[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
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.quantum-espresso.org/pipermail/users/attachments/20180216/4fa52a41/attachment.html>
More information about the users
mailing list