On the application of phase relationships to complex structures. XXVI. Developments of the Sayre-equation tangent formula

The Sayre-equation tangent formula (SETF) develops sets of phases tending to satisfy Sayre's equations for both large and small normalized structure factors. There are two components in the SETF, corresponding to contributions from phase triplets and quartets respectively. The development of objective algorithms for properly weighting these components and for gradually building up the quartet contribution has enabled the SETF, within the procedure SAYTAN, to be incorporated into MULTAN87, the latest version of the package. Examples of tests of MULTAN87 and its use in solving unknown structures are given.