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Stability of transition metal compounds can be accounted for by using the 18‐electron rule where 18 electrons are needed to fill ns ² np ⁶ and (n−1)d ¹⁰ orbitals [11]. Classic examples of complexes stabilized by the 18‐electron rule are chromium bisbenzene [Cr(C₆H₆)₂] and ferrocene [Fe(C₅H₅)₂]. C₆H₆ and C₅H₅ have six and five π electrons each. As Cr and Fe have outer electronic configuration of 3d ⁵ 4s ¹ and 3d ⁶ 4s², respectively, one can see that both Cr(C₆H₆)₂ and Fe(C₅H₅)₂ are 18‐electron systems.

Pykko and Runenberg [55] showed that an all‐metal cluster, Au₁₂W, with a HOMO–LUMO gap of 3.0 eV is very stable due to the 18‐electron rule. Here, 12 Au atoms contribute 12 electrons while W atom (3d ⁵ 4s ¹) contributes 6 electrons. This prediction was later verified in photoelectron spectroscopy experiment by Wang and collaborators [56]. A further proof of the 18‐electron rule can also be seen by measuring the electron affinity of Ta@Au₁₂. Note that with 17‐valence electrons, Ta@Au₁₂ needs one extra electron to satisfy the 18‐electron shell closure rule. Indeed, the measured electron affinity of 3.76 eV makes Ta@Au₁₂ an all‐metal superhalogen [57]. Chen et al. calculated the structure and stability of M@Au₁₂ ²⁻ (M = Ti, Zr, Hf) to see if these clusters can be stable and thus can be regarded as superchalcogens. The results are given in Figure 2.17. Note that all these structures are dynamically stable. However, Ti@Au₁₂ ²⁻ is unstable against an electron loss by 0.23 eV while M@Au₁₂ ²⁻ (M = Zr, Hf) dianions are stable against the second electron loss by 0.05 eV, due to their increased size.

Figure 2.17 (a)–(c) are the optimized geometries for MAu₁₂^0,1−,2− (M = Ti, Zr, and Hf) clusters, respectively. Yellow, dark red, purple, and blue spheres stand for Au, Ti, Zr, and Hf atoms, respectively.

Source: Chen et al. [54]. © American Chemical Society.