# Semilocal Exchange Functionals With Improved Performances: The Modified Enhancement Factor For Two Dimensional Quantum Systems

## TL;DR

This paper introduces modified semilocal exchange functionals with improved accuracy for two-dimensional quantum systems, utilizing new enhancement factors based on inhomogeneity parameters and testing them against exact exchange results.

## Contribution

The paper develops and tests new enhancement factors for semilocal exchange functionals, improving their performance for 2D quantum systems compared to previous approximations.

## Key findings

- Significant reduction in error over previous gradient approximations
- Effective performance demonstrated on 2D quantum dots
- Functional improvements align well with exact exchange results

## Abstract

Semilocal exchange-correlation functionals are the most accurate, realistic and widely used ones to describe the complex many-electron effects of two-dimensional quantum systems. Beyond local density approximation, the generalized gradient approximations(GGAs) are designed using reduced density gradient as main ingredient. An enhancement factor is constructed using the inhomogeneity parameter of GGAs by taking care of the low and high density behaviors of it. Thus, the exchange energy functional proposed by making use of the aforementioned enhancement factor, significantly reduces the error compare to the previously proposed gradient approximations. Another enhancement factor and corresponding energy functional is also constructed using the inhomogeneity parameter originally introduced by Becke [J. Chem. Phys. 109, 2092 (1998)]. Comprehensive testing and performance of both the functionals are demonstrated with respect to the exact exchange formalism by considering two-dimensional parabolically confined quantum dots with varying particle number and confinement strength as a test case.