[Wien] more qeustions regarding the supercell question from Shamik

[Dr Qiwen YAO]

Dear Professor Cottenier,
Your explanation is quite clear, I think I am understand this matter better now.

Thank you very much for your time.

kind regards,
Qiwen


------Original Message------
From:"Stefaan Cottenier"<Stefaan.Cottenier at UGent.be>
To:"A Mailing list for WIEN2k users"<wien at zeus.theochem.tuwien.ac.at>
Cc:
Subject:Re: [Wien] more qeustions regarding the supercell question from Shamik
Date:08/23/2011 07:05:33 AM(+0200)
>
>Let us take a conventional bcc unit cell (say for iron) as an example. 
>This is a cube that contains 2 atoms (*), and we call this our 1x1x1 cell.
>
>This small cell *does* represent a solid that extends infinitely over 
>all space (by periodic boundary conditions). A wien2k calculation for 
>such a cell is not a calculation for 2 atoms, it is a calculation for an 
>infinite solid.
>
>If you take a 2x1x1 supercell (two cubes glued together at one side), 
>periodic boundary conditions make sure that you represent again the 
>*same* infinite solid. The calculation is done for 4 atoms (that's where 
>you waste time), but the properties you calculate are the properties of 
>the same infinite solid and will be indistinguishable from what you 
>found for the 1x1x1 cell.
>
>The issue about 'making supercells as big as possible' arises when you 
>don't deal with pure crystalline solids, but with defects or impurities. 
>Imagine you want to calculate the properties of a single impurity atom 
>in the bcc Fe matrix. That single impurity destroys the periodicity: the 
>unit cell for this case becomes infinitely large (the impurity is never 
>repeated). That would require an infinite amount of computer time. You 
>can approximate this impurity case by a 2x2x2 supercell (16 atoms), in 
>which you replace one Fe-atom by an impurity. This is a cube with an 
>edge (2*a) that is twice as large as the ede (a) of the original cube. 
>By the periodic boundary conditions, the impurity will be copied many 
>times in space, and the distance between an impurity and the next one 
>will be 2*a. That's not really an isolated impurity, but for some 
>properties this is a decent first approximation of the isolated case. 
>You can now approximate better by making the supercell larger (3x3x3 --> 
>3*a, etc.). At every step, the approximation is better, yet the 
>computational cost increases.
>
>(*) The smallest possible unit cell (primitive cell) for this structure 
>is even smaller and contains only 1 atom. It has non-orthogonal angles, 
>and it is therefore harder to visualize, that's why I avoid it in this 
>example. Nevertheless, wien2k does use this primitive cell internally 
>for its actual calculations.
>
>Stefaan
>
>On 23/08/2011 4:22, Dr Qiwen YAO wrote:
>> Hello professor Cottenier, professor Perez-Mato,
>>
>> I like to ask more questions re this supercell question as I am not
>> very clear on this.
>>
>> I apologies if my comments/questions seem to be naive but I do like
>> to understand this concept better:
>>
>> Isn't it the case that, a supercell is to approximate the 'REAL'
>> properties of a solid crystal? so if that is true then isn't it the
>> case that the bigger the supercell is, the closer it is for its
>> properties to match the bulk crystal (and that is why we all wanting
>> to trying bigger supercells in the Wien2k or any similar softwares'
>> calculation if the computer hardware allows)?
>>
>> Or is it the case that Wien2k has the ability to 'complete the
>> picture' by adding say boundary conditions to a smaller (say 1x1x1)
>> supercell to match (equalize) the properties of the bulk crystal?
>>
>> kind regards, Qiwen
>>
>>
>> ------Original Message------ From:"shamik
>> chakrabarti"<shamikphy at gmail.com> To:"A Mailing list for WIEN2k
>> users"<wien at zeus.theochem.tuwien.ac.at> Cc: Subject:Re: [Wien]
>> Question regarding supercell Date:08/22/2011 08:17:15 PM(+0530)
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>>
>> **********************************************************
>>
>> Dr QiWen YAO
>>
>> JSPS Fellow Multifunctional Materials Group Optical and Electronic
>> Materials Unit Environment and Energy Materials Research Division
>>
>> National Institute for Materials Science
>>
>> 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan Phone:
>> +81-29-851-3354, ext. no. 6482, Fax: +81-29-859-2501
>>
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**********************************************************

Dr QiWen YAO

JSPS Fellow
Multifunctional Materials Group
Optical and Electronic Materials Unit
Environment and Energy Materials Research Division

National Institute for Materials Science

1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan
Phone: +81-29-851-3354, ext. no. 6482, Fax: +81-29-859-2501

**********************************************************