[Wannier] electric polarization of a single molecule

Nicola Marzari nicola.marzari at epfl.ch
Sun Jun 10 13:00:48 CEST 2012

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).

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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> Wannier mailing list
> Wannier at quantum-espresso.org
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Prof Nicola Marzari, Chair of Theory and Simulation of Materials, EPFL

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