<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:14pt"><div class="" style="font-size:large;"><br clear="none"></div><div class="" style="font-size:large;"><br clear="none"></div><div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 19px/normal 'Helvetica Neue';color:rgb(35,35,35);">
Dear Prof. Rubel,</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal Calibri;color:rgb(35,35,35);min-height:19px;"><br clear="none"></div>
<div dir="ltr" style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;text-align:left;font:normal normal normal 11px/normal Calibri;"><span style="font:16.0px Calibri;color:#232323;"></span> >A quick glance at these references shows that they are discussing zinc
blende structure as a zero-polarization reference. So you probably need
to make a zinc blende GaN is the same fashion as wurtzite structure.
Fig. 12 in [Physics Reports, Volume 428, Issue 1, May 2006, Pages 1-52]
will be a good starting point, but still not exactly what you need. At
the end both structures should have identical symmetry and the same # of
atoms.</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal Calibri;color:rgb(35,35,35);min-height:19px;"><br clear="none"></div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal Calibri;color:rgb(35,35,35);">We
wish to work on your above comment. But, before going through it, we
tried to first make sure that we understood the detail of tutorial1 on
spontaneous polarization (SP) of BaTiO3 sample. Although we could
reproduce the SP of the sample, P_s= P_z(lambda1)- P_z(lambda0) = <span style="font:14.0px 'Courier New';">0.312113863793-</span><span style="font:11.0px Calibri;color:#000000;"> </span><span style="font:14.0px 'Courier New';">1.52399256575e-11 = 0.312113863777760 C/m^2 </span>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. So, let us discuss the ambiguities. Maybe clarifying the
ambiguities in the BiTiO3 sample can help us to find out how to treat
with our cases.</div>
<ol style="font-size:large;list-style-type:decimal;"><li style="margin:0.0px 0.0px 0.0px 0.0px;font:16.0px Calibri;color:#232323;">1)<span class="" style="white-space:pre;"> </span>From the result we see that SP for the centro-symmetric case is almost zero, P_Z(lamda0)=<span style="font:14.0px 'Courier New';"> 1.52399256575e-11 , as expected.</span>This
is expected, because Ti atom is symmetrically surrounded by 6 O atoms,
as shown in Fig. 4 (a) of Ref. [Com. Phys. Commun. 184 (2013) 647].
Therefore, Ti-O polarization vectors cancel each other, which results in
negligible SP. The question is that why we need to calculate the
negligible P_z(lamda0)? Why would not define the P_s just as
P_z(lambda1)?</li></ol><ol style="font-size:large;list-style-type:decimal;"><li style="margin:0.0px 0.0px 0.0px 0.0px;font:16.0px Calibri;color:#232323;">2)<span class="" style="white-space:pre;"> </span>We
compared lambda0.struct and lambda1.struct by diff command and noticed
that apart from the positions of the atoms the other things like space
group, lattice parameters, and son on are similar to each other, see
below: </li></ol>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">< ATOM -2: X=0.50000000 Y=0.50000000 Z=0.51517436</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">---</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">> ATOM -2: X=0.50000000 Y=0.50000000 Z=0.50000000</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">17c17</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">< ATOM -3: X=0.50000000 Y=0.50000000 Z=0.97356131</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">---</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">> ATOM -3: X=0.50000000 Y=0.50000000 Z=0.00000000</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">23c23</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">< ATOM -4: X=0.50000000 Y=0.00000000 Z=0.48343742</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">---</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">> ATOM -4: X=0.50000000 Y=0.00000000 Z=0.50000000</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">25c25</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">< ATOM -4: X=0.00000000 Y=0.50000000 Z=0.48343742 </div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">---</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 12px/normal 'Courier New';color:rgb(35,35,35);">> ATOM -4: X=0.00000000 Y=0.50000000 Z=0.50000000</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal Calibri;color:rgb(35,35,35);min-height:19px;"><br clear="none"></div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal Calibri;color:rgb(35,35,35);">In
Ref. [Com. Phys. Commun. 184 (2013) 647] two different phases were
considered, a cubic structure for centrosymmetric phase and a tetragonal
structure for the noncentrosymmetric phase. But, in tutorial1 the
lambda0.struct and lambda1.struct are both tetragonal; none of them are
cubic, why? </div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal Calibri;color:rgb(35,35,35);">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. But, there were no forces on
atoms of lambda0.struct. Ti atom is moved up from Z=0.5 in
lambda0.struct to Z=0.51517436 in lambda1.struct. If we relax the
system, maybe lambda1 gets back to lambda0? Both of the phases are
expected to be in their relaxed positions, if the phases are really
existed in nature, and if we would consider the phase transition
according to the definition of SP. </div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal Calibri;color:rgb(35,35,35);">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. This situation can be different from the last Born
effective charge calculations, since in this case we have just moved up
the atoms, whereas in the Born effective charges two opposite
displacements have been made which can balance each other. So, unlike
Boron effective charge calculations it appears that the SP calculations
cannot give a unique result?</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal Calibri;color:rgb(35,35,35);min-height:19px;"><br clear="none"></div>
<ol style="font-size:large;list-style-type:decimal;"><li style="margin:0.0px 0.0px 0.0px 0.0px;font:16.0px 'Times New Roman';color:#232323;">3)<span class="" style="white-space:pre;"> </span>And,
why we should not fully initialize the centrosymmetric one? According
to the tutorial, we should copy lambda1* to lambda0 directory, remove
lamda1.struct, rename_files lambda1 lambda0, x kgen, x dstart. This
shows that we are not allowed to initialize the lambda0.struct from
scratch. Indeed, we did it just to check what happen. When we
initialized lambda0.struct from scratch by init_lapw -b -vxc 13 -ecut -6
-numk 230 without coping lambda1*, it stopped by error in dstart. We
traced back the initialization and found that the error was due to the
symmetry and sgroup program. So, we changed the space group from (<span style="font:12.0px 'Courier New';">99 P4mm</span>) to (<span style="font:12.0px 'Courier New';">123 P4/mmm) </span>and initialized it, then ran it and did berrypi. The result is:</li></ol>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 14px/normal 'Courier New';color:rgb(35,35,35);">TOTAL POLARIZATION: 1.41209791237e-11</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">Which is different from the last one.</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);min-height:18px;"><br clear="none"></div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">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. Where is the transition in this tutorial?</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">What will be the criterion to move up the atoms?</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">What will be the role of centrosymmetric if its SP is negligible?</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">What is the difference between SP and total polarization?</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">How can one extend SP calculations to an arbitrary case?</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">Would you discuss how we can find the centrosymmetric and noncentrosymmetric ones for any cases?</div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);min-height:18px;"><br clear="none"></div><div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);min-height:18px;">
Any comments which can help us will be highly appreciated.</div><div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);min-height:18px;">
<br clear="none"></div>
<div style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:0px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">Thank for your cooperation.</div>
<div dir="ltr" style="font-size:large;margin-top:0px;margin-right:0px;margin-bottom:10px;margin-left:0px;font:normal normal normal 16px/normal 'Times New Roman';color:rgb(35,35,35);">SH. Rahimi</div></div></body></html>