On the application of phase relationships to complex structures. XXII. Techniques for random phase refinement

Abstract In recent years there have been a number of developments in direct methods involving refinement processes applied to initially random sets of phases. Procedures which have been used for refinement include least-squares and gradient methods applied to triple-phase relationships expressed as linear equations and also the tangent formula. In the present investigation seven functions are investigated for the refinement of random phases; because of the awkward form of these functions the refinement process used is based on a parameter-shift algorithm. Some of the functions appear to be more effective than others but the most effective one was discovered through making a mistake with one of the others and no rational explanation for its efficacy can be given. Trials have been made with known structures and with three unknown structures which were originally solved by the processes described in the paper.