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The 32‐electron rule applies to clusters containing early 5f elements where complete shell closure of s ² p ⁶ d ¹⁰ f ¹⁴ orbitals give them stability and chemical inertness. The discovery of empty icosahedral Zintl ions such as Pb₁₂ ²⁻ and Sn₁₂ ²⁻ [58, 59] motivated Dognon et al. [60] to study the stability of endohedral clusters Pu@Pb₁₂. With an electronic configuration of [Rn] 5f ⁶ 7s ² for Pu and [Xe] 4f ¹⁴ 5d ¹⁰ 6s ² 6p ² for Pb, Pu@Pb₁₂ constitutes a 32‐electron system. The calculated HOMO–LUMO gap of 1.93 eV and the binding energy of 22.17 eV measured against the ionic dissociation limit confirm that the stability of Pu@Pb₁₂ arises due to the 32‐electron shell closure. In Figure 2.18 we compare the orbital energies of Pu@Pb₁₂ with that of Pb₁₂ ²⁻. One can see the strong participation of the central atom orbitals in bonding.

A few years later, Ghanty and coworkers [61] showed that the stability of Pu embedded in a C₂₄ cage also follows the 32‐electron rule, with 8 electrons contributed by Pu and 24 π electrons contributed by the C₂₄ fullerene. The authors found that the C₂ symmetry of the empty C₂₄ fullerene transforms to D_6d symmetry, once encapsulated with the Pu atom. The HOMO–LUMO gap of 1.83 eV of the bare C₂₄ cage changes to 3.26 eV following Pu encapsulation. The binding energy of the Pu@C₂₄ clusters measured with respect to atomic fragments is 6.77 eV. Other 32‐electron systems studied recently include An@C₂₈ [62], Pu@Sn₁₂ [63], (U@Si₂₀)⁶⁻ [64], and actinide‐encapsulated fullerene systems [65], U@C₂₈ [66], Ln(CO)₈ ⁻ (Ln = Tm, Yb, Lu) [67], and superatomic CBe₈H₁₂ cluster [68].

Figure 2.18 Orbital energies of Pu@Pb₁₂ and Pb₁₂²⁻. The latter have been shifted to make the HOMOs equal.

Source: Dognon et al. [60]. © John Wiley & Sons.