The discontinuous nature of the exchange-correlation functional -- critical for strongly correlated systems

TL;DR

This paper reveals the importance of the discontinuous nature of the exact exchange-correlation functional for accurately modeling strongly correlated systems in density functional theory, highlighting the need for new functionals with explicit discontinuities.

Contribution

It unifies the linearity and constancy conditions for fractional charges and spins, demonstrating the necessity of discontinuous functionals beyond smooth approximations.

Findings

Exact energy functional is a plane with a discontinuity at integer charges.

Current smooth functionals fail to capture the derivative discontinuity.

Discontinuous functionals are essential for accurately describing strongly correlated systems.

Abstract

Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified for states with both fractional charge and fractional spin: the exact energy functional is a plane, linear along the fractional charge coordinate and constant along the fractional spin coordinate with a line of discontinuity at the integer. This sheds light on the nature of the derivative discontinuity and calls for explicitly discontinuous functionals of the density or orbitals that go beyond currently used smooth approximations. This is key for the application of DFT to strongly correlated systems.