On the application of phase relationships to complex structures. IX.MULTANfailures

Abstract

The failure of the multisolution direct-methods program MULTAN to solve six crystal structures is analysed in terms of a distinction between the general strategy and the particular tactics of solution. Consideration of the interaction between the number of large E values chosen to define the structure and the number of Σ2 relationships among their phases, and the way in which MULTAN's choice of a partial set of Σ2 relationships limits the achievable accuracy of phase determination, leads to the conclusion that the best tactics are to use only as many E values as necessary but as many Σ2 relationships as possible. Different methods of calculating E values, and the use of Σ1 phase indications, are briefly discussed. The tactic of starting with more unknown phases, its effect on phase development, and the limitations set by the strategy of independent phase permutation, are examined. Finally, it is shown that there exist structures impossible to solve with MULTAN, probably because the tangent formula itself is inadequate, causing the phases to diverge from their true values under its operation. Directions along which to seek improved future strategies are suggested.