  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.
