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research over the past couple of decades has led to the design of superatoms using electron counting rules such as the octet rule, the 18‐electron rule, Hückel's aromatic rule, and the Wade‐Mingos rule [147].

“Magnetic superatoms,” the name coined by Vijay Kumar and Yoshi Kawazoe [151], is another example of how a cluster could possess a magnetic moment just as transition and rare earth metal atoms do. An early realization of this concept dates back to the work of Rao et al. [152] who showed a Li₄ cluster confined to a tetrahedral geometry has a total spin 1 while its rhombus ground state structure has a total spin 0. That the geometry of a cluster can be linked to its underlying spin structure gives scientists an unprecedented opportunity to design magnetic superatoms where the constituent atoms are not even magnetic. Similarly, clusters of antiferromagnetic elements such as Mn can be ferromagnetic while the magnetic moments of transition metal clusters can far exceed that of their bulk value [153].

Knowing that superatoms can have properties different from the atoms, one can envision a new class of materials where these superatomic clusters are used as building blocks. One of the basic requirements for this purpose is that the superatomic clusters must be stable when assembled to a form a bulk material. This class of materials is called “cluster‐assembled materials.” The advantage of cluster‐assembled materials over atom‐assembled materials is that their underlying electronic structure is different from the electronic structure of atoms. In Figure 1.5 we present the electronic orbitals of an Al atom and compare it to that of an Al₁₃ superatom [140]. We note that the energy spacing between molecular orbitals and atomic orbitals as well as their degeneracies and energy gap between highest occupied and lowest unoccupied molecular orbitals (HOMO–LUMO) are different. As these energy levels overlap and broaden when individual atoms and superatoms are brought together, the resulting energy bands would be very different. Thus, the electronic structure of cluster‐assembled materials would be different from that of atom‐assembled materials, even though the cluster is composed of the same elemental atoms. A good example is crystals made of carbon atoms and that of C₆₀ fullerene. Graphite, the ground state of atom‐assembled carbon is metallic and made of honeycomb arrangements of layers coupled weakly with each other. Fulleride, a crystal of C₆₀, on the other hand, forms an insulating fcc lattice with weakly bonded C₆₀ clusters. Alkalization of fulleride crystal gives rise to a superconductor while intercalation of graphite by alkali atoms does not. In addition to the different electronic structure between atoms and superatoms, there are other features that contribute to the unique properties of cluster‐assembled materials. For example, in a conventional crystal there is only one length scale, namely the lattice constant, while in a cluster‐assembled material, there are two length scales – the intra‐cluster distance and the inter‐cluster distance. Clusters due to their nonspherical shape can influence the potential energy surface due to their rotational degree of freedom, while in a conventional crystal, the atoms, being spherical, do not have that freedom. The phonons generated from the lattice vibration and their coupling with electrons can also render unusual properties depending upon whether the crystal has atoms vs superatoms as building blocks.

Figure 1.5 Spin polarized electron orbitals of Al atom (left panel) and the Al₁₃ cluster (right panel).

      Source: Jena [140]. © American Chemical Society.

      The central question then is: how to ensure that the superatoms retain their geometry after assembly? This can be accomplished in a number of ways: (i) The superatoms should be very stable (e.g., C₆₀) and must not coalesce or deform as they come together to form a crystal. Electron counting rules as well as atomic shell closure rules can be used to identify such superatoms. Stability of clusters satisfying the jellium shell closure rule is one such scheme that is discussed in the above. However, stable superatoms can also be designed by satisfying other electron counting rules such as the octet rule for simple elements (s² p⁶), the 18‐electron rule for transition metal elements (s² p⁶ d¹⁰), 32‐electron rule for rare earth elements (s² p⁶ d¹⁰ f¹⁴), the aromatic rule for organic molecules, and the Wade‐Mingos rule for boron‐based and Zintl clusters. (ii) Endohedral doping of metal atoms can also be used as an effective strategy to stabilize clusters. (iii) Atomic clusters can be soft‐landed on a substrate and kept apart by limiting their density or (iv) coated with ligands that protect the core when assembled. In the latter two cases, it is likely that the substrate and the ligands can interact with the atomic clusters and can affect both their geometry and properties. Instead of viewing such interactions as undesired, they can be used to tailor the properties of atomic clusters by choosing the right substrate and the ligands.

      In the following 11 chapters, various authors discuss how to design superatoms by using simple electron counting rules, how to stabilize them by endohedral doping of metal atoms, and how to protect them from coalescing with each other by coating them with suitable ligands, or soft‐landing them on a chosen substrate to form cluster‐based thin films. Cluster‐assembled materials and how their properties can be tailored to produce novel catalysts, magnetic materials, and materials for energy production, storage, and conversion are also discussed. The concluding chapter describes outstanding problems and provides an insight into the future developments.

References

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      13 13 Alonso, J.A. (2012). Structure and Properties of Atomic Nanoclusters, 2e. River Edge, NJ: World Scientific.

      14 14 Jellinek, J. (2012). Theory of Atomic and Molecular Clusters: With a Glimpse at Experiments. New York: Springer Science & Business Media.

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      17 17 Ciobanu, C.V., Wang, C.‐Z., and Ho, K.‐M. (2013). Atomic Structure Prediction of Nanostructures, Clusters and Surfaces. New York: John Wiley & Sons.

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