The density-functional theory (DFT) approximations that are the most accurate for the calculation of bandgap of bulk materials are hybrid functionals, such as HSE06, the modified Becke–Johnson (MBJ) potential, and the GLLB-SC potential. More recently, generalized gradient approximations (GGAs), such as HLE16, or meta-GGAs, such as (m)TASK, have also proven to be quite accurate for the bandgap. Here, the focus is on two-dimensional (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 [T. Rauch, M. A. L. Marques, and S. Botti, Phys. Rev. B 101, 245163 (2020); Patra et al., J. Phys. Chem. C 125, 11206 (2021)]. Due to the lack of experimental results for the bandgap of 2D systems, G₀W₀ results were taken as reference. It is shown that the GLLB-SC potential and mTASK functional provide the bandgaps that are the closest to G₀W₀. Following closely, the local MBJ potential has a pretty good accuracy that is similar to the accuracy of the more expensive hybrid functional HSE06.

中文翻译：

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二维材料的带隙：对现代交换相关泛函的全面评估

密度泛函理论 (DFT) 近似值对于计算散装材料的带隙最准确，是混合泛函，例如 HSE06、修正的 Becke-Johnson (MBJ) 势和 GLLB-SC 势。最近，广义梯度近似 (GGA)，例如 HLE16，或元 GGA，例如 (m)TASK，也被证明对于带隙非常准确。在这里，重点是二维 (2D) 材料，目标是通过考虑 298 个 2D 系统的大型测试集，提供 DFT 泛函性能的广泛概述。目前的工作是我们最近研究的延伸 [T. Rauch, MAL Marques 和 S. Botti, Phys. 修订版 B 101 , 245163 (2020)；帕特拉等人。, J. Phys. 化学 ç 125, 11206 (2021)]。由于缺乏二维系统带隙的实验结果，G ₀ W ₀结果作为参考。结果表明，GLLB-SC 电位和 mTASK 泛函提供最接近G ₀ W ₀的带隙。紧随其后，局部 MBJ 电位具有相当不错的准确度，与更昂贵的混合功能 HSE06 的准确度相似。