Character Table

Character Table#

Utilities for character table and irreducible representations.

CharacterPG#

CharacterPG manages point-group character table.

class CharacterPG(pg_tag)[source]#

Bases: dict

initialize the class.

Parameters:

pg_tag (TagGroup or str) -- point-group tag.

anti_symmetric_product_decomposition(irrep, ret_ex=False)[source]#

anti-symmetric product irreducible decomposition.

Parameters:

  • irrep (TagIrrep or str) -- irrep. tag.

  • ret_ex (bool, optional) -- return as an expression ?

Returns:

(the number of appearances, irrep.). or - sympy: decomposed expression.

Return type:

  • [(int,TagIrrep)]

character(irrep=None, all_so=False, explicit=False)[source]#

character table.

Parameters:

  • irrep (str or TagIrrep, optional) -- irrep. tag ("" = identity irrep.).

  • all_so (bool, optional) -- return characters for all symmetry operations ?

  • explicit (bool, optional) -- use explicit expression of character ?

Returns:

character table (symbol) for given irrep. or - {TagIrrep:[sympy]}: all irreps.

Return type:

  • [sympy]

compatibility_relation(pg_tag)[source]#

compatibility_relation from the present point group to a given one.

Parameters:

pg_tag (TagGroup or str) -- point-group tag to obtain compatibility relation.

Returns:

[TagIrrep]}: compatibility relation from self to other.

Return type:

{TagIrrep

irrep_decomposition(char)[source]#

irreducible decomposition.

Parameters:

char ([sympy]) -- characters to be decomposed for symmetry operations in conjugacy class, .

Returns:

(the number of appearances, irrep.).

Return type:

[(int,TagIrrep)]

parity_conversion()[source]#

parity conversion.

Returns:

TagIrrep: correspondence from self to converted one.

Return type:

{TagIrrep

symmetric_product_decomposition(irrep_pair, ret_ex=False)[source]#

symmetric product irreducible decomposition.

Parameters:

  • irrep_pair ((TagIrrep or str, TagIrrep or str)) -- a pair of irreps.

  • ret_ex (bool, optional) -- return as an expression ?

Returns:

(the number of appearances, irrep.). or - sympy: decomposed expression.

Return type:

  • [(int,TagIrrep)]

symmetry_operation(ret_num=False)[source]#

representative symmetry operations in conjugacy class.

Parameters:

ret_num (bool, optional) -- return with the number of cc operations ?

Returns:

symmetry operation. or - [TagSymmetryOperation]: symmetry operations. - [int]: the number of symmetry operations in conjugacy class.

Return type:

  • [TagSymmetryOperation]

property irrep_list#

list of irreps.

Returns:

list of irreps.

Return type:

[TagIrrep]

Notes

  • first element is identity irrep.

tag#

point-group tag.