Exact expressions for the height of the interatomic step in the exchange-correlation potential from the derivative discontinuity of the energy

TL;DR

This paper derives exact analytic expressions for the height of the interatomic step in the exchange-correlation potential in density functional theory, linking it to the derivative discontinuity of the energy, crucial for accurate dissociation and excitation descriptions.

Contribution

It provides the first explicit formulas connecting the step height in the xc potential to KS energies, enhancing understanding of the derivative discontinuity in DFT.

Findings

Derived exact expressions for the step height in xc potential.

Linked the step height to the derivative discontinuity of the energy.

Validated formulas across various atoms and molecules.

Abstract

Popular approximations to the exchange-correlation (xc) energy of density functional theory do not yield the spatial `step' structures in the exact xc potential which are necessary to describe dissociation and electron excitation with the Kohn-Sham (KS) system. Via the discontinuity in the derivative of the xc energy as a function of electron number I derive exact analytic expressions in terms of the KS single-particle energies for the height of the step in the xc potential between a variety of open- and closed-shell atoms within stretched molecules.