How to calculate planarity restraints

Planarity of some atomic groups is one of the important stereochemical features of a model under refinement. A planarity restraint is usually included in the functional to be minimized. A new method of analytical calculation of the exalet gradient value is suggested for the standard function [Schomaker, Waser, Marsh & Bergman (1959). Acta Cryst. 12, 600-604] which controls planarity in the most direct way. This approach makes it possible to refine the optimum plane orientation at the same time as atomic coordinates.