Orbital-free energy functional for electrons in two dimensions

TL;DR

This paper introduces a new orbital-free density functional for two-dimensional electrons, combining a local interaction energy formula with the Thomas-Fermi kinetic energy approximation, achieving high computational efficiency and accuracy.

Contribution

The authors develop a non-empirical orbital-free functional for 2D electrons that simplifies calculations and improves accuracy over traditional Thomas-Fermi methods.

Findings

Total energies closely match local-density approximation results.

Significantly more accurate than the traditional Thomas-Fermi approximation.

Functional is computationally efficient due to lack of orbitals and Hartree integral.

Abstract

We derive a non-empirical, orbital-free density functional for the total energy of interacting electrons in two dimensions. The functional consists of a local formula for the interaction energy, where we follow the lines introduced by Parr for three-dimensional systems [R. G. Parr, J. Phys. Chem. 92, 3060 (1988)], and the Thomas-Fermi approximation for the kinetic energy. The freedom from orbitals and from the Hartree integral makes the proposed approximation numerically highly efficient. The total energies obtained for confined two-dimensional systems are in a good agreement with the standard local-density approximation within density-functional theory, and considerably more accurate than the Thomas-Fermi approximation.