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. > >> > >> _______________________________________________ > >> 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 >
