[Pw_forum] Band gap value through charged supercell calculation

[Тимофей Перевалов]

Dear QE users,
I deal with band gap calculations for dielectrics (currently with monoclinic ZrO2).
The Eg value, obtained as the difference between ionization potential and electron affinity (I-A), is depends on the supercell size as a decreasing (like hyperbole) function. The Eg, obtained as the Kohn-Sham single particle states difference, doesn’t depend on the supercell size. In the Phys. Rev. B 78, 235104 in the “III. CORRECTION OF BAND-GAP ERRORS”, Fig.2 the similar dependence was obtained for isolated F atoms, whereas dependence is quite different for the solid (ZnO). And that's what I cannot understand.
At the forum, I found the view that «I-A is more physical and relevant to comparison with experimental band gaps».
I am using QE version 5.3, local XC functional blyp. Charged supercell calc with nspin = 2, starting_magnetization=1, occupations =smearing, smearing = mp.
I understand that dependence on the supercell size is due to compensating charge background. The Makov-Payne correction for a charged cell is not applicable because I used monoclinic system. I tried to use the Martyna-Tuckerman correction, but, firstly, the Eg value is much higher than experimental one; secondly, the dependence on the supercell size retains.

And another important question. Is it correct (possible) to calc Eg as I-A using hybrid functional?

Sincerely,
Perevalov Timofey

Rzhanov Institute of Semiconductor Physics
timson at isp.nsc.ru