# Role of Kohn-Sham Kinetic Energy Density in Designing Asymptotically Correct Semilocal Exchange-Correlation Functionals in Two Dimensions

## TL;DR

This paper investigates the role of Kohn-Sham kinetic energy density in designing accurate semilocal exchange-correlation functionals for two-dimensional quantum systems, emphasizing asymptotic behavior and orbital contributions.

## Contribution

It introduces new meta-GGA ingredients and constructs an exchange energy functional with exact asymptotic properties for 2D systems.

## Key findings

- Meta-GGA ingredients capture orbital contributions near nucleus and at asymptote.
- New exchange functional achieves exact asymptotic behavior.
- Design of semilocal functionals improves accuracy in low-dimensional quantum systems.

## Abstract

The positive definite Kohn-Sham kinetic energy(KS-KE) density plays crucial role in designing semilocal meta generalized gradient approximations(meta-GGAs) for low dimensional quantum systems. It has been rigorously shown that near nucleus and at the asymptotic region, the KE-KS differ from its von Weizs\"{a}cker(VW) counterpart as contributions from different orbitals (i.e., s and p orbitals) play important role. This has been explored using two dimensional isotropic quantum harmonic oscillator as a test case. Several meta-GGA ingredients with different physical behaviors are also constructed and further used to design an accurate semilocal functionals at meta-GGA level. In the asymptotic region, a new exchange energy functional is constructed using the meta-GGA ingredients with formally exact properties of the enhancement factor. Also, it has been shown that exact asymptotic behavior of the exchange energy density and potential can be attained by choosing accurately the enhancement factor as a functional of meta-GGA ingredients.