# [Pw_forum] Allowed symmetries in GIPAW

J. Nelson jn336 at cam.ac.uk
Mon Jul 10 10:47:59 CEST 2017

```Dear Davide,

Thanks very much for your explanation.

Could I check one further example with you. This one is (x,y,z) =>
(-x,y,-z), but, it has a fractional translation as well:

isym =  3     180 deg rotation - cart. axis [0,1,0]

cryst. s( 3) = (     0         -1          0      )  f =( -0.5000000 )
(    -1          0          0      )     ( -0.5000000 )
(     0          0         -1      )     ( -0.5000000 )

cart.  s( 3) = ( -1.0000000  0.0000000  0.0000000 )  f =( -0.3026487 )
(  0.0000000  1.0000000  0.0000000 )     (  0.0000000 )
(  0.0000000  0.0000000 -1.0000000 )     ( -0.4029274 )

Would this be allowed in GIPAW?

Many thanks,

Joseph Nelson
TCM Group
Cavendish Laboratory
University of Cambridge

On 2017-07-08 14:41, Davide Ceresoli wrote:
> Dear Joseph,
>      that operation is allowed because x=>x, y=>-y, z=>-z,
> if I read correctly. The cartesian matrices can be off
> diagonal. For example the rotation of 90° along z, is also
> allowed, because the triplet (x,y,z) => (-y,x,z) is still
> parallel to the original.
>
> Basically the problems are with hexagonal crystals and
> with system with very low symmetry.
>
> For hexagonal crystals, it's better to use ibrav=0, and
> set a,b in the xy plane, c//z, a forming an angle of 30°
> with x.
>
> In all other cases, if unsure, set nosym=.true. in the SCF
> calc.
>
> Best wishes,
>      Davide
>
>
> On 07/07/2017 12:35 PM, J. Nelson wrote:
>> Dear all QE users,
>>
>> I am using QE-6.1.
>>
>> The user guide for GIPAW explains that 'symmetry operations that do
>> not map
>> cartesian axes are not allowed (i.e. 120 deg. rotations)'.
>>
>> Does this mean that the Cartesian rotation matrices for each symmetry
>> operation
>> - e.g.:
>>
>>       isym =  4     180 deg rotation - cart. axis [1,0,0]
>>
>>  cryst.   s( 4) = (     0          1          0      )
>>                   (     1          0          0      )
>>                   (     0          0         -1      )
>>
>>  cart.    s( 4) = (  1.0000000  0.0000000  0.0000000 )  [<--this
>> matrix here]
>>                   (  0.0000000 -1.0000000  0.0000000 )
>>                   (  0.0000000  0.0000000 -1.0000000 )
>>
>> need to be diagonal for the symmetry operation to be compatible with
>> GIPAW? Are
>> symmetry operations with an associated fractional translation allowed?
>>
>>
>> Many thanks,
>>
>> Joseph Nelson
>> TCM Group
>> Cavendish Laboratory
>> University of Cambridge
>>

```