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It is challenging to model the complex nature of a catalyst structure under a dynamic reaction environment. This chapter introduces various strategies for deriving appropriate catalyst models that address this complexity by identifying thermodynamically stable catalyst structures as a function of reaction conditions. These strategies include various applications of ab initio thermodynamics, as well as Monte Carlo approaches for exploring the surface phase diagram. Model-building techniques for catalyst surfaces, clusters, and supported-cluster geometries at varying scales are discussed. This chapter also provides an overview of the interplay between site stability and activity, where we demonstrate how apparent barriers can be derived to assess the importance of metastable surface sites that often dictate catalytic activity. These modeling techniques are illustrated with straightforward examples that can be reproduced by the readers, as well as more advanced examples found in the literature.

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