[gpaw-users] Symmetry of k-points

[jensj at fysik.dtu.dk]

> I modified 'gpaw/test/symmetry.py' for finding reduced k-points on
> 3x3x3 mesh and found 5 k-points. But I think 4 k-points should be
> found if the crystal symmetry is fully searched.
>
> The line 167 in
> https://trac.fysik.dtu.dk/projects/gpaw/browser/trunk/gpaw/symmetry.py
> may be corrected by:
>
> diff = np.dot(ibzk_kc, op_cc.T) - k_c
> b_k = (diff - diff.round())**2).sum(1) < self.tol

You are quite right - thank you for pointing this out!

> After this modification, fortunately 4 k-points are found. But this is
> just lucky because inversion symmetry is forced to be included.

What do you mean?

> There may be two more problems. The first is that this code seems not
> to consider nonsymmorphic case.

What does (non)symmorphic mean?

> k-points may not be fully reduced. The
> second is that the rotation matrix in the reciprocal space is treated
> as just transpose of the rotation matrix in real space, which can be
> problem in hexagonal system. This may be fixed replaceing op_cc.T by
> op_cc_k as follows:
>
>         met = np.dot( self.cell_cv, self.cell_cv.transpose() )
>         op_scc_k_float = np.array( [ np.dot( np.linalg.inv( met ),
> np.dot( op, met ) )
>                                    for op in self.op_scc ] )
>         op_scc_k = np.array([ int(x) for x in op_scc_float.flatten()
> ]).reshape(-1,3,3)
>
>         for op_cc_k in op_scc_k:
>              ....

I think op_scc and op_scc_k contain exactly the same set of 3x3 matrices,
so it should not matter which one you use?

Thanks again,
Jens Jørgen

PS let's continue this discussion on the gpaw-developers ML.

>
> I just see the code for a short time. I'm sorry if I say something
> really wrong or strange.
>
> Togo
>
> --
> Atsushi Togo
> LEM, ONERA-CNRS, BP72
> 92322 Châtillon Cedex
> E-mail: atz.togo at gmail.com
>
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