Density gradients for the exchange energy of electrons in two dimensions

TL;DR

This paper develops a generalized gradient approximation for exchange energy in two-dimensional electron systems, improving accuracy over local density approximation by a factor of four, based on parameter tuning with quantum dot data.

Contribution

It introduces a new exchange energy functional for 2D systems, adapting Becke's approach from 3D, and demonstrates its effectiveness through testing on quantum dots.

Findings

Reduces exchange energy error by a factor of 4

Functional depends on two adjustable parameters

Shows promising results across various 2D systems

Abstract

We derive a generalized gradient approximation to the exchange energy to be used in density functional theory calculations of two-dimensional systems. This class of approximations has a long and successful history, but it has not yet been fully investigated for electrons in two dimensions. We follow the approach originally proposed by Becke for three-dimensional systems [Int. J. Quantum Chem. 23, 1915 (1983), J. Chem. Phys. 85, 7184 (1986)]. The resulting functional depends on two parameters that are adjusted to a test set of parabolically confined quantum dots. Our exchange functional is then tested on a variety of systems with promising results, reducing the error in the exchange energy by a factor of 4 with respect to the simple local density approximation.