a b s t r a c t It has been shown that the underestimated by DFT/LDA(GGA) band-gap can be efficiently corrected by an averaging procedure of transition energies over a region close to the direct band-gap transition, which we call the ∆(EIG) method (the differences in the Kohn-Sham eigenvalues). For small excitations the averaging appears to be equivalent to the ∆(SCF ) approach (differences in the self-consistent energies), which is a consequence of Janak's theorem and has been confirmed numerically. The Gaussian distribution in k-space for electronic excitation has been used (occupation numbers in the ∆(SCF ) or eigenenergy sampling in the ∆(EIG)). A systematic behavior of the k-space localization parameter σk correcting the band-gap has been observed in numerical experiments. On that basis some sampling schemes for band- gap correction have been proposed and tested in the prediction of the band-gap behavior in InxGa(1−x)N semiconducting alloy, and a very good agreement with independent calculations has been obtained. In the context of the work the issue of electron localization in the r-space has been discussed which, as it has been predicted by Mori-Sanchez et al. (P. Mori-Sanchez, A.J. Cohen, W. Yang, Phys. Rev. Lett. 100 (2008) 146401), should reduce the effect of the convex behavior of the LDA/GGA functionals and improve the band-gap prediction within DFT/LDA(GGA). A scheme for electron localization in r-space has been suggested.
['P. Scharoch', 'M. J. Winiarski']
An efficient method of DFT/LDA band-gap correction