Density functional theory and free energy of inhomogeneous electron gas

TL;DR

This paper proves the Hohenberg-Kohn theorem for inhomogeneous electron gases at finite temperature within the canonical ensemble, highlighting differences from quantum mechanics and discussing the universality of density functionals.

Contribution

It establishes the Hohenberg-Kohn theorem in the canonical ensemble for inhomogeneous electron gases at finite temperature, using variational methods.

Findings

Proves the Hohenberg-Kohn theorem in the canonical ensemble.

Highlights differences between quantum statistical and quantum mechanical descriptions.

Discusses the universality of density functionals in disordered nuclei fields.

Abstract

It is shown that in adiabatic approximation for nuclei the many-component Coulomb system cannot be described on the basis of the grand canonical ensemble. Using the variational Bogolyubov's procedure for the free energy, the Hohenberg-Kohn theorem is proved in the canonical ensemble for inhomogeneous electron gas at finite temperature. The principal difference between consideration in the framework of quantum statistics in the canonical ensemble and quantum-mechanical consideration of a finite number of particles in infinite volume is established. The problem of universality of the density functional for describing the inhomogeneous electron density in a disordered nuclei field is considered.