Rigid-body constraints and the least-squares refinement of crystal structures

To refine the orientation and location of a rigid group of atoms in a crystal it is not necessary to store the atom coordinates relative to a localized axial system. All atoms in the asymmetric unit are defined relative to a single orthonormal axial system. A local axial system is created by taking an atom in the rigid group as origin and defining the local axes as parallel to these orthonormal axes. The evaluation of the required derivatives is then very easy. The replacement of approximate atom positions by idealized atom positions is described.