Unique shifts further testing and updates

[lmhale99]

@lan496,

I created a new branch for unique-shifts as my tests show that it is not working as well as I think it should. When I loop over hkl sets with different prototypes (https://github.com/lmhale99/potentials-library/tree/master/free_surface) I see that the unique_shifts method still returns a large number of shifts despite the fact that most or all should be the same.

Small updates to your method:

• The isclose of Plane now only has atol and not rtol. Since the two internal isclose comparisons are with 0.0, rtol is meaningless.
• spglib.standardize_cell((rotated_lattice, positions, numbers), to_primitive=True) is used to get the primitive lattice vectors instead of dataset. This is done for better compatibility as dataset['primitive_lattice'] is a relatively recent addition to spglib.

I tried to figure out what your method was doing, but I wasn't entirely sure so I tried doing my own (unique_shifts2)

• In my first attempt, I used the spglib dataset operation on rcell then tried to apply the transformations to find which shifts are unique. Noting that the spglib symmetry operations are for relative box vectors, I took what I do in wrap to avoid the need of the trial image search. This did not identify all unique planes as the symmetry of the shift planes does not reflect the symmetry of the system. For instance for dc (111), the atomic planes are not evenly spaced but the shifts are...
• Next, I used the symmetry operations on the atomic planes rather than the shift planes. This has been added as unique_shifts2. This (mostly) seems to identify unique atomic planes, which then allows for unique shifts based on pairs of termination planes. This seems much better, but is still limited in that I think it is missing some distinct shifts and it is unable to tell if some termination plane sets are equivalent to others.

Maybe look over the two methods and see if you can see how to improve either.

Alternatively, I think the most complete method would be to take all of the rcell + shift systems and compare the atomic positions in those systems for equivalency.

• The shifts always place the free surface halfway between two atomic planes.
• Knowing the systems are "2D" limits the transformation and rotation searches needed.
  • in-plane translations where atoms in an end plane are translated to other positions in the same plane.
  • 180 degree flips and inversions
  • 3- or 4-fold rotations about the plane normal if it is compatible with the cell. This is perhaps the hardest one.

I also added code for a system dump style that uses spglib to return a primitive unit cell. While the code works if copied somewhere else, it is not incorporated into atomman as doing so would create recursive imports at the moment...

[lan496]

Hi @lmhale99! Thank you for your further testing and consideration. I am afraid that I have not fully understood your new method yet, but let me comment for the moment.

I tried to figure out what your method was doing, but I wasn't entirely sure so I tried doing my own (unique_shifts2)

Sorry, I should leave more comments or documents since symmetry operations on crystal planes are a bit cumbersome. Here is my implementation note. I hope this may clarify my first attempt.

I took what I do in wrap to avoid the need of the trial image search.

Is original unique_shifts failing to find distinct crystal planes due to the trial image search? I will work on investigating in which cases unique_shifts fails.

Alternatively, I think the most complete method would be to take all of the rcell + shift systems and compare the atomic positions in those systems for equivalency.

I agree on although this approach may be time-consuming. This approach seems to be used in pymatgen’s surface module with StructureMatcher.

By the way, I think requirements.txt needs to be updated to include yabadaba==0.1.1 and the newest version of potentials to work this PR.

[lmhale99]

Moved to https://github.com/lmhale99/atomman/pull/29