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Solving the Sayre equations for centrosymmetric structures with a genetic algorithm.

Yi Zhou1, Wu-Pei Su

  • 1Department of Physics and Texas Center for Superconductivity and Advanced Materials, University of Houston, 77204, USA.

Acta Crystallographica. Section A, Foundations of Crystallography
|June 26, 2004
PubMed
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A genetic algorithm optimizes crystal structure phasing by minimizing Sayre's equations, offering a more efficient global optimization method than simulated annealing for determining accurate structure factors.

Area of Science:

  • Crystallography
  • Computational Chemistry
  • Materials Science

Background:

  • Sayre's equations establish relationships between structure factors in equal-atom crystals.
  • Accurate determination of structure factor phases is crucial for solving crystal structures.
  • Traditional methods may face challenges in global optimization for phase determination.

Purpose of the Study:

  • To apply a genetic algorithm (GA) for optimizing crystal structure phasing.
  • To minimize the least-squares residual of Sayre's equations using a GA.
  • To evaluate the efficiency of GA compared to simulated annealing for phase determination.

Main Methods:

  • A genetic algorithm was employed, treating crystallographic phases as genes and the complete set of phases as a chromosome.

Related Experiment Videos

  • Each chromosome underwent local minimization via quenching after generation.
  • The algorithm was tested on synthetic data for a 92-atom structure and real data for a 62-atom structure.

    • Main Results:

    • The genetic algorithm successfully minimized the residual of Sayre's equations.
    • Trial calculations demonstrated the algorithm's applicability to both synthetic and real crystallographic data.
    • The GA proved to be a more efficient global optimization technique than simulated annealing.

    Conclusions:

    • Genetic algorithms provide an effective and efficient approach for solving the phase problem in crystallography.
    • This method offers a robust alternative to simulated annealing for crystal structure determination.
    • The GA's efficiency in global optimization is beneficial for complex crystallographic datasets.