Hohenberg-Kohn theorem is valid

TL;DR

This paper defends the validity of the Hohenberg-Kohn theorem in density functional theory, countering claims that it fails for crystalline solids in electric fields, and clarifies its applicability alongside newer theories.

Contribution

It demonstrates that the Hohenberg-Kohn theorem remains valid even when considering crystalline solids in electric fields, reaffirming its foundational role in density functional theory.

Findings

Hohenberg-Kohn theorem holds for crystalline solids in electric fields.

Gonze et al's claims do not invalidate the original theorem.

The theorem complements the density-and-polarization functional theory.

Abstract

In a recent PRL, Gonze et al claim that the density functional theory in Hohenberg-Kohn formulation is not valid for crystalline solids in a homogenious electric field. They introduce another theory, density-and-polarization functional theory, which has to substitute the DFT in the calculations of the long-wave dielectric response. We show that the theorem proven by Gonzo et al holds in addition to, and not instead of, the Hohenberg-Kohn theorem.