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Hi,

The DFT-1/2 and DFT-1/4 methods are specific corrections to the DFT method that have been developed to improve the accuracy of band gaps for certain systems. Can we use DFT-2/5 in similar fashion as DFT-1/2 and DFT-1/4, if it corrects the band gap of some particular systems?

Adjusting a parameter in a theoretical method to get agreement with a reference value (i.e., experiment) is sometimes done, but this is what is called empiricism. It is hard to give more advice without knowing the goal or the context of your study.