[Pw_forum] Symmetry operation identification for supercell

Krishnendu Mukherjee krishnendu.mukherjee789 at gmail.com
Fri Feb 16 14:54:42 CET 2018


Dear Expert,

 I have created a Zr supercell with 16 atoms (the positions of the atoms
are given in the input file below). Zr has the spacegroup P 63/m m c (No.
194).

 However, in output I notice,

Found symmetry operation: I + ( -0.5000  0.5000  0.0000)
     This is a supercell, fractional translations are disabled
     Found symmetry operation: I + ( -0.5000  0.5000  0.0000)
     This is a supercell, fractional translations are disabled

Now, although the space group has no fractional translational along a and
b, I think the fractional translations are identified as it is a supercell.
But why there is no fractional translation identified along c? There is a
fractional transformation along c in this spacegroup.

 I will be grateful for your kind explanation. I am attaching the input
below and some part of the output.
-------------------------------------------
cat > thermo_control << EOF
 &INPUT_THERMO
  what='mur_lc_elastic_constants',
  frozen_ions=.FALSE.
 /
EOF

cat > zr.elastic.in << EOF
 &control
    calculation = 'scf'
    restart_mode='from_scratch',
    prefix='zr',
    tstress = .true.,
   tprnfor = .true.,
    pseudo_dir = '$PSEUDO_DIR/',
    outdir='$TMP_DIR/'
 /
 &system
    ibrav=  4,
    celldm(1) =12.241645,
    celldm(3) = 1.59185,
    nat= 16,
    ntyp= 1,
    ecutwfc=50.0,
   ecutrho = 430,
   occupations='smearing',
   smearing='marzari-vanderbilt',
   degauss=0.02
   starting_magnetization(1) = 0.7,
   use_all_frac = .true.
 /
 &electrons
    conv_thr =  1.0d-10
 /
ATOMIC_SPECIES
 Zr  91.22  Zr.pz-spn-kjpaw_psl.1.0.0.UPF
ATOMIC_POSITIONS (angstrom)
Zr    0.000000    1.870038    1.289000
Zr    3.239000    3.740075    9.023001
Zr    1.619500    4.675094    1.289000
Zr    1.619500    0.935019    9.023001
Zr   -1.619500    4.675094    1.289000
Zr    4.858500    0.935019    9.023001
Zr    3.239000    3.740075    3.867000
Zr    1.619500    0.935019    3.867000
Zr    4.858500    0.935019    3.867000
Zr    0.000000    1.870038    6.445000
Zr    1.619500    4.675094    6.445000
Zr   -1.619500    4.675094    6.445000
Zr    3.239000    1.870038    1.289000
Zr    0.000000    3.740075    9.023001
Zr    0.000000    3.740075    3.867000
Zr    3.239000    1.870038    6.445000
K_POINTS AUTOMATIC
5 5 3 0 0 0


EOF

---------------------------------------------------------------------

Info: using nr1, nr2, nr3 values from input
     Found symmetry operation: I + ( -0.5000  0.5000  0.0000)
     This is a supercell, fractional translations are disabled
     Found symmetry operation: I + ( -0.5000  0.5000  0.0000)
     This is a supercell, fractional translations are disabled


     Computing the elastic constants at the minimum volume

     FFT mesh: (   81,   81,  135 )

     Bravais lattice:

     ibrav=  4: hexagonal
     Cell parameters:

     alat=  12.241645 a.u., c/a=   1.591850


     Starting primitive lattice vectors:
     crystal axes: (cart. coord. in units of alat)

               a(1) = (   1.000000   0.000000   0.000000 )
               a(2) = (  -0.500000   0.866025   0.000000 )
               a(3) = (   0.000000   0.000000   1.591850 )

     Starting reciprocal lattice vectors:
     reciprocal axes: (cart. coord. in units 2 pi/alat)

               b(1) = (  1.000000  0.577350 -0.000000 )
               b(2) = (  0.000000  1.154701  0.000000 )
               b(3) = (  0.000000 -0.000000  0.628200 )

     Starting atomic positions in Cartesian axes:

     site n.     atom                  positions (alat units)
         1           Zr  tau(   1) = (   0.0000000   0.2886752   0.1989812
)
         2           Zr  tau(   2) = (   0.5000000   0.5773503   1.3928684
)
         3           Zr  tau(   3) = (   0.2500000   0.7216879   0.1989812
)
         4           Zr  tau(   4) = (   0.2500000   0.1443376   1.3928684
)
         5           Zr  tau(   5) = (  -0.2500000   0.7216879   0.1989812
)
         6           Zr  tau(   6) = (   0.7500001   0.1443376   1.3928684
)
         7           Zr  tau(   7) = (   0.5000000   0.5773503   0.5969435
)
         8           Zr  tau(   8) = (   0.2500000   0.1443376   0.5969435
)
         9           Zr  tau(   9) = (   0.7500001   0.1443376   0.5969435
)
        10           Zr  tau(  10) = (   0.0000000   0.2886752   0.9949059
)
        11           Zr  tau(  11) = (   0.2500000   0.7216879   0.9949059
)
        12           Zr  tau(  12) = (  -0.2500000   0.7216879   0.9949059
)
        13           Zr  tau(  13) = (   0.5000000   0.2886752   0.1989812
)
        14           Zr  tau(  14) = (   0.0000000   0.5773503   1.3928684
)
        15           Zr  tau(  15) = (   0.0000000   0.5773503   0.5969435
)
        16           Zr  tau(  16) = (   0.5000000   0.2886752   0.9949059
)

     Starting atomic positions in crystallographic axes:

     site n.     atom                  positions (cryst. coord.)
         1           Zr  tau(   1) = (  0.1666667  0.3333334  0.1250000  )
         2           Zr  tau(   2) = (  0.8333334  0.6666667  0.8749998  )
         3           Zr  tau(   3) = (  0.6666667  0.8333334  0.1250000  )
         4           Zr  tau(   4) = (  0.3333334  0.1666667  0.8749998  )
         5           Zr  tau(   5) = (  0.1666667  0.8333334  0.1250000  )
         6           Zr  tau(   6) = (  0.8333334  0.1666667  0.8749998  )
         7           Zr  tau(   7) = (  0.8333334  0.6666667  0.3749999  )
         8           Zr  tau(   8) = (  0.3333334  0.1666667  0.3749999  )
         9           Zr  tau(   9) = (  0.8333334  0.1666667  0.3749999  )
        10           Zr  tau(  10) = (  0.1666667  0.3333334  0.6249998  )
        11           Zr  tau(  11) = (  0.6666667  0.8333334  0.6249998  )
        12           Zr  tau(  12) = (  0.1666667  0.8333334  0.6249998  )
        13           Zr  tau(  13) = (  0.6666668  0.3333334  0.1250000  )
        14           Zr  tau(  14) = (  0.3333334  0.6666667  0.8749998  )
        15           Zr  tau(  15) = (  0.3333334  0.6666667  0.3749999  )
        16           Zr  tau(  16) = (  0.6666668  0.3333334  0.6249998  )

     The energy minimization will require  9 scf calculations

     The point group 118 D_3d (-3m) is compatible with the Bravais lattice.

     The rotation matrices with the order used inside thermo_pw are:

     12 Sym. Ops., with inversion, found


                          s                  frac. trans.

      isym =  1     identity

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

 cart.    s( 1) = (  1.000  0.000  0.000 )
                  (  0.000  1.000  0.000 )
                  (  0.000  0.000  1.000 )


      isym =  2     180 deg rotation - cart. axis [1,0,0]

 cryst.   s( 2) = (  1    0    0   )
                  ( -1   -1    0   )
                  (  0    0   -1   )

 cart.    s( 2) = (  1.000  0.000  0.000 )
                  (  0.000 -1.000  0.000 )
                  (  0.000  0.000 -1.000 )


      isym =  3     120 deg rotation - cryst. axis [0,0,1]

 cryst.   s( 3) = (  0    1    0   )
                  ( -1   -1    0   )
                  (  0    0    1   )

 cart.    s( 3) = ( -0.500 -0.866  0.000 )
                  (  0.866 -0.500  0.000 )
                  (  0.000  0.000  1.000 )


      isym =  4     120 deg rotation - cryst. axis [0,0,-1]

 cryst.   s( 4) = ( -1   -1    0   )
                  (  1    0    0   )
                  (  0    0    1   )

 cart.    s( 4) = ( -0.500  0.866  0.000 )
                  ( -0.866 -0.500  0.000 )
                  (  0.000  0.000  1.000 )


      isym =  5     180 deg rotation - cryst. axis [0,1,0]

 cryst.   s( 5) = ( -1   -1    0   )
                  (  0    1    0   )
                  (  0    0   -1   )

 cart.    s( 5) = ( -0.500 -0.866  0.000 )
                  ( -0.866  0.500  0.000 )
                  (  0.000  0.000 -1.000 )


      isym =  6     180 deg rotation - cryst. axis [1,1,0]

 cryst.   s( 6) = (  0    1    0   )
                  (  1    0    0   )
                  (  0    0   -1   )

 cart.    s( 6) = ( -0.500  0.866  0.000 )
                  (  0.866  0.500  0.000 )
                  (  0.000  0.000 -1.000 )


      isym =  7     inversion

 cryst.   s( 7) = ( -1    0    0   )
                  (  0   -1    0   )
                  (  0    0   -1   )

 cart.    s( 7) = ( -1.000  0.000  0.000 )
                  (  0.000 -1.000  0.000 )
                  (  0.000  0.000 -1.000 )


      isym =  8     inv. 180 deg rotation - cart. axis [1,0,0]

 cryst.   s( 8) = ( -1    0    0   )
                  (  1    1    0   )
                  (  0    0    1   )

 cart.    s( 8) = ( -1.000  0.000  0.000 )
                  (  0.000  1.000  0.000 )
                  (  0.000  0.000  1.000 )


      isym =  9     inv. 120 deg rotation - cryst. axis [0,0,1]

 cryst.   s( 9) = (  0   -1    0   )
                  (  1    1    0   )
                  (  0    0   -1   )

 cart.    s( 9) = (  0.500  0.866  0.000 )
                  ( -0.866  0.500  0.000 )
                  (  0.000  0.000 -1.000 )


      isym = 10     inv. 120 deg rotation - cryst. axis [0,0,-1]

 cryst.   s(10) = (  1    1    0   )
                  ( -1    0    0   )
                  (  0    0   -1   )

 cart.    s(10) = (  0.500 -0.866  0.000 )
                  (  0.866  0.500  0.000 )
                  (  0.000  0.000 -1.000 )


      isym = 11     inv. 180 deg rotation - cryst. axis [0,1,0]

 cryst.   s(11) = (  1    1    0   )
                  (  0   -1    0   )
                  (  0    0    1   )

 cart.    s(11) = (  0.500  0.866  0.000 )
                  (  0.866 -0.500  0.000 )
                  (  0.000  0.000  1.000 )


      isym = 12     inv. 180 deg rotation - cryst. axis [1,1,0]

 cryst.   s(12) = (  0   -1    0   )
                  ( -1    0    0   )
                  (  0    0    1   )

 cart.    s(12) = (  0.500 -0.866  0.000 )
                  ( -0.866 -0.500  0.000 )
                  (  0.000  0.000  1.000 )


     point group D_3d (-3m)
     there are  6 classes
     the character table:

       E     2C3   3C2'  i     2S6   3s_d
A_1g   1.00  1.00  1.00  1.00  1.00  1.00
A_2g   1.00  1.00 -1.00  1.00  1.00 -1.00
E_g    2.00 -1.00  0.00  2.00 -1.00  0.00
A_1u   1.00  1.00  1.00 -1.00 -1.00 -1.00
A_2u   1.00  1.00 -1.00 -1.00 -1.00  1.00
E_u    2.00 -1.00  0.00 -2.00  1.00  0.00

     the symmetry operations in each class and the name of the first
element:

     E        1
          identity
     2C3      3    4
          120 deg rotation - cryst. axis [0,0,1]
     3C2'     2    5    6
          180 deg rotation - cart. axis [1,0,0]
     i        7
          inversion
     2S6      9   10
          inv. 120 deg rotation - cryst. axis [0,0,1]
     3s_d     8   11   12
          inv. 180 deg rotation - cart. axis [1,0,0]

     Space group identification,  12 symmetries:

     Bravais lattice   4  hexagonal
     Point group number  25 / 118  D_3d (-3m)

     Nonsymmorphic operations not found: All fractional translations vanish
     Symmetries of the point group in standard order

        1       E   1
        2      3z  27
        3     3-z  28
        4      2x   4
        5    2110  32
        6    2010  31
        7       i  33
        8     i3z  59
        9    i3-z  60
       10     i2x  36
       11   i2110  64
       12   i2010  63


     Space group nymber  164

     Space group P-3m1   (group number 164).
     The origin coincides with the ITA tables.

     The Laue class is D_3d (-3m)

     In this class the elastic tensor is

     ( c11  c12  c13  c14   .    .  )
     ( c12  c11  c13 -c14   .    .  )
     ( c13  c13  c33   .    .    .  )
     ( c14 -c14   .   c44   .    .  )
     (  .    .    .    .   c44  c14 )
     (  .    .    .    .   c14   X  )
     X=(c11-c12)/2

     It requires three strains: e1, e3, and e4
     for a total of 12 scf calculations

     ----------------------------------------------------------------------
     Ions are relaxed in each calculation
     ----------------------------------------------------------------------

--------------------------------------------------------

Thanks,
Best regards,
Krishnendu


-- 
Dr. Krishnendu Mukherjee,

Principal Scientist,
CSIR-NML,
Jamshedpur.
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