Efficient anisotropic refinement of macromolecular structures using FFT

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 rela ted atoms are described. These have been implemented in the program REFMAC and its performance with several examples is analysed. All the tests show t hat anisotropic refinement not only reduces the R value and R-free but also improves the fit to geometric targets, indicating that this parameterizati on is valuable for improving models derived from experimental data. The com puter time taken is comparable to that for isotropic refinements.