We assess the performance of the recently proposed Tao-Mo (TM) semilocal exchange-correlation functional [J. Tao and Y. Mo, Phys. Rev. Lett. 117, 073001 (2016)] using the projector-augmented-wave method with the plane wave basis set. The meta-generalized gradient approximation level semilocal functional constructed by Tao-Mo is an all-purpose exchange-correlation functional for the quantum chemistry and solid-state physics. The exchange of the TM functional is based on the density matrix expansion technique together with the slowly varying fourth order gradient expansion. The correlation functional corresponding to the exchange is based on the one-electron self-interaction-free Tao-Perdew-Staroverov-Scuseria functional. Our test includes solid-state lattice constants, bulk moduli, bandgaps, cohesive energies, magnetic moments and vacancy-formation energies of transition metals. It is observed that in the plane wave basis, the TM functional performs accurately in predicting all the solid state properties at the semilocal level.

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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.

Improved band gap of n-type semiconductor ZrS2 within semi-local density functional theory is shown. The band gap of mBR-TBMBJ agrees well with the hybrid HSE06 functional.

The experimental and theoretical realization of two-dimensional (2D) materials is of utmost importance in semiconducting applications. Computational modeling of these systems with satisfactory accuracy and computational efficiency is only feasible with semilocal density functional theory methods. In the search for the most useful method in predicting the band gap of 2D materials, we assess the accuracy of recently developed semilocal exchange–correlation (XC) energy functionals and potentials. Though the explicit forms of exchange–correlation (XC) potentials are very effective against XC energy functionals for the band gap of bulk solids, their performance needs to be investigated for 2D materials. In particular, the LMBJ [ 32097004 J. Chem. Theory Comput. 2020 16 2654 ] and GLLB-SC [ 115106 Phys. Rev. B 2010 82 ] potentials are considered for their dominance in bulk band gap calculation. The performance of recently developed meta generalized gradient approximations, like TASK [ 033082 Phys. Rev. Res. 2019 1 ] and MGGAC [ 155140 Phys. Rev. B 2019 100 ], is also assessed. We find that the LMBJ potential constructed for 2D materials is not as successful as its parent functional, i.e., MBJ [ 226401 19658882 Phys. Rev. Lett. 2009 102 ] in bulk solids. Due to a contribution from the derivative discontinuity, the band gaps obtained with GLLB-SC are in a certain number of cases, albeit not systematically, larger than those obtained with other methods, which leads to better agreement with the quasi-particle band gap obtained from the GW method. The band gaps obtained with TASK and MGGAC can also be quite accurate.