# [Pw_forum] the missing symmetry of bands

Dal Corso Andrea dalcorso at sissa.it
Wed Apr 8 14:49:58 CEST 2009

```On Wed, 2009-04-08 at 19:34 +0800, 程迎春 wrote:
> Dear PWscf users,
>         In my recent calculation of 4H-AlN (ABCB stacking sequence),
> the band symmetry seems to be missed in bands.x calculation.  The
> output of bands.x is as following:
>  **************************************************************************
>                     xk=(   0.00000,   0.00000,   0.00000  )
>      double point group C_6v (6mm)
>      there are  9 classes and  3 irreducible representations
>      the character table:
>        E     -E     C2    2C3  -2C3   2C6  -2C6   3s_v  3s_d
>                    -C2                           -3s_v -3s_d
> G_7    2.00 -2.00  0.00  1.00 -1.00  1.73 -1.73  0.00  0.00
> G_8    2.00 -2.00  0.00  1.00 -1.00 -1.73  1.73  0.00  0.00
> G_9    2.00 -2.00  0.00 -2.00  2.00  0.00  0.00  0.00  0.00
>      the symmetry operations in each class:
>      E             1
>       C2  -C2      2   -2
>       2C6          3    4
>       2C3          5    6
>       3s_v-3s_v    7   -7    9   10  -10   -9
>       3s_d-3s_d    8   -8   12  -11   11  -12
>      -E           -1
>      -2C6         -3   -4
>      -2C3         -5   -6
>      Band symmetry, C_6v (6mm)  double point group:
>      e(  1 -  2) =     -8.01764  eV     2   -->   ?
>      e(  3 -  4) =     -7.17573  eV     2   -->   ?
>      e(  5 -  6) =     -7.13551  eV     2   -->   ?
>      e(  7 -  8) =     -5.93881  eV     2   -->   ?
>      e(  9 - 10) =      1.12077  eV     2   --> G_7
>      e(  9 - 10) =      1.12077  eV     2   -->   0 G_8
>      e( 11 - 12) =      3.70317  eV     2   -->   0 G_7
>      e( 11 - 12) =      3.70317  eV     2   --> G_8
>      e( 13 - 14) =      3.76782  eV     2   -->   ?
>      e( 15 - 16) =      6.34352  eV     2   -->   ?
>      e( 17 - 18) =      6.35869  eV     2   --> G_9
>      e( 19 - 20) =      6.58061  eV     2   -->   ?
>      e( 21 - 22) =      6.59473  eV     2   --> G_9
>      e( 23 - 24) =      6.65103  eV     2   -->   ?
>      e( 25 - 26) =      6.66500  eV     2   --> G_9
>      e( 27 - 28) =      6.91040  eV     2   -->   ?
>      e( 29 - 30) =      6.92400  eV     2   --> G_9
>      e( 31 - 32) =      7.00967  eV     2   --> G_7
>      e( 31 - 32) =      7.00967  eV     2   -->   0 G_8
>      e( 33 - 34) =     11.19288  eV     2   -->   ?
>      e( 35 - 36) =     13.31415  eV     2   -->   ?
>      e( 37 - 38) =     13.59769  eV     2   -->   ?
>      e( 39 - 40) =     14.02975  eV     2   -->   ?
>      e( 41 - 42) =     17.15974  eV     2   -->   ?
>      e( 43 - 44) =     17.32327  eV     2   -->   ?
>      e( 45 - 46) =     17.92003  eV     2   -->   ?
>  **************************************************************************
> My question are :
> 1. what does "?" mean in "  e(  1 -  2) =     -8.01764  eV     2

It means that the symmetry finder is confused. The bands have not a
symmetry that it recognizes.
There are several reasons for this:

1) The 'scf' and 'bands' calculations have been run with slightly
different parameters. (solution: recheck your input)

2) Your atomic positions are not sufficiently accurate: the number of
digits is sufficient for pw.x to find the symmetries but the
wavefunctions are sufficiently inaccurate to confuse the symmetry
analyzer. (solution: correct your atomic positions)

3) If 1) and 2) do not work and you are sure about your coordinates,
then probably there is a bug in the symmetry analyzer. (solution: report
to the forum. I will try to solve it if I can).

In your particular case: I am confused. On my PC the symmetry found with
your coordinates is C_3v and the symmetry analyzer seems to work. So
atomic positions.

Hope this helps.

Andrea

>  -->   ?"      ?
> 2. what does "0" mean in "     e(  9 - 10) =      1.12077  eV     2
> -->   0 G_8" ?
> 3. In 2H-AlN(AB stacking sequence), all the symmetries of bands are
> shown. Why in 4H-AlN, it seems much more complicated.
>
> The input files about 4H-AlN for pw.x and bands.x are as following:
> scf.in
> &control
>                     title = 2h_aln,
>                       prefix = '4h_band',
>                  calculation = 'scf' ,
>                 restart_mode = 'from_scratch' ,
>                   wf_collect = .false. ,
>                       outdir = './' ,
>                       wfcdir = './' ,
>                   pseudo_dir = './' ,
>                      tstress = .true. ,
>                      tprnfor = .true. ,
>                    wf_collect = .true. ,
>  /
>  &SYSTEM
>                        ibrav = 4,
>                    celldm(1) = 5.866002785691,
>                    celldm(3) = 3.238615289089,
>                          nat = 8,
>                         ntyp = 2,
>                      ecutwfc = 80,
>                        nbnd  = 46,
>                        nosym = .false. ,
>                      lspinorb = .true.,
>                      noncolin= .true.,
>                    starting_magnetization=0.00,
>  /
>  &ELECTRONS
>             electron_maxstep = 100,
>                     conv_thr = 1.D-10,
>  /
> ATOMIC_SPECIES
>     N   14.00700  N.rel-pbe-rrkjus.UPF
>    Al   26.98200  Al.rel-pbe-rrkj.UPF
> ATOMIC_POSITIONS (crystal)
> N        0.000000000   0.000000000  -0.000722968
> N        0.000000000   0.000000000   0.499277032
> N        0.333333333   0.666666667   0.249293699
> N        0.666666667   0.333333333   0.749293699
> Al       0.000000000   0.000000000   0.188800277
> Al       0.000000000   0.000000000   0.688800277
> Al       0.333333333   0.666666667   0.437593675
> Al       0.666666667   0.333333333   0.937793675
> K_POINTS automatic
>   8 8 8 1 1 1
>
> band.in
> &control
>                       title = 2h_aln,
>                       prefix = '4h_band',
>                  calculation = 'bands' ,
>                 restart_mode = 'from_scratch' ,
>                   wf_collect = .false. ,
>                       outdir = './' ,
>                       wfcdir = './' ,
>                   pseudo_dir = './' ,
>  /
>  &SYSTEM
>                        ibrav = 4,
>                    celldm(1) = 5.866002785691,
>                    celldm(3) = 3.238615289089,
>                          nat = 8,
>                         ntyp = 2,
>                      ecutwfc = 80,
>                      nbnd=46,
>                          lspinorb = .true.,
>                      noncolin= .true.,
>                    starting_magnetization=0.0,
>  /
>  &ELECTRONS
>             electron_maxstep = 100,
>                     conv_thr = 1.D-10,
>  /
> ATOMIC_SPECIES
>     N   14.00700  N.rel-pbe-rrkjus.UPF
>    Al   26.98200  Al.rel-pbe-rrkj.UPF
> ATOMIC_POSITIONS (crystal)
> N        0.000000000   0.000000000  -0.000722968
> N        0.000000000   0.000000000   0.499277032
> N        0.333333333   0.666666667   0.249293699
> N        0.666666667   0.333333333   0.749293699
> Al       0.000000000   0.000000000   0.188800277
> Al       0.000000000   0.000000000   0.688800277
> Al       0.333333333   0.666666667   0.437593675
> Al       0.666666667   0.333333333   0.937793675
> K_POINTS
>          2
>   0.000000  0.000000  0.000000  1.00
>   0.000000  0.000000  0.083333  1.00
>
>
> bands.in
> &inputpp
> prefix='4h_band'
> outdir='./'
> filband='spin.dat'
> lsigma(3)=.true.
> lsym=.true.
> /
>
>
>
> --
> Y. C. Cheng
> Department of Phyics
> Nanjing University
> Nanjing 210093
> P. R. China
> Tel: 86-25-83592907
> Email: yccheng.nju at gmail.com
>
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--
Andrea Dal Corso                    Tel. 0039-040-3787428
SISSA, Via Beirut 2/4               Fax. 0039-040-3787528
34014 Trieste (Italy)               e-mail: dalcorso at sissa.it

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