Solving the Sayre equations for centrosymmetric structures with a genetic algorithm

Authors: Zhou, Yi; Su, Wu-Pei

Source: Acta Crystallographica Section A, Volume 60, Number 4, July 2004 , pp. 306-310(5)

Publisher: Wiley-Blackwell

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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.

Keywords: Sayre equations; genetic algorithm

Document Type: Research Article


Publication date: July 1, 2004

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