[Wien] berryphase

[Sheikh Jamil Ahmed]

Hello Shahrbano,

I also agree with Dr. Rubel that this fraction of discrepancy that you are
getting is probably due to the fact we made this tutorial on Wien2k version
11.0.

Regarding the forces for optimizing the structure, I always try to optimize
my structure to a much lower value (0.2 mRy/bohr) of forces. However, this
doesn't make much of a difference to the final result though. Compared to
the optimized structure with default force tolerance  (2 mRy/bohr), the
atomic positions varies only in fourth or fifth decimal places which might
change your polarization by 0.1 to 1 % (like you are getting). This is
negligible if you are consistent when comparing properties between two
calculations. Either use 2 mRy/bohr for both the cases or 0.2 mRy/bohr.

Also you can try to understand more about modern theory of polarization
from here
http://www.physics.rutgers.edu/~dhv/pubs/local_preprint/dv_fchap.pdf

Hope that helps.

Sheikh


On Thu, Dec 5, 2013 at 11:56 AM, Oleg Rubel <orubel at lakeheadu.ca> wrote:

> Dear Shahrbano,
>
> > ... Although we could reproduce
> > the SP of the sample, P_s= P_z(lambda1)- P_z(lambda0) = 0.312113863793-
> > 1.52399256575e-11 = 0.312113863777760 C/m^2 which is very close to the
> > readme file (but not exactly the same as it P_s= P_z(lambda1)-
> P_z(lambda0)=
> > 0.31140111708550217-1.4486341471349937e-11= 0.3114011170710158 C/m^2),
> there
> > are some things which are not clear for us.
>
> This difference is not material. Tutorials were done with an earlier
> version of Wien2k and a default SCF convergence. Possibly, a tighter
> convergence will lead to the same result in both cases.
>
> > Why would not define the P_s just as P_z(lambda1)?
>
> In general, P(lambda0) = 0 may not always be true due to pi rapping.
> So it will be a very "slippery" assumption. This is why I would insist
> on doing both calculations (lambda0, lambda1) even though you might
> expect zero.
>
> > We examined these two structures by calculating the exerted forces on the
> > atoms of them to check whether they are in their relaxed positions or
> not.
> > We found that the displaced atoms in lambda1.strcut were under
> > tension--:FOR002 and :FGL002 are not zero.
>
> Are there total or partial forces? What are the values?
>
> > In the way as discussed in tutorial1, the SP certainly will depend on the
> > displacements. If we increase the amount of displacement, then we will
> > obtain larger SP.
>
> In any case, you are need a well converged atomic positions. In our
> calculations we try to optimize structure to better than 2 mRy/Bohr.
> (Sheikh can probably comment more.)
>
> > So, unlike Boron effective charge
> > calculations it appears that the SP calculations cannot give a unique
> > result?
>
> Indeed, the SP should be unique. There should be only one well
> converged structure. Of course, it will be sensitive to the choice of
> XC functional.
>
> > 3) And, why we should not fully initialize the centrosymmetric one?
>
> We do not want Wien2k to realize its higher symmetry. Therefore, the
> initialization is done for low-symmetry lambda1 case only. Both
> structures should have identical symmetry operations in order to
> ensure consistency and comparability of the results.
>
> > In summary, according to the definition of SP, a transient from a
> > centrosymmetry to a noncentrosymmetry seems to be necessary. But, here
> both
> > of the phases are tetragonal, while in the paper one of them is
> considered
> > to be cubic.
>
> Strictly speaking, you are right. We would need a cubic structure for
> lambda0 and you can try it. What you will find in this case that it
> does not matter for P(lambda0).
>
> > Where is the transition in this tutorial?
>
> You can make a transition by choosing an intermediate structure (say
> lambda05). I am not aware of unique way to define the intermediate
> state: we know for sure only lambda0 and lambda1. But you can imagine
> lambda1 as a distorted case of lambda0. For lambda05 you need half of
> the distortions. Of course, NO optimization of atomic positions should
> be performed for lambda05. Otherwise you will end up with lambda1
> again.
>
> > What will be the criterion to move up the atoms?
>
> Zero force and stress for lambda1.
>
> > What is the difference between SP and total polarization?
>
> It is the essence of the modern polarization theory that the total
> polarization does not make sense. Only a difference matters, i.e. SP.
>
> > Would you discuss how we can find the centrosymmetric and
> noncentrosymmetric
> > ones for any cases?
>
> This part I am not sure, especially for GaN. The thinking should start
> with analysis of measurable quantities/effects, which you would like
> to model.
>
>
> Thank you
> Oleg
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