An efficient method of DFT/LDA band-gap correction

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 Δ(EIG) method (the differences in the Kohn-Sham eigenvalues). For small excitations the averaging appears to be equivalent to the Δ(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 Δ(SCF) or eigenenergy sampling in the Δ(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-Sánchez et al. [P. Mori-Sánchez, 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.