[Pw_forum] symmetry operations in PW

[Stefano Baroni]

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.
>>>>
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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                             |
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>
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---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

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