pyxtal.supergroup module

Module to search for the supergroup symmetry

pyxtal.supergroup.find_mapping(atom_sites, splitter)

Search for all mappings for a given splitter.

Parameters:

• atom_sites – list of wp object

• splitter – wp_splitter object

Returns:

unique solutions

pyxtal.supergroup.find_mapping_per_element(sites1, sites2)

Search for all mappings for a given splitter.

Parameters:

• sites1 (list) – e.g., l layer [‘4a’, ‘8b’, ‘4c’]

• sites2 (list) – e.g., 2 layers [[‘4a’], [‘8b’, ‘4c’]]

Returns:

e.g. 3 layers: [[[0], [1,2]]]

Return type:

unique solutions

pyxtal.supergroup.find_xyz(G2_op, coord, quadrant=None)

Finds the x,y,z free parameter values for positions in the G_2 basis.

Parameters:

• G2_op – a symmetry operation in G2

• coord – the coordinate that matches G2_op

• quadrant – a 3 item list (ex:[1,1,-1]) that contains information on the orientation of the molecule

Returns:

x,y,z parameters written in the G2 basis

Return type:

G2_holder

pyxtal.supergroup.new_path(path, paths)

Check if it is a new path.

pyxtal.supergroup.new_structure(struc, refs)

Check if struc is already in the reference solutions.

pyxtal.supergroup.search_G1(G, rot, tran, pos, wp1, op)

Search the best matched position in the G1 basis.

Parameters:

• G – Target space group object

• rot – Rotation matrix (3x3)

• tran – Translation vector (1x3)

• pos – Starting position

• wp1 – Wyckoff position symmetry

• op – Symmetry operation

Returns:

(closest_position, distance)

• closest_position: The best matched position in G1 basis

• distance: Distance between original and matched positions

Return type:

tuple

pyxtal.supergroup.search_G2(rot, tran, pos1, pos2, cell=None)

Search the best matched position in G2 basis.

Parameters:

• rot – Rotation matrix (3x3)

• tran – Translation vector (1x3)

• pos1 – Position in G1

• pos2 – Reference position in G2

• cell – Unit cell matrix (3x3), optional

Returns:

(pos, dist)

• pos: Matched position in G2 basis

• dist: Relative distance between matched positions

Return type:

tuple

class pyxtal.supergroup.supergroup(struc, G, random_state=None)

Bases: object

Class to find the structure with supergroup symmetry

Parameters:

• struc – pyxtal structure

• G – target supergroup number

calc_disps(split_id, solution, d_tol)

For a given solution, compute the minimum disp by adusting translation.

Parameters:

• split_id (int) – integer

• solution (list) – e.g., [[‘2d’], [‘6h’], [‘2c’, ‘6h’, ‘12i’]]

• d_tol (float) – tolerance

Returns:

maximum atomic displcement translation: overall cell translation

Return type:

max_disp

get_coord_H(splitter, id, atom_sites_H, mapping)

Extract the atomic coordinates.

get_initial_mask(splitter)

Get the mask.

make_pyxtal_in_supergroup(solution)

Make the pyxtal according to the given solution

Parameters:

solution – a tuple of (sp, mapping, translation, wyc_set_id, max_disp)

Returns:

a pyxtal structure in high symmetry

make_pyxtals_in_subgroup(solution, N_images=5)

Make the pyxtal according to the given solution

Parameters:

• solution – a tuple of (sp, mapping, translation, wyc_set_id, max_disp)

• N_images – number of images

Returns:

a list of pyxtal structures in low symmetry

make_supergroup(solutions, show_detail=False)

Create unique supergroup structures from a list of solutions

Parameters:

• solutions – list of tuples (splitter, mapping, translation, disp)

• show_detail (bool) – print out the detail

Returns:

list of pyxtal structures

print_detail(solution, coords_H, coords_G, elements)

Print out the details of tranformation

print_wp(sp, id)

A short cut to print the wp information (for debug purpose)

search_supergroup(d_tol=0.9, max_per_G=2500, max_solutions=None)

Search for valid supergroup transition

Parameters:

• d_tol (float) – tolerance for atomic displacement

• max_per_G (int) – maximum number of possible solution for each G

• max_solutions (int) – maximum number of solutions.

Returns:

list of solutions with small displacements

Return type:

solutions

sort_solutions(solutions)

symmetrize(splitter, mapping, translation)

Symmetrize the structure (G) to supergroup symmetry (H)

Parameters:

• splitter – Splitter object to specify the relation between G and H

• mapping – Atomic mapping between H and G

• translation – An overall shift from H to G, None or 3 vector

Returns:

(coords_G1, coords_G2, coords_H, elements, ordered_mapping)

• coords_G1: Coordinates in G

• coords_G2: Coordinates in G under the subgroup setting

• coords_H1: Coordinates in H

• elements: List of elements

Return type:

tuple

symmetrize_dist(splitter, mapping, mask, translation=None, d_tol=1.2)

For a given solution, search for the possbile supergroup structure based on a given translation and mask.

Parameters:

• splitter – Splitter object between G and H

• mapping – List of sites in H, e.g., [‘4a’, ‘8b’]

• mask – If there is a need to freeze the direction

• translation – An overall shift from H to G, None or 3 vector

• d_tol – The tolerance in angstrom

Returns:

(max_disp, translation, mask)

• max_disp: Maximum atomic displacement

• translation: Cell translation vector

• mask: Direction mask

Return type:

tuple

symmetrize_site_double_k(splitter, id, coord_H, translation, run_type=1)

Symmetrize two WPs (wp_h1, wp_h2) to another wp_G with higher symmetry.

Parameters:

• splitter (Splitter) – Splitter object between G and H groups

• id (int) – Index of splitter

• coord_H (array) – Array of shape (2,3) containing coordinates

• translation (array) – Translation vector of shape (3,)

• run_type (int) – Whether to return distance (1) or coordinates (0)

Returns:

float: Maximum atomic displacement run_type=0: tuple: (coord_G1, coord_G2, coord_H)

• coord_G1: coordinate in G1 basis

• coord_G2: coordinates in G2 basis

• coord_H: original coordinates in H basis

Return type:

run_type=1

symmetrize_site_double_t(splitter, id, coord_H, translation, run_type=1)

Symmetrize two WPs (wp_h1, wp_h2) to another wp_G with higher symmetry.

Parameters:

• splitter (Splitter) – Splitter object to specify relation between groups

• id (int) – Index in the splitter

• coord_H (array) – Atomic coordinates

• translation (array) – 1x3 translation vector

• run_type (int) – Whether to return distances (1) or coordinates (0)

Returns:

float: Maximum atomic displacement run_type=0: tuple: (coord_G1, coord_G2, coord_H)

• coord_G1: Coordinates in G1 basis

• coord_G2: Coordinates in G2 basis

• coord_H: Original coordinates in H basis

Return type:

run_type=1

symmetrize_site_multi(splitter, id, coord_H, translation, run_type=1)

Symmetrize multiple WPs to another with higher symmetry.

Parameters:

• splitter (Splitter) – Splitter object between G and H groups

• id (int) – Index in the splitter

• coord_H (array) – Array of atomic coordinates

• translation (array) – Translation vector of shape (3,)

• run_type (int) – Whether to return distances (1) or coordinates (0)

Returns:

float: Maximum atomic displacement run_type=0: tuple: (coord_G1, coord_G2, coord_H) - coord_G1: Coordinate in G1 basis - coord_G2: Coordinates in G2 basis - coord_H: Original coordinates in H basis

Return type:

run_type=1

symmetrize_site_single(splitter, id, base, translation, run_type=1)

Symmetrize one WP to another with higher symmetry

Parameters:

• splitter – splitter object

• id – index of splitter

• base – atomic position of site in H

• translation – 1*3 translation vector

• run_type – return distance or coordinates

Returns:

run_type=1: (dist, translation, mask)

• dist: minimum distance

• translation: optimal translation vector

• mask: direction mask

run_type=0: (coord_G1, [coord_G2], [coord_H])

• coord_G1: coordinate in G1

• coord_G2: coordinate in G2

• coord_H: coordinate in H

Return type:

Two types of results

class pyxtal.supergroup.supergroups(struc, G=None, path=None, d_tol=1.0, max_per_G=100, max_layer=5, show=False)

Bases: object

Class to search for the feasible transition to a given super group.

Parameters:

• struc – PyXtal object Input structure with subgroup symmetry (H)

• G – int, optional Target supergroup space group number

• path – list, optional List of space group numbers defining path from H to G (e.g. [62, 59, 74])

• d_tol – float, default=1.0 Maximum allowed atomic displacement during symmetry change

• max_per_G – int, default=100 Maximum number of symmetry solutions to consider per group

• max_layer – int, default=5 Maximum number of intermediate groups in path

• show – bool, default=False Whether to show detailed progress

Note

Either G or path must be provided, but not both None.

get_transformation(N_images=2)

Get the series of transformed structures between H and G

Parameters:

N_images – number of structures

Returns:

a series of pyxtal structures

print_solutions()

struc_along_path(path)

Search for the super group structure along a given path.

Parameters:

path (list) – List of space group numbers, e.g. [59, 71, 139]

Returns:

(strucs, valid_sols, working_path, valid) - strucs: List of structures along the path - valid_sols: List of valid solutions for each transition - working_path: List of space group numbers along the path - valid: True if successfully reached target group, False otherwise

Return type:

tuple

write_cifs()

Dump the cif files in sequence

pyxtal.supergroup.write_poscars(H_struc, G_struc, mappings, splitters, wyc_sets, N_images=3)

Write the intermediate POSCARs between H and G structure.

The key is to continuously change G to subgroup representations with zero displacements. Finally, call write_poscars_intermediate.

Parameters:

• H_struc – PyXtal low symmetry structure

• G_struc – PyXtal high symmetry structure

• mappings – List of atomic mappings

• splitters – List of splitter objects

• wyc_sets – List of wyc_set transformations

• N_images – Number of intermediate structures between H and G. Default is 3.

Returns:

List of POSCARs between H and G structure.