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In previous sections we have discussed the design of stable monoanions by using a single electron‐counting rule. Here, we discuss how the stability of monoanions can be further enhanced by using multiple electron‐counting rules. Recall that C₆H₆ has a negative electron affinity, which can be systematically increased by replacing H by F (see Table 2.2). Driver and Jena [73] have systematically replaced H atoms with a BO₂ moiety. Note that BO₂ ⁻ is isoelectronic with CO₂ and is a very stable molecule. Indeed, it is a superhalogen with an electron affinity of 4.46 ± 0.03 eV [96]. In Figure 2.25 we show the equilibrium geometries of neutral and anionic C₆H_{6 − x} (BO₂) _x , x = 1–6. Note that in most situations BO₂ molecules dimerize and bind to the carbon atoms. From Table 2.2 we see that the electron affinity increases systemically as H is replaced by F and BO₂ and reaches a value of 1.80 eV in C₆(BO₂)₆. Note that C₆(BO₂)₆ satisfies both the aromatic rule and the octet rule. The electron affinity can be further increased by replacing one of the C atoms with B. The equilibrium geometries of neutral and anionic BC₅H_{6 − x} (BO₂) _x , x = 1–6 are shown in Figure 2.26, and the corresponding electron affinities are given in Table 2.2. Thus, a benzene molecule can be made into a superhalogen by suitable modification, and the electron affinity of BC₅H(BO₂)₅ surpasses that of Cl. In general, the electron affinity of a cluster can be increased by choosing the composition of a cluster that satisfies multiple electron‐counting rules. This can be seen from several recent publications [97, 98].

Figure 2.25 Ground state geometries of neutral and anionic C₆H_{6 − x} (BO₂) _x . The gray, white, pink, and red spheres correspond to carbon, hydrogen, boron, and oxygen, respectively.

Source: Driver [73].

Figure 2.26 Ground state geometries of neutral and anionic C₅BH_{6 − x} (BO₂) _x . The gray, white, pink, and red spheres correspond to carbon, hydrogen, boron, and oxygen atoms, respectively.

Another example where the use of both octet rule and aromaticity rule can simultaneously give rise to stable monoanions is BC₅H_{6 − x} (CN) _x , x = 1–6. Here, the H atoms in C₆H₆ are sequentially replaced by superhalogen CN. The electron affinities of these clusters calculated using density functional theory and B3LYP hybrid exchange‐correlation potential with 6‐31 + G* basis set implemented in the Gaussian 16 code are given in Figure 2.27. Note that electron affinity of BC₅(CN)₆ is close to 6 eV, making it a hyperhaolgen. It is interesting to compare the electron affinities of these clusters with isoelectronic C₅H_{5 − x} (CN) _x , x = 1–5. The results are compared with the electron affinities BC₅H_{6 − x} (CN) _x in Figure 2.27. As the number of CN ligands increases, the electron affinities of both these two classes of clusters become identical, indicating that the ligands as well as total number of “valence” electrons play a role in stabilizing the monoanions.

Figure 2.27 Electron affinities of BC₅H_{6 − x} (CN) _x , x = 1–6 and their isoelectronic C₅H_{5 − x} (CN) _x , x = 1–5.

Unusually stable clusters can also be created by satisfying three electron‐counting rules, simultaneously. Consider, for example, Mn[BC₅(CN)₆]₂ ⁻ that satisfies the aromaticity rule, the octet rule, and the 18‐electron rule, simultaneously. The geometry of neutral and anionic Mn[BC₅(CN)₆]₂ ⁻ cluster computed by Giri et al. [94] is shown in Figure 2.28. Here, Mn is sandwiched between two BC₅(CN)₆ molecules. Another consequence of the electron shell closure is that the magnetic moment of the Mn atom is quenched. The octet shell closure enables CN to have an electron affinity of 3.86 eV. The electron affinity of BC₅(CN)₆, which satisfies both the octet rule and aromaticity rule is 5.87 eV. Mn[BC₅(CN)₆]₂, satisfying three electron‐counting rules simultaneously, has an electron affinity of 6.40 eV. This provides a recipe for designing highly stable negative ions.

Figure 2.28 Equilibrium geometries of (a) neutral and (b) anionic Mn[BC₅(CN)₆]₂ cluster.

Source: Adapted with permission from Giri et al. [94]. © Royal Society of Chemistry.