Dimensional crossover of the exchange-correlation energy at the semilocal level

TL;DR

This paper investigates the failure of semilocal density functional approximations in 2D limits and proposes new constraints and methods to improve their accuracy for dimensional crossover in exchange-correlation energy.

Contribution

It introduces exact constraints for the semilocal level to correctly handle the 2D limit and provides a method to incorporate these into existing functionals.

Findings

Semilocal functionals can recover 2D exchange-correlation energy using new constraints.

Derived exact constraints for dimensional crossover at the semilocal level.

Proposed a method to embed these constraints into existing density functionals.

Abstract

Commonly used semilocal density functional approximations for the exchange-correlation energy fail badly when the true two dimensional limit is approached. We show, using a quasi-two-dimensional uniform electron gas in the infinite barrier model, that the semilocal level can correctly recover the exchange-correlation energy of the two-dimensional uniform electron gas. We derive new exact constraints at the semilocal level for the dimensional crossover of the exchange-correlation energy and we propose a method to incorporate them in any exchange-correlation density functional approximation.