Figure 1
Reference-frame manipulations required before an input structure can be evaluated for fit into a higher-symmetry target space group. All the vertical arrows (except for the one labeled `translation x') represent change of basis operators consisting of a rotation matrix and a translation vector, each containing rational values (ratios of small whole numbers). The operators can be composed together to form an overall operator (R, T), for example, transforming the input structure into a setting that is consistent with the reference frame of the candidate symmetry. An additional real-valued translation x optimizes the position of the input model with respect to the symmetry axes of the target space group. The reference frames used for evaluating equations (1)–(3) are indicated. Importantly, the final `conventional setting' structure is still exactly superimposable with the input structure. The imposition of target symmetry constraints is a separate operation (horizontal arrow) and is discussed in §2.6. |