Non-crystallographic symmetry constraints in least-squares refinement

A least-squares refinement procedure is presented whereby noncrystallographic symmetry constraints can be imposed on the positional parameters of any group of atoms in a crystal structure. This generalized form of the rigid group refinement technique of Scheringer allows specified distortions of the `rigid' group to be refined along with the orientation parameters of the group. Thus, while the advantages of constrained refinement are retained, this generalization allows application of chemically reasonable constraints to systems whose configurations are not sufficiently well known to justify completely constrained (rigid group) refinement. This refinement technique can also be used to provide a direct assessment of the significance of an observed distortion from some idealized configuration. Several examples are presented including the refinement of a metal cluster complex wherein constraint of the refinement to the idealized C3_v symmetry lowers the number of independent positional parameters from 66 to 18.