• anisotropic refinement.

This paper gives the equations for the use of fast Fourier transformations in individual atomic anisotropic refinement. Restraints on bonded atoms, on the sphericity of each atom and between non-crystallographic symmetry related atoms are described. These have been implemented in the program REFMAC and its performance with several examples is analysed. All the tests show that anisotropic refinement not only reduces the R value and Rfree but also improves the fit to geometric targets, indicating that this parameterization is valuable for improving models derived from experimental data. The computer time taken is comparable to that for isotropic refinements.