[Paper Review] Bandgap of two-dimensional materials: Thorough assessment of modern exchange-correlation functionals

Fabien Tran, Jan Doumont+9 more|arXiv (Cornell University)|May 25, 2021

2D Materials and ApplicationsMaterials Science92 references49 citations

TL;DR

This study evaluates 298 two-dimensional (2D) materials using 15 modern exchange-correlation functionals within density functional theory (DFT), using G0W0 quasiparticle band gaps as a reference. The GLLB-SC potential and mTASK meta-GGA functional deliver the most accurate band gaps, closely followed by the local MBJ potential and HSE06 hybrid functional, demonstrating that fast, semilocal functionals can rival more expensive GW methods 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.

Motivation & Objective

• To systematically evaluate the performance of modern DFT exchange-correlation functionals for predicting band gaps in 2D materials.
• To identify the most accurate and computationally efficient functionals for 2D systems, given the lack of reliable experimental band gap data.
• To extend prior benchmarks on bulk solids to a large, diverse test set of 298 2D materials.
• To assess the role of excitonic effects and the suitability of G0W0 as a reference for band gap validation in low-dimensional systems.
• To provide a comprehensive, data-driven guide for selecting optimal DFT functionals in 2D materials research.

Proposed method

• A test set of 298 two-dimensional materials was compiled from the C2DB database.
• Band gaps were calculated using 15 DFT functionals, including hybrid (HSE06), meta-GGAs (mTASK, TASK, HLE17, MGGAC, r2SCAN), GGA (HLE16, EV93PW91), and non-energy-based potentials (GLLB-SC, local MBJ).
• G0W0 quasiparticle band gaps were used as the reference standard due to the absence of experimental data.
• Calculations were performed using the WIEN2k code with consistent computational parameters across all functionals.
• The accuracy of each functional was quantified by comparing its predicted band gap to the corresponding G0W0 result.
• Systematic error analysis was performed to evaluate mean absolute errors and relative deviations across the entire 2D material set.

Experimental results

Research questions

• RQ1 Which DFT exchange-correlation functionals yield the most accurate band gaps for 2D materials compared to G0W0 reference values?
• RQ2 How do semilocal functionals like mTASK and GLLB-SC compare in accuracy to hybrid functionals such as HSE06 and MBJ for 2D systems?
• RQ3 To what extent do excitonic effects in 2D materials affect the validity of direct comparison between DFT and experimental optical gaps?
• RQ4 Can non-hybrid, parameter-free functionals like GLLB-SC achieve accuracy comparable to expensive hybrid functionals in 2D materials?
• RQ5 How do the performance trends of functionals in bulk solids translate to 2D materials with reduced dimensionality and vacuum environments?

Key findings

• The GLLB-SC potential and mTASK meta-GGA functional deliver the most accurate band gaps, with mean absolute errors (MAE) closest to G0W0 reference values.
• The local MBJ potential performs nearly as well as HSE06, with a MAE of approximately 0.3–0.4 eV, making it a highly efficient alternative.
• The mTASK functional shows superior accuracy compared to other meta-GGAs, including TASK and HLE17, due to its modified nonlocal enhancement factor.
• HSE06, while more computationally expensive, remains highly accurate with a MAE of around 0.4 eV, confirming its reliability for 2D materials.
• The standard PBE and EV93PW91 functionals exhibit large errors (1–2 eV), confirming their poor performance for band gap prediction in 2D systems.
• The HLE16 GGA and MGGAC functionals show moderate accuracy, with MAEs around 0.5–0.6 eV, but are less accurate than GLLB-SC and mTASK.