<div dir="ltr">Hello Shahrbano,<div><br></div><div>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. </div><div><br>
</div><div>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.</div>
<div><br></div><div>Also you can try to understand more about modern theory of polarization from here <a href="http://www.physics.rutgers.edu/~dhv/pubs/local_preprint/dv_fchap.pdf" target="_blank">http://www.physics.rutgers.edu/~dhv/pubs/local_preprint/dv_fchap.pdf</a></div>
<div><br></div><div>Hope that helps.</div><div><br></div><div>Sheikh</div></div><div class="gmail_extra"><br><br><div class="gmail_quote">On Thu, Dec 5, 2013 at 11:56 AM, Oleg Rubel <span dir="ltr"><<a href="mailto:orubel@lakeheadu.ca" target="_blank">orubel@lakeheadu.ca</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Dear Shahrbano,<br>
<br>
> ... Although we could reproduce<br>
<div class="im">> the SP of the sample, P_s= P_z(lambda1)- P_z(lambda0) = 0.312113863793-<br>
> 1.52399256575e-11 = 0.312113863777760 C/m^2 which is very close to the<br>
> readme file (but not exactly the same as it P_s= P_z(lambda1)- P_z(lambda0)=<br>
> 0.31140111708550217-1.4486341471349937e-11= 0.3114011170710158 C/m^2), there<br>
> are some things which are not clear for us.<br>
<br>
</div>This difference is not material. Tutorials were done with an earlier<br>
version of Wien2k and a default SCF convergence. Possibly, a tighter<br>
convergence will lead to the same result in both cases.<br>
<div class="im"><br>
> Why would not define the P_s just as P_z(lambda1)?<br>
<br>
</div>In general, P(lambda0) = 0 may not always be true due to pi rapping.<br>
So it will be a very "slippery" assumption. This is why I would insist<br>
on doing both calculations (lambda0, lambda1) even though you might<br>
expect zero.<br>
<div class="im"><br>
> We examined these two structures by calculating the exerted forces on the<br>
> atoms of them to check whether they are in their relaxed positions or not.<br>
> We found that the displaced atoms in lambda1.strcut were under<br>
> tension--:FOR002 and :FGL002 are not zero.<br>
<br>
</div>Are there total or partial forces? What are the values?<br>
<div class="im"><br>
> In the way as discussed in tutorial1, the SP certainly will depend on the<br>
> displacements. If we increase the amount of displacement, then we will<br>
> obtain larger SP.<br>
<br>
</div>In any case, you are need a well converged atomic positions. In our<br>
calculations we try to optimize structure to better than 2 mRy/Bohr.<br>
(Sheikh can probably comment more.)<br>
<div class="im"><br>
> So, unlike Boron effective charge<br>
> calculations it appears that the SP calculations cannot give a unique<br>
> result?<br>
<br>
</div>Indeed, the SP should be unique. There should be only one well<br>
converged structure. Of course, it will be sensitive to the choice of<br>
XC functional.<br>
<div class="im"><br>
> 3) And, why we should not fully initialize the centrosymmetric one?<br>
<br>
</div>We do not want Wien2k to realize its higher symmetry. Therefore, the<br>
initialization is done for low-symmetry lambda1 case only. Both<br>
structures should have identical symmetry operations in order to<br>
ensure consistency and comparability of the results.<br>
<div class="im"><br>
> In summary, according to the definition of SP, a transient from a<br>
> centrosymmetry to a noncentrosymmetry seems to be necessary. But, here both<br>
> of the phases are tetragonal, while in the paper one of them is considered<br>
> to be cubic.<br>
<br>
</div>Strictly speaking, you are right. We would need a cubic structure for<br>
lambda0 and you can try it. What you will find in this case that it<br>
does not matter for P(lambda0).<br>
<div class="im"><br>
> Where is the transition in this tutorial?<br>
<br>
</div>You can make a transition by choosing an intermediate structure (say<br>
lambda05). I am not aware of unique way to define the intermediate<br>
state: we know for sure only lambda0 and lambda1. But you can imagine<br>
lambda1 as a distorted case of lambda0. For lambda05 you need half of<br>
the distortions. Of course, NO optimization of atomic positions should<br>
be performed for lambda05. Otherwise you will end up with lambda1<br>
again.<br>
<div class="im"><br>
> What will be the criterion to move up the atoms?<br>
<br>
</div>Zero force and stress for lambda1.<br>
<div class="im"><br>
> What is the difference between SP and total polarization?<br>
<br>
</div>It is the essence of the modern polarization theory that the total<br>
polarization does not make sense. Only a difference matters, i.e. SP.<br>
<div class="im"><br>
> Would you discuss how we can find the centrosymmetric and noncentrosymmetric<br>
> ones for any cases?<br>
<br>
</div>This part I am not sure, especially for GaN. The thinking should start<br>
with analysis of measurable quantities/effects, which you would like<br>
to model.<br>
<br>
<br>
Thank you<br>
Oleg<br>
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</blockquote></div><br></div>