pyxtal.supergroup module

Module to search for the supergroup symmetry

pyxtal.supergroup.find_mapping(atom_sites, splitter, max_num=720)

search for all mappings for a given splitter

Parameters:

• atom_sites – list of wp object
• splitter – wp_splitter object
• max_num (int) – maximum number of atomic mapping

Returns:

unique solutions

pyxtal.supergroup.find_mapping_per_element(sites1, sites2, max_num=720)

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’]]
• max_num (int) – maximum number of atomic mapping

Returns:

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

Return type:

unique solutions

pyxtal.supergroup.find_xyz(G2_op, coord, quadrant=[0, 0, 0])

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 G1 basis

Parameters:

• G – the target space group object
• rot – rotation, 3*3 matrix
• tran – translation, 1*3 vector
• pos – starting position
• wp1 – wyckoff symmetry
• op – one symmetry operation

Returns:

the cloest position and the distance

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

search the best matched position in G2 basis

Parameters:

• rot – 3*3 rotation matrix
• tran – 1*3 translation vector
• pos1 – position in G1
• pos2 – reference position in G2
• cell – 3*3 matrix

Returns:

matched position in G2 dist: relative distance

Return type:

pos

class pyxtal.supergroup.supergroup(struc, G)

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:

coordinates in G coords_G2: coordinates in G under the subgroup setting coords_H1: coordinates in H elements: list of elements

Return type:

coords_G1

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:

atomic displacement cell translation vector mask

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 object
• id – index of splitter
• coord_H – 2*3 coordinates
• translation – 1*3 transaltion vector
• run_type – return distance or coordinates

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 object
• id – the id in the splitter
• coord_H – coordinates to work on
• translation – 1*3 transaltion vector
• run_type – return distance or coordinates

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

Symmetrize multiple WPs to another with higher symmetry

Parameters:

• splitter – splitter object
• id – the id in the splitter
• coord_H – coordinates to work on
• translation – 1*3 transaltion vector
• run_type – return distance or coordinates

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

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 structure
• G (int) – the desired super group number
• path – the path to connect G and H, e.g, [62, 59, 74]
• d_tol (float) – tolerance for largest atomic displacement
• show (bool) – whether or not show the detailed process

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 – [59, 71, 139] Returns:list of structures along the path working_path: valid: True or False Return type:strucs

write_cifs()

Dump the cif files in sequence

class pyxtal.supergroup.symmetry_mapper(struc_H, struc_G, max_d=1.0)

Bases: object

Class to map the symmetry relation between two structures

Parameters:

• struc_H – pyxtal structure with low symmetry (H)
• struc_G – pyxtal structure with high symmetry (G)
• max_d – maximum displacement to be considered

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

Write the intermediate POSCARs betwee H and G structure. The key is to continuously change G to subgroup represenations with zero displacements. Finally, call write_poscars_intermediate.

Parameters:

• H_struc – PyXtal low symmetry structure
• G_strucs – a list of PyXtal high symmetry structures
• mapping – a list of atomic mappings
• splitter – a list of splitter object
• wyc_set – a list of wyc_set transformation
• N_images – number of intermediate structures between H and G

Returns:

a list of POSCARs