Sub-nano surface-supported catalytic clusters, especially in the presence of adsorbates, generally have many low-energy isomers
accessible at el    evated temperatures of catalysis. The most stable isomer may not be the most catalytically active.
Additionally, isomers may interconvert with barriers of varying heights, in response to the environment, i.e. exhibit
fluxionality, during catalysts. We model such catalysts as statis    tical ensembles in realistic conditions, using a number of
novel methods. We will show how all practically-important properties of cluster catalysts, such as size-dependent activity,
selectivity, and stability against deactivation, are in fact ensemble-average. Side-by-side with th    e experiment, we
demonstrate that, and explain why Pt7 on alumina is much more active toward alkene dehydrogenation than Pt8 and Pt4 on this
support. We will then present the design nano-alloys of Pt clusters, which are remarkably selective against coke in this
reaction, as again c    onfirmed experimentally (coking is one of the main ways in which cluster catalysts deactivate). These
findings were possible only within the ensemble representation of the catalyst.