Magic clusters

If one applies the same procedure to Figure 1.10B, an iron-sulfur cluster often used as a model for those in biological systems, the same magic number of 60 would be obtained. Cluster magic numbers would occur as 48 e for a triangular clusters, 60 e for tetrahedral, 72 e for trigonal bipyramidal, 74 e for square pyramidal, 86 e for octahedral, 90 e for trigonal prisms, and 120 e for cubic structures. 

A derivation and full explanation of cluster magic numbers is given by Teo, B. K. Sloane, N. J. 

Reproduction of metal-cluster magic numbers using a -deformed, 3-dimensional, harmonic oscillator model... 

Despite the fact that building up nanostructures from the atomic level yields a useful intellectual framework, the physical properties of nanoclusters and other nanoscale structures are normally related to those of the bulk, with appropriate corrections for the nanoscale size. This approach is particularly useful for larger particles not subject to large specific quantum or other special effects (such as achieving a cluster magic number). When spheres of material are considered the bulk properties can be corrected for the finite size of the sphere. 

G. Seifert, J. TamuUene and S. Gemming. MonS2n-rx clusters—Magic numbers and platelets. Comput. Mater. Sci. 35, 2006, 316—320. 

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