molsym

Molecular symmetry point group and irreducible representation objects supporting algebraic operations for Python.

This package is under development. Names and functionality are likely to change.

Currently supported point groups: C1, C2v, D3, D2h, D6h.

Additional point groups can be easily added in pointgroup.py.

Resources used for creating this package:

• J.M. Hollas, "Symmetry in Molecules," Chapman&Hall, London (1972)
• Gernot Katzer, "Character Tables for Point Groups used in Chemistry"

Examples

>>> d2h = D2h()
>>> print(repr(d2h))
D2h()

>>> print(d2h.b2g * d2h.b1u)
b3u

>>> print(d2h.b2g**2)
ag

>>> print(repr(d2h.b1g))
IrreducibleRepresentation(pg=D2h(), irrep=(1, 1, -1, -1, 1, 1, -1, -1), degenerate=False)

>>> print(D2h('b2g') * D2h('b1u'))
b3u

>>> d6h = PointGroup('D6h')
>>> print(repr(d6h))
PointGroup(pg="dnh", n=6)

>>> product = d6h.e1g**2
>>> print(*(str(x) for x in product))
a1g a2g e2g

>>> product = d6h.e2u + d6h.e1g * d6h.e2u * d6h.e2u + d6h.a1g
>>> print(*(str(x) for x in product))
a1g b1g b2g e1g e1g e1g e2u

TODO / Backlog

* General:
    * add __all__ = [...]
    * unit tests

* `PointGroup`:
    * implement comparison methods by group order and self.n
          x.__lt__(y), x<=y calls x.__le__(y), x==y calls x.__eq__(y), x!=y calls x.__ne__(y),
          x>y calls x.__gt__(y), and x>=y calls x.__ge__(y).
    * add attribute to return totally symmetric irrep
    * in __init__:
          * raise AttributeError if pg invalid
          * check lower bound for n depending on point group
    * generate irreps and character table from the generating symmetry operations

* `IrreducibleRepresentation`:
    * remove `degenerate` parameter, not neccessary:
        Degeneracy = Dimension = character of symmetry operation `E`
        simply reduce every Representation before multiplication, then
        degeneracy does not matter anymore
    * implement correct Mulliken symbols:
        1-dimensional characters `A` und `B`
        2-dimensional charakters `E`
        3-, 4-, 5-dimensional charakters `T`, `G`, `H`
    * lowering of symmetry when multiplied with an irrep from a different point group, if possible.

* `SymmetryOperation` class
    * analytic implementation of symmetry operation application
    * can then be used to generate all point groups