[Wannier] calculations of electric polarization in BaTiO3

[Nicola Marzari]

Dear EunMe Lee,


happy new year, and welcome to wannier.

Short answer: you can consider the center of each Wannier function
as a "classical" electron. So, the vectorial sum of all the Wannier
centers gives you an overall electronic polarization vector (you need
to multiply it by 2, if spin unpolarized, then by the charge of one
electron, and divide it by the volume of the unit cell). The
*difference* in this polarization vector between two phases (e.g. cubic
and tetragonal) gives you the *physical* quantity that you want (you
also need to add the same, trivial, for the ionic valence charges, to
have the total polarization difference).

You need to pay attention to the fact that each Wannier center can be 
located in one unit cell, or in any other periodic repetition, so you 
need consistency in where your Wannier centers are located in the two
calculations, and also on other details (certain high symmetry cubic 
phases can have an unusual polarization vector).

Long answer: read carefully the introductory review (especially the
part on mapping polarization onto Wannier centers) "Theory of 
Polarization: a modern approach" by Resta and Vanderbilt, available
as publication 198 from David Vanderbilt website: 
http://www.physics.rutgers.edu/~dhv/pubs/pub_list.html

			nicola




EunMe lee wrote:
> Dear Wannier developpers and users,
>  
> I am beginner in using the wannier code, I have please a question and I 
> would like to ask if someone can tell me how to calculate the electric 
> polarization from wannier function code. I have read in examples of the 
> code but I could not figure out how to get the electric polarization for 
> BaTiO3.
>  
> Your help and support are very appreciate.
>  
> I wish merry christmass and happy new year " 2009 " to all developpers 
> and users.
>  
> Regards,
>  
> EunMe Lee,
> Chem Eng, Materials Science
> Postech, Pohang, South Korea
> 
> 
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Prof Nicola Marzari   Department of Materials Science and Engineering
13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
tel 617.4522758 fax 2586534 marzari at mit.edu http://quasiamore.mit.edu