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Figure 1.2 Schematic diagram of an atom and atomic orbitals (left panel) where the positively charged nucleus is localized at a point, and jellium model of a cluster where the positive charge is smeared over a sphere of finite radius with corresponding electronic orbitals (right panel).

      Source: Adapted with permission from Ref. [140]. Copyright 2013 American Chemical Society.

where n ₀ is the density of the positive charge and R is the radius of the sphere. Θ(r − R) = 1 for r ≤ R and Θ(r − R) = 0 for r > R. The electrons responding to this charge distribution occupy orbitals similar to those in the atoms. The major difference is that in this case the orbitals of clusters are characterized as 1S 1P 1D 2S 1F 2P . . . . shells. Because the number of free electrons in a Na cluster is equal to the number of Na atoms, the magic numbers observed in Na clusters, namely 2, 8, 20, 40, . . . correspond to electronic shell closure of 1S², 1S² 1P⁶, 1S² 1P⁶ 1D¹⁰ 2S², 1S² 1P⁶ 1D¹⁰ 2S² 1F¹⁴ 2P⁶, . . . . orbitals, respectively. The validity of the jellium model has since been established in simple as well as noble metals. Of particular note is the Al₁₃ ⁻ cluster, which contains 40 electrons. Will Castleman and coworkers noted that Al₁₃ ⁻ with a conspicuous peak in the mass spectra is indeed a very stable cluster [141] and is much less reactive toward oxygen than the neighboring clusters (Figure 1.3). In addition, Al₁₃, having an icosahedral geometry, also represents an atomically shell closed structure. The extraordinary stability of Al₁₃ ⁻, therefore, derives from both electronically and atomically closed shell system.

      The above findings led Khanna and Jena to propose that neutral Al₁₃ cluster, with 39 electrons should behave the same way as a halogen atom, as both need one extra electron to close their electronic shells, the former being consistent with the jellium rule and the latter being consistent with the octet rule [137]. Indeed, calculations and experiments showed that the electron affinity of Al₁₃, namely 3.57 eV, is identical to that of Cl [142, 143]. That Al₁₃ mimics the chemistry of halogens that was later shown theoretically [144] by studying its interaction with K. KAl₁₃ was shown to be an ionically bonded cluster just like KCl. Experimental confirmation that KAl₁₃ is indeed ionically bonded validates the superatom concept [145].

For the sake of history, it should be mentioned that properties of clusters have been linked to atoms as early as 1981 when Gutsev and Boldyrev [146] showed that the electron affinity of a cluster with composition MX _{k + 1}, where M is a metal atom with valence k and X is a halogen atom, can exceed that of a halogen atom. Note that MX _{k + 1} cluster, just like a halogen atom, would need an extra electron to close its electronic shell. Because the size of MX _{k + 1} cluster is larger than that of a halogen atom, the Coulomb repulsion experienced by the extra electron decreases as the size increases. Hence, the electron affinity of MX _{k + 1} is larger than that of X. The authors coined the word “superhalogen” to describe these clusters. In a subsequent publication, Gutsev and Boldyrev also showed that the ionization potential of a cluster with composition M _{k + 1}X is less than that of the alkali atom, M where k is the valence of atom X, and coined the word “superalkali” to describe these clusters. Thus, superhalogens and superalkalis that mimic the chemistry of alkali and halogen atoms in the periodic table, respectively, can be regarded as the first demonstration of what is now commonly termed as “superatoms.” Figure 1.4 shows an example of a three‐dimensional periodic table where superhalogens and superalkalis constitute the third dimension representing Group 1 and Group 17 elements [147].

Figure 1.3 Series of mass spectra showing progression of the etching reaction of Al anions with oxygen in 0.0 SCCM (a), 7.5 SCCM (b), and 10.0 SCCM s(c).

      Source: Leuchtner, et al. [141]. © AIP Publishing.

A few years later, Saito and Ohnishi [148] noted that Na₈ satisfying electronic shell closure (1S² 1P⁶) according to the jellium model should be chemically inert like the noble gas atoms, which have their outermost s and p shells closed. Similarly, Na₁₉ lacks an electron to achieve electronic shell closure and should behave like a halogen atom. The authors termed these as “giant atoms.” However, atomic clusters neither have spherical geometries nor do their electrons behave as if they are free electrons. On the contrary, the electrons are confined within the cluster. A later calculation that took explicit account of the cluster geometry showed that Na₈ retains its geometry up to 600 K on a NaCl substrate, but it spontaneously collapses forming an epitaxial layer on a Na (110) surface [149]. When two Na₈ clusters interact, instead of remaining as individual clusters, they coalesce and form a Na₁₆ cluster. Similarly, no evidence exists to demonstrate that Na₁₉ can form a salt‐like molecule, analogous to KAl₁₃, while interacting with an alkali atom.

Figure 1.4 Three‐dimensional periodic table with superatoms mimicking the chemistry of halogens and alkalis. Examples are those of superalkalis designed using the octet rule (Li₃O, Na₃O, K₃O, Rb₃O, Cs₃O) and jellium rule (Al₃) and superhalogens designed using the octet rule (AuF₆, LiF₃, MnCl₃, BO₂) and Wade‐Mingos rule (B₁₂H₁₃).

      In later years, superatoms have been described in terms of their molecular orbital structures specific to their optimized geometries. Instead of using the jellium model and identifying superatoms as they fill the jellium orbitals, superatoms are regarded as a single unit with their molecular orbitals filled much the same way as electrons fill orbitals of a single atom. The chemistry of the superatoms is then determined by the outer molecular orbitals. As an example, consider Al₁₃I₂ ⁻ [150]. Since Al₁₃ behaves as a halogen, one could regard Al₁₃I₂ ⁻ mimicking a triiodide I₃ ⁻ ion. Indeed, the outer electronic orbitals of Al₁₃I₂ ⁻ and I₃ ⁻ ion have similar features. Similarly, Al₁₄I⁻ can be viewed as Al₁₄ ²⁺.3I⁻,

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