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Ill-conditioned Shake-and-Bake: the trap of the false minimum
1Hauptman-Woodward Medical Research Institute, Buffalo, NY 14203, USA. xu@hwi.buffalo.edu
Summary
The Shake-and-Bake procedure can lead P1 structures to false minima, identified by uranium peaks. Recognizing these minima using minimal function values helps avoid errors in crystallographic structure determination.
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.
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