Re: [Spglib-users] Can not find atoms related by space group symmetry

[Đorđe D. <dan...@ho...>]

Hello again,

I apologize I accidently hit send.

I apologize for the confusion. I was copy/paste-ing part from a larger code and I have not checked the script.  I am attaching the script with the email. Test contains the python code.

Let’s say the position of an atom in the primitive cell in crystal coordinates is x1, and it is a component of the vector of all atomic positions inside primitive cell X. If I act with the space group symmetry on x1 I would get, as you said x’:

x' = (R|t) x1 = Rx1 + t

Part of the code that does that should be:

new_pos = np.einsum('ij,jk->ik', scaled_positions, rotations[irot]) + translations[irot]

Now, I would expect that x’ is also a position of some atom in the primitive cell, maybe translated by the lattice vector. If I compare x’ with each component of X I should get a match for some x2. That would mean that my original x1 that I transformed transforms to some other atomic position x2 (which could be the same). Now I could say that space group symmetry (R|t) maps atom x1 to atom x2. Am I correct in saying this? Matching of transformed and original atomic positions should be done with this part of the code:

        for iat in range(natom):
                found = False
                for jat in range(natom):
                        pos = new_pos[iat] - scaled_positions[jat]
                        pos -= np.rint(pos)
                        if(check_if_R(pos)):
                                atom_image[irot, iat] = jat
                                found = True
                                break

I hope now you can run the code and see that I do not match all of the transformed atoms. Can you help me fix this?

Kind regards,

Đorđe

From: Atsushi Togo<mailto:atz...@gm...>
Sent: Tuesday 29 March 2022 03:04
To: spglib-users<mailto:spg...@li...>
Subject: Re: [Spglib-users] Can not find atoms related by space group symmetry

Hi,

Please define what you want to do more clearly. For example,

Given a space group operation (R|t), and a point x in crystallographic
coordinates

x' = (R|t) x = Rx + t

Then what do you want to do?

In addition, your script doesn't work as it is.

Togo

On Mon, Mar 28, 2022 at 4:26 PM Dorde Dangic <Dan...@ho...> wrote:
>
> Dear all,
>
> I am having trouble finding atoms related by a spacegroup symmetry. I am not sure what I am doing wrong. I am sending a script that I am using to find symmetry-related atoms.
>
> POSCAR:
>
>   H
>   1.00000000
>   0.59175841  -0.59175841  1.52600353
>   0.59175841  0.59175841  1.52600353
>   -0.59175841  -0.59175841  1.52600353
>   H
> 2
> Direct
>   0.00000000  0.00000000  0.00000000
>   0.50000000  -0.25000000  0.25000000
>
> test.py:
>
> import numpy as np
> import spglib
> from phonopy.interface.calculator import read_crystal_structure
>
> # Function to check if the vector is the translational lattice vector
> def check_if_R(vec):
>         rvec = False
>         for i in range(-1,2):
>                 if not rvec:
>                         for j in range(-1,2):
>                                 if not rvec:
>                                         for k in range(-1,2):
>                                                 vec1 = vec + np.array([float(i), float(j), float(k)])
>                                                 if(np.linalg.norm(vec1) < 1.0e-5):
>                                                         rvec = True
>                                                         break
>         return rvec
>
> unitcell, _ = read_crystal_structure("POSCAR", interface_mode='vasp') # read in structure
> cell = (unitcell.cell, unitcell.scaled_positions, unitcell.numbers)
>
> dataset = spglib.get_symmetry_dataset(cell, symprec=1e-5, angle_tolerance=-1.0, hall_number=0) # get datasets
> rotations = dataset['rotations'].copy()
> translations = dataset['translations'].copy()
>
> print(scaled_positions)
>
> atom_image = np.zeros((len(rotations), len(numbers))) + len(numbers) # array to store to which atom we go with symmetry
> for irot in range(len(rotations)):
>         new_pos = np.einsum('ij,jk->ik', scaled_positions, rotations[irot]) + translations[irot] # symmetry operation on the scaled positions
>         for iat in range(natom): # Try to match rotated atom with the original set
>                 found = False
>                 for jat in range(natom):
>                         pos = new_pos[iat] - scaled_positions[jat]
>                         pos -= np.rint(pos)
>                         if(check_if_R(pos)):
>                                 atom_image[irot, iat] = jat
>                                 found = True
>                                 break
>                 if(not found): # Print rotated atom if could not match
>                         print(irot, iat)
>                         print(new_pos[iat])
> # Print atom images
> print(atom_image)
>
> Could you please tell me what am I missing?
>
> Thank you for your help.
> _______________________________________________
> Spglib-users mailing list
> Spg...@li...
> https://lists.sourceforge.net/lists/listinfo/spglib-users



--
Atsushi Togo


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