Constrained refinements of crystal structures and their programming

The method of factorizing the derivatives matrix when applying constraints is discussed in terms of three similar examples. First `symmetry constraint', in which molecules in the crystal must conform to a given molecular symmetry. Second `identical molecule constraint', in which molecules of the same chemical type but unrelated by symmetry are required to have the same shape. Finally the well established `shape constraint', where parts of a structure are constrained to a definite well known shape. A flow diagram for one of the constrained refinements is given, showing how the addition of the constraint can be done by additional programming rather than large scale alteration of the basic program. This suggests a program system with a different philosophy from that in present use, giving greater flexibility and efficiency than heretofore.