Incorporating tangent refinement in the Shake-and-Bake formalism

Shake-and-Bake is a direct-methods procedure in which phase refinement and Fourier refinement are alternated repetitively, unconditionally and automatically. The traditional Shake-and-Bake approach invoked a parameter-shift routine to perform phase refinement in an effort to reduce the value of minimal function. In this paper, parameter shift is replaced with the tangent formula as a means of phase refinement. This study shows that the tangent formula is more efficient than parameter shift for small structures when the number of refinement cycles and number of applications of the tangent formula per Shake-and-Bake cycle 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 produced recognizable solutions for the difficult 317 non-H-atom structure gramicidin A.