Clusters: A bridge across the disciplines of physics and chemistry

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Abstract
The properties of elements from atoms to bulk can be divided into two regimes: ( i ) a scalable regime where properties vary smoothly as some power law until they reach the bulk limit and ( ii ) a nonscalable regime where the variation is highly nonmonotonic (1). In this latter region, characterized by clusters, unusual things can and often do arise because of quantum confinement and boundary effects. Clusters of nonmagnetic elements become magnetic, semiconducting materials exhibit metallic properties, metallic systems become semiconducting, the color of particles changes with size, noble metals become reactive, and brittle materials become malleable. These properties arise because of the unusual structure of the clusters and because the electrons belong to molecular orbitals and exhibit an energy gap, referred to as the highest occupied molecular orbital–lowest unoccupied molecular orbital (HOMO-LUMO) gap. The magnitude of the HOMO-LUMO gap varies with both size and composition of the cluster, and the way these orbitals are filled determines not only the stability of the clusters but also their properties. A systematic study of the structure and properties of clusters composed of a variety of elements has bridged many fields of physics, particularly atomic, molecular, nuclear, and condensed-matter physics. ### Clusters and Nuclear Physics. The pioneering of work of Knight et al . (2) on the mass spectra of Na clusters provided the first insight that clusters and nuclear physics may have something in common. They observed that Na clusters consisting of 2, 8, 20, 40, … atoms were unusually stable (Fig. 1) and coincided with the “magic numbers” in nuclear physics where nuclei with the same numbers of protons and/or neutrons were known to be very stable. Following the nuclear shell model, these authors assumed that a … †To whom correspondence may be addressed. E-mail: pjena{at}vcu.edu or awc{at}psu.edu