<html><body><div style="color:#000; background-color:#fff; font-family:HelveticaNeue, Helvetica Neue, Helvetica, Arial, Lucida Grande, Sans-Serif;font-size:14pt"><div><br></div><div style="font-size: large;">Dear Prof. Rubel and Sheikh,</div><div style="font-size: large;"><span style="color: rgb(0, 0, 0); font-size: 13px;">> Are there total or partial forces? What are the values?</span><br></div><div style="font-size: large;">Oops! It was partial force that was large: </div><div style="font-size: large;"><div style="font-size: large;">:FOR002: 2.ATOM 6.892 0.000 0.000 6.892 partial forces</div><div style="font-size: large;"><br></div><div style="font-size: large;">Then, I performed one more iteration by adding -fc flag to my run to sum the Hellmann-Feynman, core, and valance forces, run_lapw -fc 1. Here, I
would confirm that lambda1 is indeed in its relaxed position since the total forces are very small, as Sheikh also indicated:</div><div style="font-size: large;">:FOR002: 2.ATOM 0.160246 0.000000 0.000000 -0.160246 total forces</div><div><br></div><div>So, most of the ambiguities are now made clear by your valuable comments. </div><div><br></div><div><span style="color: rgb(0, 0, 0); font-size: 13px;">> We do not want Wien2k to realize its higher symmetry. Therefore, the<br clear="none"> initialization is done for low-symmetry lambda1 case only. Both<br clear="none">structures should have identical symmetry operations in order to<br clear="none">ensure consistency and comparability of the results.</span><br></div><div><br></div><div>Most of our ambiguities originated from lambda0 structure, since it was not cubic. We suspected that the tetragonal lambda1 is
created by moving up the atoms of the tetragonal lambda0. This was why when we got nonzero forces, we carelessly thought that the system was under stress. I suggest to change lambda0 structure to a cubic one in the next release of the BerryPi code. In this cases users will more easily realize that a phase transition is occurred from lambda0 to lambda1. This will be also more compatible with the BerryPi paper. For sure, we used the cubic structure, and the result is not changed too much.</div><div><br></div></div><div><span style="color: rgb(0, 0, 0); font-size: 13px;"><div id="yiv2172167512yui_3_13_0_ym1_1_1386043842584_55268"><div style="font-size: large; display: inline;">> </div>Also you can try to understand more about modern theory of polarization from here <a id="yiv2172167512yui_3_13_0_ym1_1_1386043842584_55270" style="margin: 0px; padding: 0px; color: rgb(25, 106, 212); text-decoration: underline; outline-style: none;"
href="http://www.physics.rutgers.edu/~dhv/pubs/local_preprint/dv_fchap.pdf" target="_blank" rel="nofollow" shape="rect">http://www.physics.rutgers.edu/~dhv/pubs/local_preprint/dv_fchap.pdf</a></div><div><br></div></span></div><div><div style="font-size: large;">Sheikh, I was reading PRB47, 1651 and PRL101, 037210 of David Vanderbilt and his coauthors. Thank you Sheikh, your informed manuscript of David and coworkers will certainly help me. </div><br></div><span style="color: rgb(0, 0, 0); font-size: 13px;"><div style="font-size: large; display: inline;"> > </div><div>This part I am not sure, especially for GaN. The thinking should start<br clear="none">with analysis of measurable quantities/effects, which you would like<br clear="none"></div></span><div><span style="color: rgb(0, 0, 0); font-size: 13px;">to model.</span><span style="color: rgb(0, 0, 0); font-size: 13px;"><div style="font-size: large; display: inline;">
</div></span></div><div><span style="color: rgb(0, 0, 0); font-size: 13px;"><div style="font-size: large; display: inline;"> </div></span></div><div><span style="color: rgb(0, 0, 0); font-size: 13px;"><div style="font-size: large; display: inline;"> We are thinking about it. Based on the definition of PS, "the change in polarization that occurs when the crystal undergoes a phase change from the centrosymmetric structure to a structure without an inversion symmetry (Ps=Pnc-Pc)" as given in the BerryPi paper, we are not sure whether we can use the following trick to create the noncentrosymmetic structure from a centrosymmetric structure.</div> </span></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display: inline;"> The trick is that we apply spin-orbit coupling on the centrosymmetic structure by initso_lapw. In this
case initso_lapw will create a new structure with no inversion symmetry. Maybe we can use this structure as our noncentrosymmetric structure. </div> <br></span></font></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display: inline;"> What do you think about this trick?</div></span></font></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display: inline;"><br></div></span></font></div><div><span style="color: rgb(0, 0, 0); font-size: 13px;"><div style="font-size: large; display: inline;"> > </div>You can make a transition by choosing an intermediate structure (say<br clear="none">lambda05). I am not aware of unique way to define the intermediate<br clear="none">state: we know for sure only lambda0 and lambda1.
But you can imagine<br clear="none"> lambda1 as a distorted case of lambda0. For lambda05 you need half of<br clear="none">the distortions. Of course, NO optimization of atomic positions should<br clear="none">be performed for lambda05. Otherwise you will end up with lambda1<br clear="none"> again.<br clear="none"></span></div><div><span style="color: rgb(0, 0, 0); font-size: 13px;"><br></span></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display: inline;"> Do you think that the intermediate is necessary? By transition I meant transition between lambda0 as the centrosymmetric phase and lambda1 as the noncentrosymmetic phase.</div></span></font></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display:
inline;"><br></div></span></font></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display: inline;"> Thank you for your cooperation,</div></span></font></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display: inline;"><br></div></span></font></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display: inline;"> Best regards,</div></span></font></div><div><font color="#000000" face="'Helvetica Neue', 'Segoe UI', Helvetica, Arial, 'Lucida Grande', sans-serif" size="4"><span><div style="font-size: large; display: inline;" dir="ltr"> SH. Rahimi</div></span></font></div></div></body></html>