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

Yi Zhou·Wu-Pei Su
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Abstract

Sayre's equations give a set of relationships that exist among the structure factors of an equal-atom structure. In order to obtain the correct phases of the structure factors, a genetic algorithm is used to minimize a least-squares residual of Sayre's equations. In the genetic algorithm, a phase is treated as a gene and the whole set of phases is considered as a chromosome. Every chromosome is relaxed to a nearby local minimum by quenching after being produced from a previous generation. Trial calculations for a structure containing 92 non-H equal atoms with synthetic data and another structure containing 62 non-H equal atoms with real data are presented. Compared to simulated annealing, a genetic algorithm is a more efficient means of global optimization.

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AlgorithmsCrystallography, X-RayModels, GeneticMolecular StructureJournal ArticleResearch Support, Non-U.S. Gov't

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Yi Zhou, Wu-Pei Su. 2004-06-24. Solving the Sayre equations for centrosymmetric structures with a genetic algorithm.. https://doi.org/10.1107/s0108767304010001

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