Alexandra: are you by any chance a student/collaborator of Alfonso's? One of the few persons that I know, still able to teach group theory, and the one who taught me long ago, when group theory was not yet considered archeo-physics in our community. Cheers - Stefano
On Feb 10, 2009, at 10:19 AM, 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. > (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 --- Stefano Baroni - SISSA & DEMOCRITOS National Simulation Center - Trieste [+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype) La morale est une logique de l'action comme la logique est une morale de la pens?e - Jean Piaget Please, if possible, don't send me MS Word or PowerPoint attachments Why? See: http://www.gnu.org/philosophy/no-word-attachments.html -------------- next part -------------- An HTML attachment was scrubbed... URL: http://www.democritos.it/pipermail/pw_forum/attachments/20090210/dfbb3b08/attachment-0001.htm
