Why do atoms at the surface of a cluster have lower average binding energies than atoms inside bulk matter?

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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.

In a body of bulk matter, nearly all constituent particles are located in the interior, whereas in a cluster, a significant proportion of the particles reside on the surface.1

Surface atoms are bonded only to atoms within their own layer and to those directly beneath them. Consequently, these atoms have fewer neighbors holding them to the main body of the material compared to atoms located in the interior. Because these surface atoms lack the full coordination found in the bulk, they contribute to a lower average binding energy per atom. As a result, the average binding energies of atoms in clusters are generally considerably lower than those observed in bulk matter.1