Ensemble effect for single-atom, small cluster and nanoparticle catalysts

A large family of heterogeneous catalytic reactions require active sites with more than one metal atom, that is, an ensemble of metal atoms. The ensemble requirement, which refers to the minimum number of metal atoms that are needed to catalyse a reaction with optimal efficiency, is a useful metric to evaluate the effectiveness of catalysts for reactions with different site requirements. In this Review, we revisit the traditional ensemble effect and lay out the principles for its incorporation within efficient metal catalysts. Single-atom catalysts can also be described through the ensemble effect theory, as the coordination groups of single-atom catalysts constitute an ensemble that is vital for their reactivity. The understanding of the ensemble requirement for metal catalysts provides insights into catalyst design with both optimized activity and atomic efficiency, and contributes to the development of sustainable heterogeneous catalytic transformations.