[Wannier] electric polarization of a single molecule

[Pedro Augusto F. P. Moreira]

   Dear all,

  I am trying to calculate the electric polarization of an isolated 
water molecule as Silvestrelli and Parrinello did in 1999 (PRL).

  I did a molecule relaxation with QE and calculated the electric 
polarization, using Wannier functions centres (from W90) and ions 
positions. I considered my initial and final states, the initial and 
final conditions on relaxation. However, I found a different value from 
expected one.

  Prof. Nicola Marzari answered before in this list:

http://www.democritos.it/pipermail/wannier/2009-January.txt

"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)."

My question is: How should I choice two "phases" for a single molecule?

  In other words: I know the formula for calculating the electric 
polarization, but I do not know how to determine the initial and final 
states to do the math.

  Any advice would be appreciated,

  Pedro

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  Pedro Moreira

  IFGW - Unicamp - Brazil