# [Pw_forum] the missing symmetry of bands

Dal Corso Andrea dalcorso at sissa.it
Thu Apr 9 10:23:38 CEST 2009

```On Thu, 2009-04-09 at 15:53 +0800, 程迎春 wrote:
> Actually the symmetry of 4H-AlN is C_6v, but the pw.x can not find all
> the 12 operations. So I followed the user's guide Page 60, I changed
> PW/eqvect.f90. The value of accep is changed to be 10^-3.  The changed
> pw.x can find all 12 operations.  This change is the reason why you
> got C_3v symmetry.
>
> After I rechanged the value of accep to be 10^-5, pw.x only can find 6
> operations ?

If you want to classify the bands with C_6v symmetry you need
coordinates that have C_6v symmetry. Probably, you have to check your
coordinates by writing a small code and change the coordinates that
break the symmetry. Are you sure that you started vc-relax
with coordinates that had C_6v symmetry? I think that in this case you
should obtain final coordinates with the same symmetry. If it is
vc-relax that breaks the symmetry then, please, report the input of
vc-relax because this should not happen. However I am not an expert on
this part of QE, so maybe somebody else will look into this.

Andrea

>
>
> 2009/4/8 Dal Corso Andrea <dalcorso at sissa.it>
>
>         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
>         your
>         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.
>         > /
>         >
>         > Thank you in advance!
>         >
>         >
>         > --
>         > 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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>         > Pw_forum at pwscf.org
>         > http://www.democritos.it/mailman/listinfo/pw_forum
>         --
>         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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>         http://www.democritos.it/mailman/listinfo/pw_forum
>
>
>
> --
> Y. C. Cheng
> Department of Phyics
> Nanjing University
> Nanjing 210093
> P. R. China
> Tel: 86-25-83592907
> Email: yccheng.nju at gmail.com
> _______________________________________________
> Pw_forum mailing list
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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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