# [Pw_forum] Parity wave function

Andrea Dal Corso dalcorso at sissa.it
Fri Sep 11 11:47:35 CEST 2015

```The group should have inversion to check the parity with respect
inversion symmetry. You can have all the information that are in the
character tables when you know how a wavefunction transforms for a
symmetry operation, but which information is of interest to you depends
on your problem, it cannot be found in a QE manual.

Andrea

On Fri, 2015-09-11 at 13:59 +0430, Mohsen Modaresi wrote:
> Hi Andrea,
>
>
> In the bands out put,
>
>  **************************************************************************
>
>                     xk=(   0.00000,   0.00000,   0.00000  )
>
>      double point group C_s (m)
>      there are  4 classes and  2 irreducible representations
>      the character table:
>
>        E     -E    s     -s
>
> G_3    1.00 -1.00  0.00  0.00
> G_4    1.00 -1.00  0.00  0.00
>
>      imaginary part
>
>        E     -E    s     -s
>
> G_3    0.00  0.00  1.00 -1.00
> G_4    0.00  0.00 -1.00  1.00
>
>      the symmetry operations in each class and the name of the first
> element:
>
>      E             1
>
>      -E           -1
>
>      s             2
>
>      -s           -2
>
>
>      Band symmetry, C_s (m)     double point group:
>
>      e(  1 -  2) =    -27.61275  eV     2   --> G_3
>      e(  1 -  2) =    -27.61275  eV     2   --> G_4
>      e(  3 -  4) =    -27.58856  eV     2   --> G_3
>      e(  3 -  4) =    -27.58856  eV     2   --> G_4
>      e(  5 -  6) =    -26.57390  eV     2   --> G_3
>      e(  5 -  6) =    -26.57390  eV     2   --> G_4
>      e(  7 -  8) =    -26.48621  eV     2   --> G_3
>      e(  7 -  8) =    -26.48621  eV     2   --> G_4
>      e(  9 - 10) =    -26.25165  eV     2   --> G_3
>      e(  9 - 10) =    -26.25165  eV     2   --> G_4
>      e( 11 - 12) =    -26.23208  eV     2   --> G_3
>      e( 11 - 12) =    -26.23208  eV     2   --> G_4
>      e( 13 - 14) =    -25.55156  eV     2   --> G_3
>      e( 13 - 14) =    -25.55156  eV     2   --> G_4
>      e( 15 - 16) =    -25.46597  eV     2   --> G_3
>      e( 15 - 16) =    -25.46597  eV     2   --> G_4
>      e( 17 - 18) =    -25.45110  eV     2   --> G_3
>      e( 17 - 18) =    -25.45110  eV     2   --> G_4
>      e( 19 - 20) =    -25.42772  eV     2   --> G_3
>      e( 19 - 20) =    -25.42772  eV     2   --> G_4
>      e( 21 - 22) =    -25.11231  eV     2   --> G_3
>      e( 21 - 22) =    -25.11231  eV     2   --> G_4
>      e( 23 - 24) =    -25.02944  eV     2   --> G_3
>      e( 23 - 24) =    -25.02944  eV     2   --> G_4
>      e( 25 - 26) =    -13.43448  eV     2   --> G_3
>      e( 25 - 26) =    -13.43448  eV     2   --> G_4
>      e( 27 - 28) =    -10.07434  eV     2   --> G_3
>      e( 27 - 28) =    -10.07434  eV     2   --> G_4
>      e( 29 - 30) =     -8.47022  eV     2   --> G_3
>      e( 29 - 30) =     -8.47022  eV     2   --> G_4
>      e( 31 - 32) =     -8.15897  eV     2   --> G_3
>      e( 31 - 32) =     -8.15897  eV     2   --> G_4
>      e( 33 - 34) =     -8.08388  eV     2   --> G_3
>      e( 33 - 34) =     -8.08388  eV     2   --> G_4
>      e( 35 - 36) =     -7.98657  eV     2   --> G_3
>      e( 35 - 36) =     -7.98657  eV     2   --> G_4
>      e( 37 - 38) =     -7.93692  eV     2   --> G_3
>      e( 37 - 38) =     -7.93692  eV     2   --> G_4
>      e( 39 - 40) =     -5.34727  eV     2   --> G_3
>      e( 39 - 40) =     -5.34727  eV     2   --> G_4
>      e( 41 - 42) =     -4.91485  eV     2   --> G_3
>      e( 41 - 42) =     -4.91485  eV     2   --> G_4
>      e( 43 - 44) =     -4.52985  eV     2   --> G_3
>      e( 43 - 44) =     -4.52985  eV     2   --> G_4
>      e( 45 - 46) =     -3.10125  eV     2   --> G_3
>      e( 45 - 46) =     -3.10125  eV     2   --> G_4
>      e( 47 - 48) =     -1.48519  eV     2   --> G_3
>      e( 47 - 48) =     -1.48519  eV     2   --> G_4
>      e( 49 - 50) =     -1.22583  eV     2   --> G_3
>      e( 49 - 50) =     -1.22583  eV     2   --> G_4
>
>  **************************************************************************
>
> Still the Parity is missing?
> I saw some articles that report the parity interpretation with QE (Although
> most of works are with VASP).
>
> Best,
>
> On Fri, Sep 11, 2015 at 1:38 PM, Andrea Dal Corso <dalcorso at sissa.it> wrote:
>
> > The numbers indicate, for each band, the number of the representation of
> > the small group of K. The character table for the point group is written
> > in the output of the bands.x program and the number corresponds to the
> > number of the representation in the character table.
> >
> > HTH,
> >
> > Andrea
> >
> > On Fri, 2015-09-11 at 13:23 +0430, Mohsen Modaresi wrote:
> > > Dear users,
> > >
> > > I need parity wave of each bands of  band structure (in some specific K
> > > points known as TRIM points) [PRB 76, 045302] to determine the
> > > topological-->trivial phase transition.
> > > In 2013 some body ask about the parity and Prof. Giannozzi suggest to use
> > > bands.x. I did and get a .rap file. But I can not find any document to
> > > understand the out file.
> > > Here for example, I bring data file for one K point (Gama point).
> > > %%%
> > >            0.000000  0.000000  0.000000    T
> > >        1       2       1       2       1       2       1       2
> > > 1       2
> > >        1       2       1       2       1       2       1       2
> > > 1       2
> > >        1       2       1       2       1       2       1       2
> > > 1       2
> > >        1       2       1       2       1       2       1       2
> > > 1       2
> > >        1       2       1       2       1       2       1       2
> > > 1       2
> > > %%%
> > >
> > > any suggestion is appreciated.
> > > Best,
> > >
> > > Mohsen Modarresi,
> > > Department of Physics, Ferdowsi University of Mashhad, Iran.
> > > Phone +98-913-345-2131
> > > _______________________________________________
> > > Pw_forum mailing list
> > > Pw_forum at pwscf.org
> > > http://pwscf.org/mailman/listinfo/pw_forum
> >
> > --
> > 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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> > http://pwscf.org/mailman/listinfo/pw_forum
> >
>
>
>
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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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