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electron affinities and gain energy by accepting an electron in a chemical reaction. Thus, when an alkali atom and a halogen atom approach each other, electron transfer from the alkali to the halogen atom satisfies the octet rule of both the atoms, resulting in the formation of a salt and an ionic bond between the cations and anions. In other cases, such as H2, O2, and N2, electron shell closure is achieved not by transferring electrons from one atom to the other but rather by sharing electrons. This leads to a covalent bond, which, in general, is stronger than an ionic bond. A fourth kind of bonding appears as atoms from groups 2–13 and some elements in the higher groups upto 16 come together to form a crystal. Here, each atom contributes its outer valence electrons to a common pool. These electrons move “freely” and collectively, forming a metal. Note that, the ionic cores of the metal also have electronic shell closure.

Schematic illustration of the periodic table of elements.

      In this chapter we examine if the electron‐counting rules, known to explain the stability of atoms and compounds, can be used to rationally design stable clusters. The first glimpse of such a possibility came from the experiment of Knight and collaborators in 1984 [6]. The authors observed conspicuous peaks in the mass spectra of Na clusters containing 2, 8, 20, 40, . . . atoms. Realizing that similar observation was made in nuclear physics where nuclei with 2, 8, 20, 40, . . . nucleons were found to be very stable, Knight et al. suggested an electronic shell model, analogous to the nuclear shell model [7], to explain the magic numbers in Na clusters. They used the jellium model where free electrons move in a uniform distribution of positive ion charge. Assuming that a Na cluster has a spherical geometry and the charges on the positive ion cores are distributed uniformly, they showed that the stability of the magic Na clusters is due to shell closures of their electronic orbitals such as 1S2, 1S2 1P6, 1S2 1P6 1D10 2S2, 1S2 1P6 1D10 2S2 1F14 2P6, . . . .

      In the following, we first study clusters of simple metals whose stability can be well explained by the jellium model and see if magic clusters can be assembled to make a bulk material. Next, we explore a number of other electron‐counting rules such as the octet rule for sp elements [8–10], 18‐electron rule for transition metal elements [11], 32‐electron rule for rare earth elements, Hückel's aromaticity rule for organic molecules [12, 13], and Wade‐Mingos rule [14–17] for boron‐based clusters and Zintl ions [18, 19]. We focus not only on neutral but also on charged clusters that can be stabilized by using any one of the above rules and combinations thereof.

      2.2.1 Jellium Rule

Schematic illustration of binding-energy curves of (Na19)2 for two different electronic configurations.

      Source: Saito and Ohnishi [20]. © American Physical Society.

Schematic illustration of binding energy as a function of distance between two Na atoms.

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