Global Optimization in Microclusters
In this chapter, we introduce the reader to the fundamental developments of global optimization for the structure prediction of clusters. Section 14.1 presents an introduction to the research area of microclusters and provides some background information. Section 14.2 discusses the problem definition. Section 14.3 presents the novel difference of convex functions (DC) transformation which is based on eigenvalue analysis for a variety of potential energy models, and which results in explicit ways of defining the parameter a. Section 14.4 presents the mathematical model, along with its modifications, that satisfy the convergence conditions of the GOP algorithm. Section 14.5 discusses the detailed algorithmic procedure for determining the global minimum structure of microclusters. Section 14.6 presents computational results on small microclusters. Section 14.7 introduces a relaxation of the global optimization approach that allows for the computational studies of larger Lennard-Jones and Morse clusters. Finally, section 14.8 discusses the results with reference to magic numbers and interatomic spacing. The material presented in the chapter is based on the work of Maranas and Floudas (1992), (1993).
KeywordsGlobal Optimization Dual Problem Total Potential Energy Morse Potential Interatomic Spacing
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