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How does the chemical reactivity of a metal cluster depend on its size?

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cluster Figure 1: The four stable geometric structures of the seven-atom cluster of argon, in order of increasing energy: (A) A pentagonal bipyramid. (B) A regular octahedron with one face capped by the seventh atom. (C) A regular tetrahedron with three of its faces capped by other atoms. (D) A trigonal bipyramid with two of its faces capped by other atoms; although this has the highest energy of the four structures, it is very close in energy to the tricapped tetrahedron.

The chemical reactivity of a metal cluster is highly dependent on its size, as the properties of these aggregates vary significantly with the number of constituent atoms ( $N$ ).1

In small clusters, properties do not change uniformly with size; instead, they are heavily influenced by quantum mechanical phenomena. Because small clusters have few available quantum states, their electrons occupy discrete energy levels rather than the dense bands found in bulk metals. This leads to unique reactivity patterns, particularly for clusters with specific "magic numbers" of atoms. These magic-number clusters form unusually stable geometric structures, resulting in higher binding energies and, consequently, lower chemical reactivity compared to clusters of other sizes that lack such stable configurations.1

As clusters increase in size, their properties begin to transition. Medium-size clusters exhibit electronic energy states that start to resemble the bands of bulk metals, and their properties vary more smoothly with $N$ . However, because a high proportion of atoms in a cluster reside on the surface—where they have fewer neighbors to hold them in place—the average binding energy remains lower than that of bulk matter. As clusters grow larger, their properties gradually merge into those of their bulk counterparts.1