# [Pw_forum] about C2/c point group symmetry of a monoclinic lattice.

Andrea Dal Corso dalcorso at sissa.it
Wed Dec 17 15:47:21 CET 2014

```You cannot obtain 8 symmetry operations for a monoclinic system.
C_2h is the correct point group for a system with space group C2/c.
Actually the last four symmetry equivalent positions are due to the
translations of the base centered monoclinic Bravais lattice. Using
ibrav=-13 it is not necessary to add these atoms in the list of atoms
inside the unit cell.

HTH,

Andrea

On Wed, 2014-12-17 at 13:08 +0000, Mutlu COLAKOGULLARI wrote:
> Dear All,
> I am working on a monoclinic material which has space group 15. It has C2/c point group.
> When I run the pwscf, it gives me the C2/m point group that corresponds to the space group 12.
>      point group C_2h (2/m)
>      there are  4 classes
>      the character table:
>               E     C2      i     s_h
> A_g    1.00  1.00  1.00  1.00
> B_g    1.00 -1.00  1.00 -1.00
> A_u    1.00  1.00 -1.00 -1.00
> B_u    1.00 -1.00 -1.00  1.00
> The symmetry operations of these two monoclinic space groups have 8 symmetry operations.  pwscf symmetry calculations found just 4...what about the other 4?
> I have checked the space groups  from "http://www.cryst.ehu.es/cryst/get_gen.html":
> General Positions of the Group 12 (C2/m) [unique axis b]
> 1. x,y,z
> 2. -x,y,-z
> 3. -x,-y,-z
> 4. x,-y,z
> 5. x+1/2,y+1/2,z
> 6. -x+1/2,y+1/2,-z
> 7. -x+1/2,-y+1/2,-z
>
> 8. x+1/2,-y+1/2,z
> General Positions of the Group 15 (C2/c) [unique axis b]
> 1. x,y,z
> 2. -x,y,-z+1/2
> 3. -x,-y,-z
> 4. x,-y,z+1/2
> 5. x+1/2,y+1/2,z
> 6. -x+1/2,y+1/2,-z+1/2
> 7. -x+1/2,-y+1/2,-z
> 8. x+1/2,-y+1/2,z+1/2
> Here is the lite-input:
>
> &control
>         calculation  = 'scf',
>         restart_mode = 'from_scratch',
>         pseudo_dir   = '/home//tlg2/pseudos',
>         outdir       = './outdir',
>         prefix       = 'TlGaSe2',
>         verbosity    = 'high'
>
> /
>
> &system
> ibrav = -13
>
> celldm(1)=20.166973593
> celldm(2)=0.999721681046
> celldm(3)=1.453103256
> celldm(5)=-0.173527859407
>         nat              = 32
>         ntyp             = 3
>         ecutwfc          = 65
>         ecutrho          = 650
> /
> &electrons
>         diagonalization = 'david'
>         diago_david_ndim  = 8
>         mixing_mode      = 'plain'
>         mixing_beta      = 0.7
>         mixing_ndim      = 8
>         conv_thr         = 1.0d-8,
> /
>
> ATOMIC_SPECIES
>  Tl   204.3833  Tl.pbesol-dn-rrkjus_psl.1.0.0.UPF
>  Ga    69.7230  Ga.pbesol-dn-rrkjus_psl.1.0.0.UPF
>  Se    78.9600  Se.pbesol-dn-rrkjus_psl.1.0.0.UPF
> ATOMIC_POSITIONS crystal
> Tl   0.153800000000000   0.775600000000000   0.114000000000000
> Tl   0.224400000000000   0.846200000000000   0.386000000000000
> Tl   0.846200000000000   0.224400000000000   0.886000000000000
> Tl   0.775600000000000   0.153800000000000   0.614000000000000
> Tl   0.222100000000000   0.346700000000000   0.386400000000000
> Tl   0.653300000000000   0.777900000000000   0.113600000000000
> Tl   0.777900000000000   0.653300000000000   0.613600000000000
> Tl   0.346700000000000   0.222100000000000   0.886400000000000
> Se   0.946000000000000   0.054000000000000   0.250000000000000
> Se   0.054000000000000   0.946000000000000   0.750000000000000
> Se   0.426000000000000   0.574000000000000   0.250000000000000
> Se   0.574000000000000   0.426000000000000   0.750000000000000
> Se   0.145000000000000   0.269000000000000   0.071000000000000
> Se   0.731000000000000   0.855000000000000   0.429000000000000
> Se   0.855000000000000   0.731000000000000   0.929000000000000
> Se   0.269000000000000   0.145000000000000   0.571000000000000
> Se   0.952000000000000   0.572000000000000   0.252000000000000
> Se   0.428000000000000   0.048000000000000   0.248000000000000
> Se   0.048000000000000   0.428000000000000   0.748000000000000
> Se   0.572000000000000   0.952000000000000   0.752000000000000
> Se   0.736000000000000   0.360000000000000   0.438000000000000
> Se   0.640000000000000   0.264000000000000   0.062000000000000
> Se   0.264000000000000   0.640000000000000   0.562000000000000
> Se   0.360000000000000   0.736000000000000   0.938000000000000
> Ga   0.909000000000000   0.291000000000000   0.162000000000000
> Ga   0.709000000000000   0.091000000000000   0.338000000000000
> Ga   0.091000000000000   0.709000000000000   0.838000000000000
> Ga   0.291000000000000   0.909000000000000   0.662000000000000
> Ga   0.707000000000000   0.583000000000000   0.339000000000000
> Ga   0.417000000000000   0.293000000000000   0.161000000000000
> Ga   0.293000000000000   0.417000000000000   0.661000000000000
> Ga   0.583000000000000   0.707000000000000   0.839000000000000
> K_POINTS automatic
> 2 2 1 1 1 1
> The primitive cell has been created by cif2cell code using the cif file as following:
> _journal_issue                   12
> _journal_name_full               'Chemistry of Materials'
>
> _journal_page_first              3120
> _journal_volume                  23
> _journal_year                    2011
> _chemical_formula_structural     'Tl Ga Se2'
> _chemical_formula_sum            'Ga Se2 Tl'
> _chemical_name_systematic        'Thallium Gallium Selenide'
> _space_group_IT_number           15
> _symmetry_Int_Tables_number      15
> _symmetry_space_group_name_Hall  '-C 2yc'
> _symmetry_space_group_name_H-M   'C 1 2/c 1'
> _audit_creation_date             2008/02/01
> _cell_angle_alpha                90.
> _cell_angle_beta                 99.993(6)
> _cell_angle_gamma                90.
> _cell_formula_units_Z            16
> _cell_length_a                   10.779(2)
> _cell_length_b                   10.776(1)
> _cell_length_c                   15.663(5)
> _cell_volume                     1791.7(7)
> _refine_ls_R_factor_all          0.0652
> _[local]_cod_data_source_file    cm200946y_si_002.cif
> _[local]_cod_data_source_block   157752-ICSD
> _[local]_cod_chemical_formula_sum_orig 'Ga1 Se2 Tl1'
> _cod_original_cell_volume        1791.73
> _cod_database_code               4000782
> loop_
> _symmetry_equiv_pos_site_id
> _symmetry_equiv_pos_as_xyz
> 1 'x, -y, z+1/2'
> 2 '-x, -y, -z'
> 3 '-x, y, -z+1/2'
> 4 'x, y, z'
> 5 'x+1/2, -y+1/2, z+1/2'
> 6 '-x+1/2, -y+1/2, -z'
> 7 '-x+1/2, y+1/2, -z+1/2'
> 8 'x+1/2, y+1/2, z'
> loop_
> _atom_site_aniso_label
> _atom_site_aniso_type_symbol
> _atom_site_aniso_U_11
> _atom_site_aniso_U_22
> _atom_site_aniso_U_33
> _atom_site_aniso_U_12
> _atom_site_aniso_U_13
> _atom_site_aniso_U_23
> Tl1 Tl1+ 0.052(6) 0.063(5) 0.06(2) -0.022(3) 0.005(8) 0.000(5)
> Tl2 Tl1+ 0.044(6) 0.044(6) 0.07(2) -0.022(3) 0.005(8) 0.002(5)
> Ga1 Ga3+ 0.015(9) 0.001(6) 0.05(3) 0.009(6) 0.01(2) -0.019(9)
> Ga2 Ga3+ 0.019(7) 0.037(9) 0.00(3) -0.008(9) -0.01(1) -0.01(1)
> Se1 Se2- 0.03(1) 0.02(1) 0.06(5) 0. 0.02(2) 0.
> Se2 Se2- 0.006(9) 0.001(7) 0.06(4) 0. -0.01(2) 0.
> Se3 Se2- 0.04(1) 0.05(1) 0.01(4) 0.01(1) -0.01(2) -0.02(1)
> Se4 Se2- 0.012(6) 0.021(7) 0.06(4) 0.01(1) -0.018(9) -0.018(5)
> Se5 Se2- 0.05(1) 0.06(1) 0.00(4) -0.053(9) -0.01(2) -0.02(1)
> loop_
> _atom_site_label
> _atom_site_type_symbol
> _atom_site_symmetry_multiplicity
> _atom_site_Wyckoff_symbol
> _atom_site_fract_x
> _atom_site_fract_y
> _atom_site_fract_z
> _atom_site_occupancy
> _atom_site_attached_hydrogens
> Tl1 Tl1+ 8 f 0.4647(6) 0.3109(5) 0.1140(9) 1. 0
> Tl2 Tl1+ 8 f 0.2844(4) 0.0623(5) 0.3864(8) 1. 0
> Ga1 Ga3+ 8 f 0.100(1) 0.191(2) 0.162(2) 1. 0
> Ga2 Ga3+ 8 f 0.145(1) 0.438(1) 0.339(2) 1. 0
> Se1 Se2- 4 e 0. 0.054(2) 0.250 1. 0
> Se2 Se2- 4 e 0. 0.574(1) 0.250 1. 0
> Se3 Se2- 8 f 0.207(1) 0.062(1) 0.071(2) 1. 0
> Se4 Se2- 8 f 0.262(1) 0.310(1) 0.252(2) 1. 0
> Se5 Se2- 8 f 0.048(2) 0.312(1) 0.438(3) 1. 0
> loop_
> _atom_type_symbol
> _atom_type_oxidation_number
> Ga3+ 3
> Se2- -2
> Tl1+ 1
> loop_
> _citation_id
> _citation_year
> _citation_page_first
> _citation_page_last
> primary 2007 663 666
> Are there something wrong in my input file or primitive cell?
> With my best wishes,
>      Mutlu.
>
> ------------------------------------------Dr. Mutlu COLAKOGULLARITrakya Universitesi Fen FakultesiFizik Bolumu22030 Merkez-EDİRNE
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--
Andrea Dal Corso                    Tel. 0039-040-3787428
SISSA, Via Bonomea 265              Fax. 0039-040-3787249
I-34136 Trieste (Italy)             e-mail: dalcorso at sissa.it

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