To address your questions...

> I4/mcm is centrosymmetric. I studied the tutorial related to GaN and it 
> helped me very much. So I conclude to calculate the difference in 
> polarization, two structures that at least one of them should not be 
> centrosymmetric are needed, Is it correct?

That’s correct. When the structure file contains the inversion symmetry, Wien2k 
switches from complex to real version for wave functions. Then there is no 
phase information to be processed.

> Would you please guide me whether it is allowed to calculate the difference 
> in polarization between a strained and unstrained state of a system by 
> implementing the berryPI on each of them separately and then subtract them ?! 
> if it going to, what does the derived polarization  describe?! 
> Piezoelectricity(since it is the difference in polarization caused by strain) 
> or spontaneous polarization?

You are heading towards piezoelectric coefficients. There are some 
technicalities, such as clamped vs relaxed ion approximation, proper vs 
improper. Here is a good reference:
I do not see any barriers from BerryPI perspective.

Best regards

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