[Wien] more qeustions regarding the supercell question from Shamik

[Stefaan Cottenier]

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:
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