| X-ray crystallography is an experimental technique that uses X-ray diffraction to study the molecular structures of crystalline compounds. One of the major problems in X-ray crystallography is the calculation of the electron density map from the diffraction pattern. Inability to measure the phases of the diffracted beams directly brings about the so-called phase problem of X-ray crystallography.; By formulating the phase problem as a global minimization problem, simulated annealing has been employed in a series of papers for structural determination. It is well-known that genetic algorithm is in general a better technique of global optimization than simulated annealing. Its role in solving the phase problem is explored in this dissertation.; Sayre's equations give a set of relationships which exist among the structure factors of an equal-atom structure. In order to obtain the correct phases of the structure factors, our genetic algorithm minimizes a least-square residual of Sayre's equations. In the genetic algorithm, a phase is treated as a gene and the whole set of phases is considered a chromosome. Every chromosome is relaxed to a nearby local minimum by quenching after being produced from a previous generation. Trial calculations for structures containing up to 126 non-H atoms with synthetic data and a structure containing 62 non-H atoms with real data are presented. Compared to simulated annealing, genetic algorithm is more efficient for solving the phase problem. |
