The Genetic Algorithm: Foundations and Apllications in Structure Solution from Powder Diffraction Data

Recently, new methods based on the use of genetic algorithms have been explored and developed for solving crystal structures directly from powder diffraction data. In implementing genetic algorithms in such applications, several different aspects of the technique and strategy are open to optimization, leading to a versatile and powerful approach. In this paper, the fundamental concepts underlying genetic algorithms are discussed and the implementation of the genetic algorithm for structure solution from powder diffraction data is described. The opportunities, scope and potential for future developments in the foundations and applications of genetic algorithms in this field are highlighted. The genetic algorithm approach adopts the `direct-space' philosophy for structure solution, with trial structures generated independently of the experimental diffraction data and the quality of each structure assessed by comparing the calculated and experimental powder diffraction patterns; in this work, this comparison is made using the profile R factor R<sub>wp</sub>. In the genetic algorithm, a population of trial structures is allowed to evolve subject to well defined rules governing mating, mutation and `natural selection'. The `fitness' of each structure in the population is a function of its profile R factor. The successful application of the genetic algorithm approach for structure solution of molecular crystals from powder diffraction data is demonstrated with examples of previously known and previously unknown structures.