INCORPORATING TANGENT REFINEMENT IN THE SHAKE-AND-BAKE FORMALISM

Shake-and-Bake is a direct-methods procedure in which phase, refinemen t and Fourier refinement are alternated repetitively, unconditionally and automatically. The traditional Shake-and-Bake approach invoked a p arameter-shift routine to perform phase refinement in an effort to red uce the value of the minimal function. In this paper, parameter shift is replaced with the tangent formula as a means of phase refinement. T his study shows that the tangent formula is more efficient than parame ter shift for small structures when the number of refinement cycles an d number of applications of the tangent formula per Shake-and-Bake cyc le are chosen very carefully. For larger structures, including the 400 non-H-atom crambin structure, the two methods generally perform with similar efficiency. However, only parameter shift has successfully pro duced recognizable solutions for the difficult 317 non-H-atom structur e gramicidin A.