[Pw_forum] Band gap value through charged supercell calculation

毛飞 200921220018 at mail.bnu.edu.cn
Thu May 26 18:32:03 CEST 2016

Dear Perevalov and Mostafa,
Having seen the discussions you contributed to the forum, I am more concerned about how to calculate the ionization energy (I) of semiconductors or insulators by pwscf codes. The definition of I=E(N-1) - E(N), I can obtained E(N) as the ground state energy of the neutral system, but how to get the ground state energy of positively charged system E(N).
Your comments are appreciated.
USC, China

在2016-05-26,Mostafa Youssef <myoussef at mit.edu> 写道:-----原始邮件-----
发件人: Mostafa Youssef <myoussef at mit.edu>
发送时间: 2016年5月26日 星期四
收件人: "pw_forum at pwscf.org" <pw_forum at pwscf.org>
主题: Re: [Pw_forum] Band gap value through charged supercell calculation

Dear Perevalov,

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.
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.

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.

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. 

 For  monoclinic ZrO2,  the first order M-P correction was reported here:


Of course based on the lattice parameters and supercells that the authors reported.

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

Mostafa  Youssef


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