Size and shape selectivity, e?ect of the support on the reactivity, analysis of large grids ofmolecular events and nucleation of homo- and hetero-metallic clusters with growth algorithmon honeycomb-structured supports will be in the following treated through the discussion ofsome selected studies, recently appeared in the literature. Generally speaking the theoretical4methods applied in all these works are based on DFT.Size and shape selectivity and topology of active sitesShape and size selectivity are topics of great interest, especially when the size of the catalystis so minuscule that activity toward a given reaction might drop dramatically only removingor adding a single metal atom. The high control on the causality, intrinsic of computationalmodeling, allows one to precisely account for the change in reactivity due to very smallvariations in the features of the catalyst, and made the theoretical approaches highly suitablefor these kinds of investigations.Pd subnanometric clusters were investigated – using a periodic DFT approach – as catalystsin various reactions such as, for example, the methanol decomposition23 or wateroxidation24. In the latter, a pronounced size selectivity was in particular observed: Pd4actually shows no reaction while Pd6 and Pd17 are among the most active catalysts known.A seemingly di?erent behavior could be ascribed to platinum, another Group 10 metal.As an example, ethylene hydrogenation on platinum, despite few exceptions acknowledgingthe importance of the particle size e?ects25,26, has been historically recognized to be as astructure-insensitive reaction27. The reasons behind the structure-insensitivity of a heterogeneouscatalytic reaction were discussed by Boudart28. Besides the formation of specificsurface species, a simple explanation might reside in the microscopic equivalence of thereactive surface sites. This condition unlikely does hold for subnanometric metal clusters,whose reactive sites could show extremely di?erent activity, according to their local topologyhence to their coordination with other metal or support atoms. Indeed, Crampton et al.29demonstrated, through a combination of experiments and DFT-based calculations, that theconcept of structure sensitivity-insensitivity should be rediscussed, at least, in the case ofsubnanometric Pt clusters supported on MgO. In particular the activity towards ethylenehydrogenation was demonstrated to be extremely dependent upon the cluster size, goingfrom a nearly inactive condition, for small clusters like Pt9, towards high activity, actuallysuperior to Pt(111) extended surfaces, for Pt13.Yang et al.30 performed a systematic study of size and support e?ects for CO2 hydrogenationat atmospheric pressure using a combination of in situ X-ray absorption spectroscopy5and catalytic activity measurements as well as first-principles’ calculations. The catalytic activityfor methanol synthesis was found to be strongly influenced by the cluster size, showingthe Cu4/Al2O3 catalyst the highest turnover rate in the CH3OH production. With just oneatom less, the Cu3 cluster conversely showed less than a half activity. However, DFT calculationsdemonstrated that on the whole the catalytic activity of the not supported gas-phaseCu clusters increases as the cluster size decreases. Again it, clearly, appears the many tacitimplications, which are involved in the elementary statement, claiming that “every singleatom counts”.Another crucial result that stimulate theoretical investigations was the experimental evidencethat gold catalysts active for CO oxidation are subnanometric species containing 10Au atoms. Lopez and Nørskov, in particular, showed that even an isolated Au10 clustershould be able to catalyze the CO oxidation reaction even below room temperature31. Furthermore,the authors identified the very low coordinated Au corner atoms belonging tothe Au10 cluster as the responsible of the increased reactivity with respect to the plain Ausurfaces.Not only removing or adding a single metal atom might change the overall activitybehavior of the subnanometric catalyst. Indeed, the active site topology might be alsocrucial in determining the selectivity of a given cluster. As an example in a combinedexperimental-theoretical study performed by Crespo et al.32,33, it was demonstrated that thehydrogenation of the alkyne C???C moiety preferentially occurs in correspondence of planesites, with respect to either corner or edge ones. On the contrary, the so produced alkenewas solely hydrogenated in correspondence of low coordinated edge or corner sites.