On the application of phase relationships to complex structures. VIII. An extension of the magic-integer approach

A magic-integer approach, called the P-S set method is described. A primary (P) set of reflexions contains some which fix the origin and enantiomorph and others expressed symbolically in magic-integer form. Probable phases for a secondary (S) set of reflexions are derived, also in symbolic form, from single triple-phase relationships containing a pair of P reflexions. Relationships which link the combined P and S sets give rise to the terms of a Fourier map, the peaks of which indicate likely sets of phases for all the reflexions under consideration. These sets of phases are used as starting points for the computer program MULTAN. The process is completely automated and is illustrated by the solution of the structure of cephalotaxine, C₁₈H₂₁O₄N, the space group of which is C2 with two molecules in the asymmetric unit.