On the application of phase relationships to complex structures. X. MAGLIN – a successor to MULTAN

The MULTAN system has almost reached the limit of possible development. For complicated structures the starting set must be so large that even the largest computers cannot handle the number of phase permutations required. Another difficulty is that for some structures a correct set of phases is unstable under tangent-formula refinement. In the MAGLIN program now being developed initial sets of phases will be found for 30 or so reflexions by an application of magic integers to Karle-Hauptman determimants with the use of the Tsoucaris maximum-determinant rule. Further phases are then found by repeated application of magic integers. Phase refinement is carried out by a least-squares solution of a set of linear equations with each Σ₂ relationship represented by one equation. A novel technique is described whereby a set of equations involving M reflexions may be solved for the phases of only m( < M) of them. This leads to a considerable saving of time in running the MAGLIN process. For complicated structures it is expected that MAGLIN will not only be more effective than MULTAN but also considerably less time-consuming.