[Wannier] electric polarization of a single molecule

[Pedro Augusto F. P. Moreira]

  Hi Nicola,

  thank you for your answer. If you allow me, I have another question 
that arose from your answer. I am trying to calculate the polarization 
for a solid and was doing the calculations with a single molecule to 
learn how to use W90.

  I want to calculate polarizations caused by vacancies in solids, for 
example Si crystal. I am thinking to calculate the vacancy polarization, 
subtracting the polarization of a bulk with vacancy from a pristine 
bulk. So, I would need to determine the polarization in each case first. 
Note that the bulk is in the same state in both cases, but for a defect.

  How would I choose the final and initial states (for the bulk) in this 
case?

  with best regards,

  Pedro Moreira

Em 10-06-2012 08:00, Nicola Marzari escreveu:
>
>
> Hi Pedro,
>
>
> the discussion you quote was for a solid, where polarization is always
> meant as a polarization difference between two phases.
>
> No need for such subtlety in a molecule - once you have relaxed it to 
> its equilibirum configuration, you can calculate its dipole by summing
> the electrical and the ionic dipole.
>
> The electrical dipole is given by the sum of the WF centers, and the 
> ionic dipole by the ion charges (for water using pseudopotentials, the
> hydrogens are +1, and the oxygens +6).
>
> Note that the WF centers are defined modulo a lattice vector, so make
> sure that you bring them all back, if needed, to the same unit cell.
>
> Last - note that this is a somewhat inefficient way to calculate
> dipoles in isolated systems - the WF centers are calculates using the
> reciprocal space version of the position operator (using derivatives in
> k-space), and so they require larger supercells or k-point meshes
> even for isolated systems - not to converge better the electronic
> structure, but to converge better the position operator.
>
> It would be more accurate to calculate the dipole in real space,
> just by intergrating r times the charge density (of course, you can't
> do that in a solid).
>
>         nicola
>
>
>
> On 06/06/2012 20:15, Pedro Augusto F. P. Moreira wrote:
>>     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
>>
>> -----------------------------
>>
>>    Pedro Moreira
>>
>>    IFGW - Unicamp - Brazil
>>
>>
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>
>

-- 
Pedro Moreira

IFGW - Unicamp - Brazil