Exchange-energy functionals for finite two-dimensional systems

TL;DR

This paper develops new exchange-energy density functionals for finite two-dimensional systems, improving accuracy in modeling electrons in quasi-2D structures relevant to nanotechnology.

Contribution

It introduces both implicit and explicit density functionals for exchange energy in 2D systems, validated against exact data, enhancing computational tools for nanostructure analysis.

Findings

Excellent agreement with exact exchange-hole potentials

Accurate exchange energies for 2D electron gas and quantum dots

Significant improvement over previous functionals

Abstract

Implicit and explicit density functionals for the exchange energy in finite two-dimensional systems are developed following the approach of Becke and Roussel [Phys. Rev. A 39, 3761 (1989)]. Excellent agreement for the exchange-hole potentials and exchange energies is found when compared with the exact-exchange reference data for the two-dimensional uniform electron gas and few-electron quantum dots, respectively. Thereby, this work significantly improves the availability of approximate density functionals for dealing with electrons in quasi-two-dimensional structures, which have various applications in semiconductor nanotechnology.