Ground state energy in the external field and the problem of density functional approximations

TL;DR

This paper derives exact inhomogeneous density functionals for particle energy in external fields, showing limitations of the Hohenberg-Kohn lemma for systems with more than two electrons, but confirming its validity for bosons due to Bose condensation.

Contribution

It demonstrates that the Hohenberg-Kohn lemma does not hold for systems with more than two electrons, challenging the universality of the density functional in such cases.

Findings

Exact expressions for particle energy as inhomogeneous density functionals.

The energy cannot be an inhomogeneous density functional for systems with more than two electrons.

Hohenberg-Kohn lemma is valid for bosons due to Bose condensation.

Abstract

Based on the Schrodinger equation, exact expressions for the non-relativistic particle energy in the local external field and the external field potential are derived as inhomogeneous density functionals. On this basis, it is shown that, when considering more than two noninteracting electrons, the energy of such a system cannot be an inhomogeneous density functional. The result is extended for the system of interacting electrons. This means that the Hohenberg-Kohn lemma which assert that in the ground state to each inhomogeneous density corresponds only one potential of the external field cannot be a justification of the existence of the universal density functional in the general case. At the same time, statements of the density functional theory remain valid when considering any number of noninteracting ground-state bosons due to the Bose condensation effect.