Large two-dimensional electronic systems: Self-consistent energies and densities at low cost

TL;DR

This paper introduces a computationally efficient, self-consistent local approximation for 2D electronic systems that accurately predicts energies and densities, significantly reducing the cost compared to traditional methods.

Contribution

A novel orbital-free local approximation for 2D systems that simplifies calculations while maintaining accuracy, validated against Kohn-Sham results.

Findings

Accurate energies and densities for 2D nanostructures with minimal computational effort.

The method performs well up to 600 electrons, matching Kohn-Sham calculations.

Assessment of a local upper bound for the Hartree energy.

Abstract

We derive a self-consistent local variant of the Thomas-Fermi approximation for (quasi-)two-dimensional (2D) systems by localizing the Hartree term. The scheme results in an explicit orbital-free representation of the electron density and energy in terms of the external potential, the number of electrons, and the chemical potential determined upon normalization. We test the method over a variety 2D nanostructures by comparing to the Kohn-Sham 2D-LDA calculations up to 600 electrons. Accurate results are obtained in view of the negligible computational cost. We also assess a local upper bound for the Hartree energy.