Global search in photoelectron diffraction structure determination using genetic algorithms

Photoelectron diffraction (PED) is an experimental technique widely used to perform structural determinations of solid surfaces. Similarly to low-energy electron diffraction (LEED), structural determination by PED requires a fitting procedure between the experimental intensities and theoretical results obtained through simulations. Multiple scattering has been shown to be an effective approach for making such simulations. The quality of the fit can be quantified through the so-called R-factor. Therefore, the fitting procedure is, indeed, an R-factor minimization problem. However, the topography of the R-factor as a function of the structural and non-structural surface parameters to be determined is complex, and the task of finding the global minimum becomes tough, particularly for complex structures in which many parameters have to be adjusted. In this work we investigate the applicability of the genetic algorithm (GA) global optimization method to this problem. The GA is based on the evolution of species, and makes use of concepts such as crossover, elitism and mutation to perform the search. We show results of its application in the structural determination of three different systems: the Cu(111) surface through the use of energy-scanned experimental curves; the Ag(110)-c(2 × 2)-Sb system, in which a theory-theory fit was performed; and the Ag(111) surface for which angle-scanned experimental curves were used. We conclude that the GA is a highly efficient method to search for global minima in the optimization of the parameters that best fit the experimental photoelectron diffraction intensities to the theoretical ones. © IOP Publishing Ltd.The authors would to thank Fundaçâo de Amparo à Pesquisa de Estado de Minas Gerais (FAPEMIG), Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPQ), and Coordenaçâo de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) (Brazilian Research Agencies) for financial support. MAVH was supported by City University of Hong Kong Grant No. 9380041.Peer Reviewe