-Kohn Theorem

TL;DR

This paper explores the fundamental conditions under which the Hohenberg-Kohn theorem holds, emphasizing the biuniqueness of density and potential functionals and proposing a method to determine the energy functional.

Contribution

It demonstrates that the Hohenberg-Kohn theorem follows from the unique functional relationship between energy and external potential, clarifying the theorem's necessary conditions.

Findings

Hohenberg-Kohn lemma and theorem are consequences of energy functional uniqueness.

Nonuniform density and external potential are biunique functionals under certain conditions.

A procedure for determining the density functional for energy is proposed.

Abstract

It is shown that the Hohenberg-Kohn lemma and theorem are direct consequences of the statement that the ground state energy (or free energy) of a system of interacting particles in an external field is a unique functional of the potential of this field. This means that, if the Hohenberg-Kohn theorem is valid, the nonuniform density in the equilibrium system and the external field potential are biunique functionals. In this case, the nonuniform density is intimately related to the inverse response function. On this basis, a regular procedure can be constructed for determining the density functional for the free energy or ground state energy.