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<p class="MsoNormal">Dear developers of QE,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Hope you are all doing well in this hard time!<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">I’m trying to fix conflictions between the k-point branch and the phonon code (Merge Request !292). As I was debugging the search of small group of q points, I found the inversion detection of ph.x could get wrong result. The part of the
code is in LR_Modules/set_small_group_of_q.f90, Line 54 – Line 62:<o:p></o:p></p>
<p class="MsoNormal"> nsymq = copy_sym ( nsym, sym )<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"> !<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"> CALL inverse_s ( )<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"> !<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"> ! check if inversion (I) is a symmetry. If so, there should be nsymq/2<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"> ! symmetries without inversion, followed by nsymq/2 with inversion<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"> ! Since identity is always s(:,:,1), inversion should be s(:,:,1+nsymq/2)<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"> !<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"> invsymq = ALL ( s(:,:,nsymq/2+1) == -s(:,:,1) )<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><o:p> </o:p></p>
<p class="MsoNormal">Since the list of sym ops in s(:,:,48) has been rotated by copy_sym() once for each distinct q point, there is no guarantee that inversion symmetry must sit at “nsymq/2 + 1”. It’s true only if copy_sym() is called once on s(:,:,48).
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">As an example, I ran phonon on Si with a 4x4x4 q point grid. The small group of (0.5,-0.5,0.5) had inversion, but it’s listed at 9 out of 12 operations. Invsymq was subsequently set to .False.. The list of sym. ops. for small group of this
q, in the order after calling copy_sym(), is:<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">identity
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">inv. 180 deg rotation - cart. axis [-1,0,1]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">120 deg rotation - cart. axis [-1,1,-1]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">inv. 180 deg rotation - cart. axis [1,1,0]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">120 deg rotation - cart. axis [1,-1,1]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">inv. 180 deg rotation - cart. axis [0,1,1]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">180 deg rotation - cart. axis [0,1,1]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">inversion
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">180 deg rotation - cart. axis [-1,0,1]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">180 deg rotation - cart. axis [1,1,0]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">inv. 120 deg rotation - cart. axis [1,-1,1]
<o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in">inv. 120 deg rotation - cart. axis [-1,1,-1]
<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">A simple fix would be to replace the line “invsymq = ALL ( s(:,:,nsymq/2+1) == -s(:,:,1) )” by an iteration over the first nsymq operations of s(:,:,48). Although this invsymq is not propagated to other routines, it might be worth checking
similar places of searching inversion in other parts of phonon code / LR code.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">The confliction of git branch “k-point” is almost fixed, and a detailed description can be found at:
<a href="https://arxiv.org/abs/1907.13610">https://arxiv.org/abs/1907.13610</a>. Any opinion and suggestion on its integration with QE are welcomed and appreciated!<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Best wishes,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Yunzhe (Phil) Wang<o:p></o:p></p>
<p class="MsoNormal">Mueller Research Group<o:p></o:p></p>
<p class="MsoNormal">Department of Materials Science and Engineering<o:p></o:p></p>
<p class="MsoNormal">Johns Hopkins University<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
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