Leading gradient correction to the kinetic energy for two-dimensional fermion gases

TL;DR

This paper demonstrates that contrary to previous beliefs, the leading gradient correction to the kinetic energy in two-dimensional fermion gases does not vanish and significantly improves density functional theory calculations.

Contribution

It introduces a new perspective showing the non-vanishing of the leading gradient correction in 2D DFT, challenging long-standing assumptions.

Findings

The leading gradient correction in 2D does not vanish.

This correction contributes perturbatively to the total energy.

The approach extends standard DFT with an effective potential energy functional.

Abstract

Density functional theory (DFT) is notorious for the absence of gradient corrections to the two-dimensional (2D) Thomas-Fermi kinetic-energy functional; it is widely accepted that the 2D analog of the 3D von Weizs\"acker correction vanishes, together with all higher-order corrections. Contrary to this long-held belief, we show that the leading correction to the kinetic energy does not vanish, is unambiguous, and contributes perturbatively to the total energy. This insight emerges naturally in a simple extension of standard DFT, which has the effective potential energy as a functional variable on equal footing with the single-particle density.