Efficient Band Structure Calculation of Two-Dimensional Materials from Semilocal Density Functionals.

Abhilash Patra,Subrata Jana,Jan Doumont,Peter Blaha,Fabien Tran,Leila Kalantari,Prasanjit Samal

doi:10.1021/acs.jpcc.1c02031

Abstract

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 [J. Chem. Theory Comput.2020, 16, 265432097004] and GLLB-SC [Phys. Rev. B82, 2010, 115106] potentials are considered for their dominance in bulk band gap calculation. The performance of recently developed meta generalized gradient approximations, like TASK [Phys. Rev. Res.1, 2019, 033082] and MGGAC [Phys. Rev. B. 100, 2019, 155140], is also assessed. We find that the LMBJ potential constructed for 2D materials is not as successful as its parent functional, i.e., MBJ [Phys. Rev. Lett.102, 2009, 22640119658882] 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.

Highlights

The one-atom-thick layers of exfoliating materials have attracted the attention of the scientific community for their exceptional properties with many applications.[1,2] The weak interaction between the layered bulk materials allows us to obtain the monolayer, and the most successful example is graphene,[3,4] a single layer of graphite
When M belongs to group 6, in most cases, the band gaps obtained with the meta-generalized gradient approximation (GGA) energy functionals can be ordered as high local exchange 2017 (HLE17)< strongly constrained and appropriately normed (SCAN) < MGGAC < TASK, and only TASK leads to values clearly larger than PBE
The goal was to assess the accuracy of the considered density functional theory (DFT) methods for band gap calculations, more local MBJ (LMBJ), which has been developed very recently

Summary

■ INTRODUCTION

The one-atom-thick layers of exfoliating materials have attracted the attention of the scientific community for their exceptional properties with many applications.[1,2] The weak interaction between the layered bulk materials allows us to obtain the monolayer, and the most successful example is graphene,[3,4] a single layer of graphite. For a set of 472 solids, the MAE and MARE of GLLB-SC (0.7 eV and 39%) error are larger than the MAE of HSE (0.5 eV and 31%).[18] By considering both the MAE and MARE, the modified Becke−Johnson (MBJ)[25] potential is overall the best in predicting the band gaps for both sets of solids.[18] Though MBJ is efficient for bulk calculations, the unit cell-dependent parameter present in the potential cannot be used in the case of systems with vacuum, like 2D materials or molecules To address this problem, Rauch et al.[46] proposed a model to bypass the unit cell-dependent function with a locally averaged function (see the Theory section for details), and the resulting potential is known as the local MBJ (LMBJ) potential. Spin−orbit coupling (SOC) was included in the calculations involving transition-metal atoms, i.e., for the TMDs and MXenes

■ RESULTS AND DISCUSSION

■ SUMMARY AND CONCLUSIONS

■ REFERENCES