Isolated catalyst sites on amorphous supports: A systematic algorithm for understanding heterogeneities in structure and reactivity

Methods for modeling catalytic sites on amorphous supports lag far behind methods for modeling catalytic sites on metal surfaces, zeolites, and other crystalline materials. One typical strategy for amorphous supports uses cluster models with arbitrarily chosen constraints to model the rigid amorphous support, but these constraints arbitrarily influence catalyst site activity. An alternative strategy is to use no constraints, but this results in catalytic sites with unrealistic flexibility. We present a systematic ab initio method to model isolated active sites on insulating amorphous supports using small cluster models. A sequential quadratic programming framework helps us relate chemical properties, such as the activation energy, to active site structure. The algorithm is first illustrated on an empirical valence bond model energy landscape. We then use the algorithm to model an off-pathway kinetic trap in olefin metathesis by isolated Mo sites on amorphous SiO₂. The cluster models were terminated with basis set deficient fluorine atoms to mimic the properties of an extended silica framework. We also discuss limitations of the current algorithm formulation and future directions for improvement.