Functional relations for the density functional exchange and correlation functionals connecting functionals at three densities

TL;DR

This paper derives a new functional relation connecting exchange and correlation functionals at three densities, providing a tool to test the internal consistency of density functional approximations.

Contribution

It introduces a novel equation linking exchange and correlation functionals evaluated at three densities and two particle numbers, enhancing the validation of DFT approximations.

Findings

Derivation of a functional relation for exchange and correlation functionals.

Provides a new test for the self-consistency of DFT approximations.

Applicable to various density functional approximations.

Abstract

It is shown that the DFT exchange and correlation functionals satisfy an expression that couples exchange and correlation functionals and functional derivatives evaluated at three different densities and for two particle numbers. This equation can be used as a stringent test to check the internal self-consistency of approximations to the exchange and correlation functionals.