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. > >>>> > >>>> _______________________________________________ > >>>> Pw_forum mailing list > >>>> Pw_forum at pwscf.org > >>>> http://www.democritos.it/mailman/listinfo/pw_forum > >>>> > >>> > >>> _______________________________________________ > >>> Pw_forum mailing list > >>> Pw_forum at pwscf.org > >>> http://www.democritos.it/mailman/listinfo/pw_forum > >>> > >> -- > >> > >> > >> 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 > >> _______________________________________________ > >> Pw_forum mailing list > >> Pw_forum at pwscf.org > >> http://www.democritos.it/mailman/listinfo/pw_forum > >> > > > > > > _______________________________________________ > > Pw_forum mailing list > > Pw_forum at pwscf.org > > http://www.democritos.it/mailman/listinfo/pw_forum > > > > -- > > > 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 > _______________________________________________ > Pw_forum mailing list > Pw_forum at pwscf.org > http://www.democritos.it/mailman/listinfo/pw_forum >