In the context of
molecular symmetry, a
symmetry operation is a
permutation of atoms such that the
molecule or
crystal is transformed into a state indistinguishable from the starting state. Two basic facts follow from this definition, which emphasize its usefulness.
- Physical properties must be invariant with respect to symmetry operations.
- Symmetry operations can be collected together in groups which are isomorphous to permutation groups.
Wavefunctions need not be invariant, because the operation can multiply them by a phase or mix states within a degenerate representation, without affecting any physical property.