Identities for density functionals linking functionals of different densities

TL;DR

This paper derives a formal identity linking density functionals of N and N-1 electron systems in density functional theory, providing insights into the relationships between different density functionals and their properties.

Contribution

The paper introduces a new formal identity connecting functionals of N and N-1 electron densities, enhancing the theoretical understanding of density functionals in electron density functional theory.

Findings

The identity is satisfied by the sum of Hartree and exchange-correlation energies.

The formal property aids in constructing and testing approximate density functionals.

Provides a theoretical link between densities of different electron counts.

Abstract

In electron density functional theory formal properties of density functionals play an important role in constructing and testing approximate functionals. In this paper it is shown that a set of density functionals satisfy an equation that links functionals of densities of N and N-1 systems of the same Hamiltonian. In particular the identity is satisfied by the sum of the Hartree and exchange-correlation energies.