# [Pw_forum] shift of energy

Stefano de Gironcoli degironc at sissa.it
Mon Apr 4 12:24:12 CEST 2011

```Dear  All,
let me clarify a little point.
The potential (hence the eigenvalues) of  any calculation in
periodic boundary conditions, not just a plane-wave one , is defined up
to  an additive constant... In a finite system a reeference can be fixed
by requiring that the potential goes to zero at infinite distance but in
a periodic system this cannot be defined as there is nothing like a
point at infinite distance ...
In most codes (and in pw.x) this arbitrary constant is fixed by
setting the average electrostatic potential to zero. If the supercell is
properly constructed, with the properly scaled dimensions, the same
cutoff, equivalent k-points etc.. the two calculations should be
equivalent and the eigenvalues should be exactly mapped, the average
potential should be the same, the total energy should be an exact
multiple of the one of the original cell.

If this does not happen one is NOT doing the supercell calculation properly.

So if when doing a supercell you do not get the scaled result check your
system definition.

stefano

On 04/04/2011 11:46 AM, Giuseppe Mattioli wrote:
> Dear all
> I suspect that a a little misunderstanding has been going on here...
> I try to reformulate the question: in the case of a 8-atoms cell the valence
> band maximum (VBM) has been found around 10 eV and the conduction band
> minimum (CBM) around 12 eV with a 2 eV band gap. So there is a shift in the
> position of VBM and CBM when calculated in a 72-atoms supercell, but the band
> gap value is the same. Then, the answer to P Shok could be: plane wave
> pseudopotential calculations do not ensure an universal alignment of
> eigenvalues. You should use some "internal" reference, like the 1s eigenvalue
> of an He atom, in your cell; or trust that the two VBM values are aligned "de
> facto".
> HTH
>
> Giuseppe
>
> On Monday 04 April 2011 09:39:18 Gabriele Sclauzero wrote:
>> Yes,
>>
>>     I perfectly agree with Eyvaz! Moreover the experimental bandgap is
>> underestimated within LDA or GGA, and for 4H-SiC you would get about
>> 2.2-2.3 eV with LDA.
>>
>>     How do you measure the bandgap? Beware that in the fundamental cell the
>> bandgap is not a direct one, but it might become such when you use a
>> supercell (because of the refolding of the Brillouin zones).
>>
>>
>> HTH
>>
>> GS
>>
>> Il giorno 03/apr/2011, alle ore 10.59, Eyvaz Isaev ha scritto:
>>> Hi,
>>>
>>>> The bandgap of 8-atoms is around 10-12 eV,
>>>> but that of 72-atom is around 5-7 eV.
>>> This is unbelievable, as SiC is an indirect band gap semiconductor and
>>> the bandgap is around (2.5 - 3)eV depending on crystal modification
>>> (3C-SiC, 2H-SiC; 4H-SiC; 6H-SiC, etc.).
>>> See http://www.matprop.ru/SiC_bandstr
>>>
>>> So, check carefully your input/output files.
>>>
>>> Bests,
>>> Eyvaz.
>>>
>>> -------------------------------------------------------------------
>>> Prof. Eyvaz Isaev,
>>> Department of Physics, Chemistry, and Biology (IFM), Linkoping
>>> University, Sweden Theoretical Physics Department, Moscow State Institute
>>> of Steel&  Alloys, Russia, isaev at ifm.liu.se, eyvaz_isaev at yahoo.com
>>>
>>>
>>> From: pari shok<parishok at gmail.com>
>>> To: pw_forum at pwscf.org
>>> Sent: Sun, April 3, 2011 1:34:51 AM
>>> Subject: [Pw_forum] shift of energy
>>>
>>> Dear Paolo,
>>> DOS of 72-atom SiC shows a shift of energy with respect to 8-atom SiC.The
>>> bandgap of 8-atoms is around 10-12 eV, but that of 72-atom is around 5-7
>>>
>>> Thanks again.
>>> P Shok
>>> UMD
>>>
>>> On Apr 1, 2011, at 21:36 , pari shok wrote:
>>>> The DOS of 72-atom SiC (supercell) shows a shift of energy.
>>> a shift with respect to what?
>>> ---
>>> Paolo Giannozzi, Dept of Chemistry&Physics&Environment,
>>>
>>> Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
>>> Phone +39-0432-558216, fax +39-0432-558222
>>>
>>> _______________________________________________
>>> Pw_forum mailing list
>>> Pw_forum at pwscf.org
>>> http://www.democritos.it/mailman/listinfo/pw_forum
>> § Gabriele Sclauzero, EPFL SB ITP CSEA
>>     PH H2 462, Station 3, CH-1015 Lausanne
>
>

```