[gpaw-users] dipole corrections

[Ask Hjorth Larsen]

Hi

On Thu, 15 Dec 2011, Sampsa Riikonen wrote:

> Dear List,
>
> I am a novice here..
>
> .. so nice to meet you all.
>
> My question concerns the dipole corrections in gpaw.
>
> The module can be found here:
>
> https://wiki.fysik.dtu.dk/gpaw/epydoc/gpaw.dipole_correction.DipoleCorrection-class.html
>
> Does this module implement the dipole corrections in a similar way to..?
>
> dx.doi.org/10.1103/PhysRevB.59.12301
>
> The electrostatic potential is forced to zero on the (z) boundaries.
> This is equivalent to
> adding something to the charge distribution.  This "something" is then
> eliminated once
> the potential has been calculated using the poisson equation, by
> subtracting a linear
> V(z) term from the potential.
>
> Then gpaw is actually calculating the potential using "open" boundary
> conditions and there
> is no problem with anything, i.e. it is exact.
>
> Am I right..?

Yes, the charge distribution is modified before solving the Poisson 
equation, so the total moment is zero.  Then after the equation is solved, 
the appropriate correction is added back so it regains the right boundary 
conditions.  There is a test in the test suite which verifies that the 
potential of two symmetrically arranged H2O molecules (total dipole moment 
0) have a potential which is consistent with that a single 
dipole-corrected H2O molecule.

>
> However, in the following post
>
> https://listserv.fysik.dtu.dk/pipermail/gpaw-users/2010-April/000101.html
>
> it is said that ..
>
> "Atomic forces may be a bit off for dipole-corrected calculations"
>
> Is this still a problem...?  Why the forces "may be a bit off" ?

I suppose we can regard the energy as depending on atomic positions R (in 
a way independent of dipole correction) as well as the dipole correction 
m.  Then by the chain rule:

   dE/dR = [dE/dR]_m + [dE/dm]_R dm/dR

where the [dX/dY]_x denotes that x is constant in that derivative. There 
is no explicit term in the force expression to account for the latter of 
these terms (containing dm/dR), but it is the dipole-corrected potential 
which is used during the force evaluation.  I have never quite worked out 
whether an explicit correction is necessary.  Do you know that it isn't?

>
> And continuing the same theme..
>
> Are there any plans (or maybe this has already been implemented to some
> recent
> development version of gpaw) to make a similar kind of correction for
> molecules?  i.e. the potential
> is not corrected only to the z direction but to all directions.
>
> Kind Regards,
>
> Sampsa

I haven't tried this, but a simple hack would be to wrap three dipole 
corrections around each other.  They will then correct along each 
direction independently.

Regards
Ask