Ill-conditioned Shake-and-Bake: The trap of the false minimum

The alternation of phase refinement with the imposition of real-space constraints is the essence of the Shake-and-Bake procedure. Typically, these constraints prevent trial structures from falling into local minima. Nevertheless, P1 structures appear to migrate to false minima with significant frequency. These false minima are characterized by the presence of a large 'uranium' peak on the corresponding Fourier map. Fortunately, they can be recognized and avoided by considering the values of the minimal function both before and after the application of constraints. However, it appears that finding solutions for large P1 structures is likely also to require parameter-shift conditions different from those that have been found to work well in other space groups. In fact, these conditions often yield an unusually high percentage of solutions.