Equation satisfied by electron-electron mutual Coulomb repulsion energy density functional

TL;DR

This paper derives an equation relating the electron-electron Coulomb repulsion energy density functional to its derivatives across N-electron and (N-1)-electron densities, enhancing understanding of density functional theory.

Contribution

It introduces a new equation linking functionals and derivatives at different electron counts for densities from the same scaled potential.

Findings

Establishes a fundamental equation for Coulomb energy density functional.

Provides insights into the behavior of functionals under electron number changes.

Potentially aids in developing more accurate density functional approximations.

Abstract

The electron-electron mutual Coulomb repulsion energy density functional satisfies an equation that links functionals and functional derivatives at N-electron and (N-1)-electron densities for densities determined from the same adiabatic scaled external potential for the N-electron system.