[Pw_forum] symmetry operations in PW

[Gabriele Sclauzero]

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.
>>>>
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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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-- 


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