[Pw_forum] symmetry operations in PW

[alexandra.carvalho at epfl.ch]

Dear Gabriele and Manoj,

In fact I should clarify that I meant that rotations about directed axes belong
to different classes if the axes are not inverted by symmetry.
(The word 'equivalent' was a poor choice...)

Alexandra

Quoting Gabriele Sclauzero <sclauzer at sissa.it>:

> Dear Manoj and Alexandra,
>
>    in my limited and maybe naive knowledge of group theory I think that
>
> alexandra.carvalho at epfl.ch wrote:
> > Dear Manoj,
> >
> > I do not know about the definitions intrinsic to pwscf,
> > but in group theory directed opperations are not allways equivalent.
>
>
> Rotation of 90 deg about z and about -z are _different_ operations (in every
> group to
> which they belong...). Maybe pwscf uses a naive way to call symmetry
> operations, but you
> may call rotation of 90 deg about -z as "rotation of -90 deg about z" so
> maybe it's more
> clear (do you know the right hand rule?).
> If the rotation of 90 deg about z is present, also the rotation of -90 deg
> about z must be
> present (from the definition of group), as well as the rotation of 180 deg
> about z (which
> you can obtain by applying the rotation of 90 twice). This gives you a C_4
> symmetry about
> the z axis (then if you will add more symmetry operations you will have
> higher symmetry).
>
>  > In this case, the rotations about -z and z will be inequivalent
> > if there is no opperation of the group which reverses the sense of the z
> axis.
>
> I don't understand what do you mean by "equivalent/inequivalent" in this
> case...
>
> Hope it helps,
>
> GS
>
> >
> > For example, in the T group there are 8 C3 opperations although there
> > are only four cube diagonals- see Tinkham "Group Theory and Quantum
> > mechanics" 2003 pp 58.
> >
> > Alexandra Carvalho
> > EPFL Lausanne
> >
> > Quoting Manoj Srivastava <manoj at phys.ufl.edu>:
> >
> >> Dear PWSCF users and developers,
> >>  I was looking into the code where it calculates symmerty operations for
> >> the group. Now the symmetry operations are defined as ' 90 deg rotation -
> >> cart. axis [0,0,-1]', &  ' 90 deg rotation - cart. axis [0,0,1]
> >> I did not understand the point of defining rotation about z and -z
> >> axis. Is this because of some numerical constraint? Also, there are
> >> elements with 'theta' and '-theta' rotation in the same group. I was just
> >> wondering the reason behind this. Any help will be appreciated.
> >>
> >> Regards,
> >> Manoj Srivastava
> >> Department of Physics
> >> University of Florida
> >> Gainesville, FL, USA.
> >>
> >> _______________________________________________
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> >>
> >
> >
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>
> --
>
>
> o ------------------------------------------------ o
> | Gabriele Sclauzero, PhD Student                  |
> | c/o:   SISSA & CNR-INFM Democritos,              |
> |        via Beirut 2-4, 34014 Trieste (Italy)     |
> | email: sclauzer at sissa.it                         |
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