Identity for the second functional derivative of the density functional Hartree plus exchange-correlation functional

TL;DR

This paper establishes a fundamental identity linking the second functional derivative of the Hartree plus exchange-correlation functional to the difference in charge densities between N- and (N-1)-electron systems, revealing a key theoretical property.

Contribution

It proves a new integral identity involving the second functional derivative of the density functional and charge density differences, advancing theoretical understanding in density functional theory.

Findings

Integral of charge density difference times second derivative equals a constant

Provides a theoretical foundation for properties of density functionals

Enhances understanding of functional derivatives in DFT

Abstract

It is shown that the integral of the product of the charge density difference of the N- and (N-1)-electron densities of the same Hamiltonian and the second functional derivative of the Hartree plus exchange-correlation functional of the N-electron density is equal to a constant.