[Pw_forum] symmetry operations in PW

[Manoj Srivastava]

Dear Alexandra and Gabriele, 
 Thank you for the help.

-manoj 
On Tue, 10 Feb 2009, Gabriele Sclauzero wrote:

> Dear Alexandra,
> 
> alexandra.carvalho at epfl.ch wrote:
> > 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.
> 
> OK, I agree. Anyway when pwscf lists symmetry operations includes all elements of the 
> symmetry group (which may or may not belong to the same class, this is irrelevant at this 
> stage). The important point here is that those two rotations must always appear together, 
> otherwise you will not obtain a group.
> 
> GS
> 
> 
> > (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                         |
> >> | phone: +39 040 3787 511                          |
> >> | skype: gurlonotturno                             |
> >> o ------------------------------------------------ o
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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                         |
> | phone: +39 040 3787 511                          |
> | skype: gurlonotturno                             |
> o ------------------------------------------------ o
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