# [Pw_forum] Band gap value through charged supercell calculation

Layla Martin-Samos lmartinsamos at gmail.com
Thu May 26 19:05:06 CEST 2016

```DEar Evan, you cannot get ionization energies in a bulk, unless you use a
cluster of atoms to model your material (with a "welldefined" 0 energy
reference).

cheers

Layla

2016-05-26 18:32 GMT+02:00 毛飞 <200921220018 at mail.bnu.edu.cn>:

> 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).
>
>
>
>
> Evan
>
> 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:
>
> http://journals.aps.org/prb/abstract/10.1103/PhysRevB.75.104112
>
> 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
>
>  Regards,
> Mostafa  Youssef
> MIT
>
>
>
>
>
>
>
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>
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