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<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">Dear Perevalov,<br>
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The K-S gap in left panel of Fig.2 in the paper is not what you get directly from the occupations of the neutral cell. What is shown in the figure is calculated using equation 13 which uses eigenvalues from the neutral cell and occupations from charged cell.
This way there will a dependence on carrier concentration.<br>
I believe what you plotted and found to be independent of "cell size" is K-S gap using both eignevalues and occupations of the neutral cell.<br>
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You mentioned; "I understand that dependence on the supercell size is due to compensating charge background". In fact even if you correct for the compensating background , you will still observe dependence on the charge density for I-A and K-S calculated
with equation 13. In the dilute limit of charged carriers you should converge to K-S gap of the neutral cell in the case of functionals that do not have exact exchange (LDA, GGA, BYLP, ...). For hybrid functionals that contains exact exchange (PBE0, HSE,
...) there will be a difference between I-A and K-S (neutral) even in the dilute limit. This is also discussed in the paper you cited right before Fig. 2.<br>
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It is common, at least in semiconductor defects studies , to regard I-A as "the" band gap of the material. Some may agree , others do not.
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For monoclinic ZrO2, the first order M-P correction was reported here:<br>
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<a href="http://journals.aps.org/prb/abstract/10.1103/PhysRevB.75.104112" target="_blank">http://journals.aps.org/prb/abstract/10.1103/PhysRevB.75.104112</a><br>
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Of course based on the lattice parameters and supercells that the authors reported.<br>
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In computing the K-S gap of a neutral cell I would use the tetrahedron method or fixed occupations (i.e no smearing) and a dense K-point mesh<br>
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Regards,<br>
Mostafa Youssef<br>
MIT<br>
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