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

The experimental and theoretical realization of two-dimensional (2D) materials is of utmost importance in semi-conducting 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, 2654] and GLLB-SC [Phys. Rev. B 82, 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, 226401] 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.