Section 18.4.2.2. Anisotropic scaling

The intensity data from a crystal may display anisotropy, i.e., the intensity fall-off with resolution will vary with direction, and may be much higher along one crystal axis than along another. If the structure is to be refined with an isotropic atomic model (either because there are insufficient data or the programs used cannot handle anisotropic parameters), then the fall-off of the calculated values will, of necessity, also be isotropic. In this situation, an improved agreement between observed and calculated values can be obtained either by using anisotropic scaling during data reduction to the expected Wilson distribution of intensities, or by including a maximum of six overall anisotropic parameters during refinement. This will result in an isotropic set of values. For crystals with a high degree of anisotropy in the experimental data, this can lead to a substantial drop of several per cent in R and R_free (Sheriff & Hendrickson, 1987; Murshudov et al., 1998).

This ambiguity effectively disappears with use of an anisotropic atomic model. The individual ADPs, including contributions from both static and thermal disorder, take up relative individual displacements, but also the overall anisotropy of the experimental values. The significance of the overall anisotropy is a point of some contention, and its physical meaning is not clear. It may represent asymmetric crystal imperfection or anisotropic overall displacement of molecules in the lattice related to TLS parameters. Refinement of TLS parameters, which can be performed using, for example, RESTRAIN (Driessen et al., 1989), removes the overall crystal contribution to the ADP.