The modified Becke-Johnson exchange potential [F. Tran and P. Blaha, Phys. Rev. Lett. 102, 226401 (2009)] (TB-mBJ) yields very accurate electronic band structures and gaps for various types of semiconductors and insulators (e.g., sp
semiconductors, noble-gas solids, and transition-metal oxides).
However, the TB-mBJ potential has, for a few groups of solids, the
tendency to underestimate the band gap. This has led us to examine the
possibility to further improve over the original TB-mBJ potential by
either reparametrizing its coefficients using a larger test set of
solids or defining a parametrization for small-/medium-size band-gap
semiconductors only. We also checked alternatives to the average of |∇ρ|/ρ in the unit cell for the determination of parameter c,
which determines the amount of the screening contribution. Among these
different possibilities, the best one seems to be a reparametrization of
the coefficients, which leads to a much more balanced description of
the band gaps.
My name is Dr Abderrahmane Reggad. I'm a 54 year old and I am a researcher in materials' sciences. 
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