[Pw_forum] symmetry operations in PW

[Gabriele Sclauzero]

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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