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

Area of Science:

• Crystallography
• Structural Biology
• Materials Science

Background:

• The Shake-and-Bake procedure is a common method for crystallographic structure refinement.
• Real-space constraints are typically used to prevent trial structures from entering local minima.

Purpose of the Study:

• To investigate the tendency of P1 structures to converge to false minima during crystallographic refinement.
• To identify characteristics of these false minima and propose methods for their recognition and avoidance.

Main Methods:

• Alternating phase refinement with real-space constraints (Shake-and-Bake procedure).
• Analysis of Fourier maps and minimal function values.
• Investigation of parameter-shift conditions for large P1 structures.

Main Results:

• P1 structures frequently migrate to false minima, characterized by a significant 'uranium' peak in Fourier maps.
• Monitoring minimal function values before and after constraint application can identify these false minima.
• Standard parameter-shift conditions may be suboptimal for large P1 structures, with alternative conditions yielding a high percentage of solutions.

Conclusions:

• False minima in P1 structures can be recognized and avoided by analyzing minimal function behavior.
• Optimized parameter-shift conditions are crucial for successful structure determination of large P1 structures.
• The Shake-and-Bake procedure requires careful application and monitoring for complex crystallographic problems.