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This paper is a continuation of our detailed study [Phys. Rev. B 86, 195106(2012)] of the performance of the recently proposed modified Becke-Jonhsonpotential (mBJLDA) within the known Wien2k code. From the 41 semiconductorsthat we have considered in our previous paper to compute the band gap value, weselected 27 for which we found low temperature experimental data in order topinpoint the relative situation of the newly proposed Wien2k(mBJLDA) method ascompared to other methods in the literature. We found that the GWA gives themost accurate predictions. The Wien2k (mBJLDA) code is slightly less precise,in general. The Hybrid functionals are less accurate, on the overall. The GWAis definitely the most precise existing method nowadays. In 88% of thesemiconductors considered the error was less than 10%. Both, the GWA and themBJLDA potential, reproduce the band gap of 15 of the 27 semiconductorsconsidered with a 5% error or less. An extra factor to be taken into account isthe computational cost. If one would seek for precision without taking thisfactor into account, the GWA is the method to use. If one would prefer tosacrifice a little the precision obtained against the savings in computationalcost, the empirical mBJLDA potential seems to be the appropriate method. Weinclude a graph that compares directly the performance of the best threemethods, according to our analysis, for each of the 27 semiconductors studied.The situation is encouraging but the problem is not yet a closed issue.

The band gap problem: the accuracy of the Wien2k code confronted