Using pattern search methods for surface structure determination of nanomaterials

Abstract

Atomic-scale surface structure plays an important role in describing many properties ofmaterials, especially in the case of nanomaterials. One of the most effective techniques forthe determination of surface structure is low-energy electron diffraction (LEED), which canbe used in conjunction with optimization to fit simulated LEED intensities to experimentaldata. This optimization problem has a number of characteristics that make itchallenging: it has many local minima, the optimization variables can be eithercontinuous or categorical, the objective function can be discontinuous, there are noexact analytical derivatives (and no derivatives at all for categorical variables)and function evaluations are expensive. In this study we show how to apply aparticular class of optimization methods known as pattern search methods toaddress these challenges. These methods do not explicitly use derivatives, and areparticularly appropriate when categorical variables are present, an importantfeature that has not been addressed in previous LEED studies. We have found thatpattern search methods can produce excellent results compared to previouslyused methods, both in terms of performance and in locating optimal results.