"the modified Becke-Johnson exchange potential + LDA-correlation ([Tran and Blaha, 2009]) allows
the calculation of band gaps with an accuracy similar to very expensive GW calculations. It is a semilocal approximation to an atomic “exact-exchange” potential and a screening term".
A good paper to read about the issue is:
First principle study of band gap nature, spontaneous polarization,
hyperfine field and electric field gradient of desirable multiferroic bismuth ferrite (BiFeO3)
Journal of Physics and Chemistry of Solids 148 (2021) 109737