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Benchmarking exchange-correlation potentials with the mstar60 dataset: Importance of the nonlocal exchange potential for effective mass calculations in semiconductors

The accuracy of effective masses predicted by density functional theory depends on the exchange-correlation functional employed, with nonlocal hybrid functionals giving more accurate results than semilocal functionals. In this article, we benchmark the performance of the Perdew-Burke-Ernzerhof (PBE), Tran-Blaha modified Becke-Johnson (TB-mBJ), and the hybrid Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functionals and potentials for the calculation of effective masses with perturbation theory. We introduce the mstar60 dataset, which contains 60 effective masses derived from 18 semiconductors. The ratio between experimental and calculated effective masses is $1.70 \pm 0.20$ for PBE, $0.76 \pm 0.04$ for TB-mBJ, $0.99 \pm 0.04$ for HSE06. We reveal that the nonlocal exchange in HSE06 enlarges the optical transition matrix elements leading to the superior accuracy of the hybrid functional in the calculation of effective masses. The omission of nonlocal exchange in the transition operator for HSE leads to serious errors. For the semilocal PBE functional, the errors in the bandgap and the optical transition matrix elements partially cancel out in the calculation of effective masses. The TB-mBJ functional yields PBE-like matrix elements paired with realistic bandgaps leading to a consistent overestimation of effective masses. However, if only limited computational resources are available, experimental masses can be estimated by multiplying TB-mBJ masses with the factor of 0.76. We then compare effective masses of transition metal dichalcogenide bulk and monolayer materials: we show that changes in the matrix elements are important in understanding the layer-dependent effective mass renormalization.