Local correlation functional for electrons in two dimensions

TL;DR

This paper introduces a new local correlation functional for two-dimensional electrons, derived from a Gaussian approximation and modified to better capture long-range and kinetic contributions, showing excellent agreement with exact energies.

Contribution

The paper presents a novel local correlation functional for 2D systems, improving upon the local-density approximation with better accuracy and simplicity.

Findings

Excellent agreement with exact correlation energies in test cases

Outperforms the local-density approximation

Applicable to quantum dots and homogeneous electron gas

Abstract

We derive a local approximation for the correlation energy in two-dimensional electronic systems. In the derivation we follow the scheme originally developed by Colle and Salvetti for three dimensions, and consider a Gaussian approximation for the pair density. Then, we introduce an ad-hoc modification which better accounts for both the long-range correlation, and the kinetic-energy contribution to the correlation energy. The resulting functional is local, and depends parametrically on the number of electrons in the system. We apply this functional to the homogeneous electron gas and to a set of two-dimensional quantum dots covering a wide range of electron densities and thus various amounts of correlation. In all test cases we find an excellent agreement between our results and the exact correlation energies. Our correlation functional has a form that is simple and straightforward to implement, but broadly outperforms the commonly used local-density approximation.