Bandgap of two-dimensional materials: Thorough assessment of modern exchange-correlation functionals

TL;DR

This study evaluates the performance of various density functional theory (DFT) exchange-correlation functionals in predicting the band gaps of 2D materials, using a large test set and $G_{0}W_{0}$ results as reference.

Contribution

It provides a comprehensive assessment of modern DFT functionals for 2D materials, highlighting the most accurate approaches compared to $G_{0}W_{0}$ benchmarks.

Findings

GLLB-SC and mTASK yield band gaps closest to $G_{0}W_{0}$

MBJ potential has accuracy similar to hybrid HSE06

GGA and meta-GGA functionals show promising results for 2D materials

Abstract

The density functional theory (DFT) approximations that are the most accurate for the calculation of band gap of bulk materials are hybrid functionals like HSE06, the MBJ potential, and the GLLB-SC potential. More recently, generalized gradient approximations (GGA), like HLE16, or meta-GGAs, like (m)TASK, have proven to be also quite accurate for the band gap. Here, the focus is on 2D materials and the goal is to provide a broad overview of the performance of DFT functionals by considering a large test set of 298 2D systems. The present work is an extension of our recent studies [Rauch et al., Phys. Rev. B 101, 245163 (2020) and Patra et al., J. Phys. Chem. C 125, 11206 (2021)]. Due to the lack of experimental results for the band gap of 2D systems, $G_{0}W_{0}$ results were taken as reference. It is shown that the GLLB-SC potential and mTASK functional provide the band gaps that are the closest to $G_{0}W_{0}$. Following closely, the local MBJ potential has a pretty good accuracy that is similar to the accuracy of the more expensive hybrid functional HSE06.