[Pw_forum] Symmetry operation identification for supercell

Paolo Giannozzi p.giannozzi at gmail.com
Fri Feb 16 19:28:37 CET 2018


On Fri, Feb 16, 2018 at 2:54 PM, Krishnendu Mukherjee <
krishnendu.mukherjee789 at gmail.com> wrote:

>
> 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
>
> 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.
>

The symmetry-detecting algorithm does not allow symmetry operations with
fractional translations in a supercell. It's a limitation of the algorithm
and there is no easy workaround.

Paolo


>
>
>  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.
>



-- 
Paolo Giannozzi, Dip. Scienze Matematiche Informatiche e Fisiche,
Univ. Udine, via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222
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