Description of molecular distortions in terms of symmetry coordinates

Symmetry coordinates are useful for describing nuclear arrangements of molecules that can be regarded as being distorted versions of more symmetrical reference structures. The symmetry coordinate description provides a basis for analysing how displacements along particular subsets of symmetry coordinates destroy certain symmetry elements of the reference structure but preserve others (kernel and co-kernel symmetries). It also helps in visualising the symmetry properties of special subspaces of the (3N-- 6)-dimensional internal coordinate space. Some problems concerning the choice of the reference point group are mentioned. It is shown that the symmetry properties of molecules possessing N cyclic degrees of freedom (e.g. torsion angles) are conveniently described in terms of N-dimensional space groups.