Re: [Spglib-users] symmetrizing positions/cell vectors without altering cell?

[Atsushi T. <atz...@gm...>]

Your sample script is busy, and I want to see only essential
information. In addition I don't have ASE in my computer.

By the way, do you understand the difference between transformation
and rotation? The former is a change of basis and the later is rigid
rotation of whole crystal in Cartesian coordinates. The former is
applied from the right and the later is applied from the left if I am
correct.

Togo

On Tue, Dec 19, 2017 at 1:18 AM, Noam Bernstein
<noa...@nr...> wrote:
>
> On Dec 16, 2017, at 2:08 AM, Atsushi Togo <atz...@gm...> wrote:
>
> You can obtain more information by spg_get_dataset:
> https://atztogo.github.io/spglib/api.html#spg-get-dataset-and-spg-get-dataset-with-hall-number
>
>
> Thanks - I now see transformation matrix, which is very helpful.  I’m
> slightly confused by the output I get, however.
>
> I tried a simple example, identifying a rotated FCC lattice.  Lattice
> vectors start out as (1,1,0) etc, and are rotate by 45 deg around \hat{z}.
>
> import ase, ase.io, sys, spglib, numpy as np
>
> at = ase.Atoms(cell=[[0,1.41421356237309504880,0],
>      [.70710678118654752440,.70710678118654752440,1],
>      [-.70710678118654752440,.70710678118654752440,1]], numbers=[32])
> ase.io.write(sys.stdout, at, format="extxyz")
>
> symprec=0.1
> dataset = spglib.get_symmetry_dataset((at.get_cell(), at.get_positions(),
> at.get_atomic_numbers()), symprec=symprec)
> sys.stderr.write("loose initial symmetry group number {}, international
> (Hermann-Mauguin) {} Hall {} prec
> {}\n".format(dataset["number"],dataset["international"],dataset["hall"],symprec))
> print "std lattice\n", dataset['std_lattice']
> print "orig cell\n", at.get_cell()
> print "supposed to be orig cell\n", np.dot(dataset['std_lattice'].T,
> dataset['transformation_matrix']).T
> print "supposed to be standardized cell\n", np.dot(at.get_cell().T,
> np.linalg.inv(dataset['transformation_matrix'])).T
>
>
> I expected the second to last line to print out something identical to the
> original cell, according to the documentation at
> https://atztogo.github.io/spglib/api.html#api-origin-shift-and-transformation
> which says that "(a b c) = (as bs cs) P” (I’m using 1.9.9).  However, the
> output is actually
>
> 1
> Lattice="0.0 1.41421356237 0.0 0.707106781187 0.707106781187 1.0
> -0.707106781187 0.707106781187 1.0" Properties=species:S:1:pos:R:3:Z:I:1
> pbc="F F F"
> Ge       0.00000000       0.00000000       0.00000000       32
> loose initial symmetry group number 225, international (Hermann-Mauguin)
> Fm-3m Hall -F 4 2 3 prec 0.1
> std lattice
> [[ 2.  0.  0.]
>  [ 0.  2.  0.]
>  [ 0.  0.  2.]]
> orig cell
> [[ 0.          1.41421356  0.        ]
>  [ 0.70710678  0.70710678  1.        ]
>  [-0.70710678  0.70710678  1.        ]]
> supposed to be orig cell
> [[  0.00000000e+00   1.00000000e+00  -1.00000000e+00]
>  [ -1.00000000e+00   1.00000000e+00   3.92523115e-17]
>  [ -1.00000000e+00  -1.50274614e-16  -1.00000000e+00]]
> supposed to be standardized cell
> [[  0.00000000e+00  -2.22044605e-16  -2.00000000e+00]
>  [  1.41421356e+00   1.41421356e+00   0.00000000e+00]
>  [  1.41421356e+00  -1.41421356e+00   0.00000000e+00]]
>
> so the “supposed to be orig cell” line prints out something that is a
> _rotated_ version of the original cell.  That’s actually fine in practice,
> but it’s not what I was expecting.  Am I just misunderstanding the
> documentation, or am I actually doing something wrong?
>
> thanks,
> Noam



-- 
Atsushi Togo
Elements Strategy Initiative for Structural Materials, Kyoto university
E-mail: atz...@gm...