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
