The essence of electronic polarization is that it is a “relative” quantity, 
i.e., its calculation (and measurement too) requires a reference point. The 
reference structure is not always centrosymmetric. An example of 
non-centrosymmetric reference structure is zinc-blende GaN that is taken as P=0 
in computing the spontaneous polarization of the wurtzite GaN (see 
https://github.com/spichardo/BerryPI/wiki/Tutorial-4:-Polarization-in-GaN).

For the second part of the question on EuTiO3, enclosed structure files would 
certainly help. One possible strategy would be to explore a gradual evolution 
of the polarization between cubic and tetragonal structures.


I hope this will help
Oleg



> On Sep 7, 2015, at 3:42 AM, nilofar hadaeghi <n.hadae...@gmail.com> wrote:
> 
> Dear all
>      I have studied some papers whose authors are S.J.Ahmed or O.Rubel  in 
> which building the centrosymmetric and noncentrosymmetric structure for the 
> calculation of spontaneous polarization has been explained, but it is still 
> ambiguous for me.
> Could you please help me whether the noncentrosymmetric structure must exist 
> in the nature or it is enough to apply a displacement to the central atom of 
> the centrosymmetric structure and then use the new structure as the 
> noncentrosymmetric one?!
> For instance I am working on EuTiO3 in which a structural transition at 
> temperature 282(k) from cubic to tetragonal ( from Pm3m space group to 
> I4/mcm) occurs. Now, would you please help me whether I use the structure in 
> I4/mcm space group as the noncentrosymmetric structure or I must change the 
> positions of the centrosymmetric structure and use the achieved structure as 
> the noncentrosymmetric one?
> I am using WIEN2k 14.2, Python version: 2.7.3 and Numpy version: 1.6.2.
> Sincerely yours,
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