[QE-users] Discrepancy in matrix representations of symmetry between crystal and cartesian coordinates

[박민규]

Dear all,

This is to make the discussion done in gitlab more accessible to everyone.

If you want to use the matrix representations of the symmetry written in the output of QE to identify the (magnetic) space group, please refer to https://gitlab.com/QEF/q-e/-/issues/271

HTH,
============================================
Minkyu Park
Research Institute of Basic Sciences, University of Ulsan,
93, Daehak-ro, Nam-gu, Ulsan, 44610 Republic of Korea
minkyupark at ulsan.ac.kr<mailto:minkyupark at ulsan.ac.kr>
+82-52-259-1473
============================================

On 20 Jan 2021, at 10:06 AM, 박민규 <minkyupark at ulsan.ac.kr<mailto:minkyupark at ulsan.ac.kr>> wrote:

Dear all,

I observed something strange in symmetry analysis.

For example, if we run any calculation with space group Pm-3m (#221), all symmetries are written in the output. I excerpted some of them (see below). I used qe-6.6.

My question is following. For simple cubic system I expect crystal and cartesian coordinate can be taken as same if there is no special reason to take them different. Then why do we have different matrix representations for 90 deg rotation (isym = 15, 16) and 120 deg rotation (isym = 17) depending on the coordinate system?

Is it intended or just a kind of bug?


      isym = 14     180 deg rotation - cart. axis [0,1,-1]

 cryst.   s(14) = (    -1          0          0      )
                  (     0          0         -1      )
                  (     0         -1          0      )

 cart.    s(14) = ( -1.0000000  0.0000000  0.0000000 )
                  (  0.0000000  0.0000000 -1.0000000 )
                  (  0.0000000 -1.0000000  0.0000000 )


      isym = 15      90 deg rotation - cart. axis [-1,0,0]

 cryst.   s(15) = (     1          0          0      )
                  (     0          0         -1      )
                  (     0          1          0      )

 cart.    s(15) = (  1.0000000  0.0000000  0.0000000 )
                  (  0.0000000  0.0000000  1.0000000 )
                  (  0.0000000 -1.0000000  0.0000000 )


      isym = 16      90 deg rotation - cart. axis [1,0,0]

 cryst.   s(16) = (     1          0          0      )
                  (     0          0          1      )
                  (     0         -1          0      )

 cart.    s(16) = (  1.0000000  0.0000000  0.0000000 )
                  (  0.0000000  0.0000000 -1.0000000 )
                  (  0.0000000  1.0000000  0.0000000 )


      isym = 17     120 deg rotation - cart. axis [-1,-1,-1]

 cryst.   s(17) = (     0          0          1      )
                  (     1          0          0      )
                  (     0          1          0      )

 cart.    s(17) = (  0.0000000  1.0000000  0.0000000 )
                  (  0.0000000  0.0000000  1.0000000 )
                  (  1.0000000  0.0000000  0.0000000 )


Best regards,
============================================
Minkyu Park
Research Institute of Basic Sciences, University of Ulsan,
93, Daehak-ro, Nam-gu, Ulsan, 44610 Republic of Korea
minkyupark at ulsan.ac.kr<mailto:minkyupark at ulsan.ac.kr>
+82-52-259-1473
============================================

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