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The accuracy of effective masses predicted by density functional theorydepends on the exchange-correlation functional employed, with nonlocal hybridfunctionals giving more accurate results than semilocal functionals. In thisarticle, we benchmark the performance of the Perdew-Burke-Ernzerhof (PBE),Tran-Blaha modified Becke-Johnson (TB-mBJ), and the hybridHeyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functionals and potentialsfor the calculation of effective masses with perturbation theory. We introducethe mstar60 dataset, which contains 60 effective masses derived from 18semiconductors. The ratio between experimental and calculated effective massesis $1.70 \pm 0.20$ for PBE, $0.76 \pm 0.04$ for TB-mBJ, $0.99 \pm 0.04$ forHSE06. We reveal that the nonlocal exchange in HSE06 enlarges the opticaltransition matrix elements leading to the superior accuracy of the hybridfunctional in the calculation of effective masses. The omission of nonlocalexchange in the transition operator for HSE leads to serious errors. For thesemilocal PBE functional, the errors in the bandgap and the optical transitionmatrix elements partially cancel out in the calculation of effective masses.The TB-mBJ functional yields PBE-like matrix elements paired with realisticbandgaps leading to a consistent overestimation of effective masses. However,if only limited computational resources are available, experimental masses canbe estimated by multiplying TB-mBJ masses with the factor of 0.76. We thencompare effective masses of transition metal dichalcogenide bulk and monolayermaterials: we show that changes in the matrix elements are important inunderstanding the layer-dependent effective mass renormalization.

physical review. b./physical review. b

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