Find the mapping/transformation relationship between the Cartesian coordinates of all atoms of two POSCARs.

[hongyi-zhao]

The two POSCARs, which come here, are listed below:

$ cat POSCAR_ms 
Si2-primitive cell from MS software
1.0
3.8670001030         0.0000000000         0.0000000000
1.9335000515         3.3489203256         0.0000000000
1.9335000515         1.1163067752         3.1573923625
Si
2
Direct
0.000000000         0.000000000         0.000000000
0.250000002         0.250000005         0.249999992

$ cat POSCAR_vaspkit 
Si2-primitive cell from VASPKIT software
  1.000000
0.00000000000000    2.73436403275000    2.73436403275000
2.73436403275000    0.00000000000000    2.73436403275000
2.73436403275000    2.73436403275000    0.00000000000000
Si
2
DIRECT
0.0000000000000000    0.0000000000000000    0.0000000000000000    Si1
0.2500000000000000    0.2500000000000000    0.2500000000000000    Si2

The Cartesian coordinates of all atoms are shown below:

In [14]: from pymatgen.io.vasp import Poscar
    ...: 
    ...: # Reading the POSCAR files
    ...: poscar_ms = Poscar.from_file("POSCAR_ms")
    ...: poscar_vaspkit = Poscar.from_file("POSCAR_vaspkit")
    ...: 
    ...: # Getting the Cartesian coordinates of all atoms in both structures
    ...: cart_coords_ms = poscar_ms.structure.cart_coords
    ...: cart_coords_vaspkit = poscar_vaspkit.structure.cart_coords
    ...: 
    ...: # Printing the Cartesian coordinates of all atoms in the original structure (POSCAR_ms)
    ...: print("Cartesian coordinates of all atoms in the original structure (POSCAR_ms):")
    ...: for i, coords in enumerate(cart_coords_ms, start=1):
    ...:     print(f"Atom {i}: {coords}")
    ...: 
    ...: # Printing the Cartesian coordinates of all atoms in the target structure (POSCAR_vaspkit)
    ...: print("\nCartesian coordinates of all atoms in the target structure (POSCAR_vaspkit):")
    ...: for i, coords in enumerate(cart_coords_vaspkit, start=1):
    ...:     print(f"Atom {i}: {coords}")
    ...: 
Cartesian coordinates of all atoms in the original structure (POSCAR_ms):
Atom 1: [0. 0. 0.]
Atom 2: [1.93350005 1.11630678 0.78934807]

Cartesian coordinates of all atoms in the target structure (POSCAR_vaspkit):
Atom 1: [0. 0. 0.]
Atom 2: [1.36718202 1.36718202 1.36718202]

Then, how can I find the mapping/transformation relationship between the Cartesian coordinates of all atoms of these two structures?

Regards,
Zhao

[hongyi-zhao]

I got it, as shown below:

In [79]: from pymatgen.core import Structure
    ...: from pymatgen.analysis.structure_matcher import StructureMatcher
    ...: 
    ...: poscar1 = 'POSCAR_ms'
    ...: poscar2 = 'POSCAR_vaspkit'
    ...: 
    ...: structure1 = Structure.from_file(poscar1)
    ...: structure2 = Structure.from_file(poscar2)
    ...: 
    ...: matcher = StructureMatcher(primitive_cell=False)
    ...: matches = matcher.fit(structure1, structure2)
    ...: 
    ...: if matches:
    ...:     try:
    ...:         transformation = matcher.get_transformation(structure1, structure2)
    ...:         print(transformation)
    ...:     except ValueError as e:
    ...:         print(f"error：{str(e)}")
    ...: else:
    ...:     print("Failed to match.")
    ...: 
(array([[ 0,  0, -1],
       [ 0, -1,  0],
       [-1,  0,  0]]), array([0.25, 0.25, 0.25]), [1, 0])

In [80]: from numpy import array
    ...: from numpy.linalg import inv
    ...: from pymatgen.core import Structure
    ...: s1=Structure.from_file("POSCAR_ms")
    ...: s2=Structure.from_file("POSCAR_vaspkit")
    ...: 
    ...: m1=s1.lattice.matrix
    ...: m2=s2.lattice.matrix
    ...: 
    ...: R=transformation[0]
    ...: t=transformation[1]
    ...: 
    ...: print(m2.T@(R@inv(m1.T)@array([0,0,0]) + t))
    ...: print(m2.T@(R@inv(m1.T)@array([1.93350005, 1.11630678, 0.78934807]) + t))
[1.36718201 1.36718201 1.36718203]
[-1.69082426e-08  6.72491127e-09  1.75588875e-08]

See below for the related discussions and specifications:

https://www.vasp.at/forum/viewtopic.php?p=26107#p26107
https://yxli8023.github.io/2020/09/25/Vasp-DC.html
https://www.vasp.at/wiki/index.php/POSCAR