title: Solving the Sayre equations for centrosymmetric structures with a genetic algorithm.
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.
authors.affiliation: Department of Physics and Texas Center for Superconductivity and Advanced Materials, University of Houston, 77204, USA.
authors.forename: Yi
authors.initials: Y
authors.lastname: Zhou
authors.forename: Wu-Pei
authors.initials: WP
authors.lastname: Su
mesh_terms: D000465:Algorithms; D018360:Crystallography, X-Ray; D008957:Models, Genetic; D015394:Molecular Structure