Superatoms. Группа авторов

the Wade‐Mingos rule, was developed by Wade [14, 15] and Mingos [16, 17] to account for the structure and bonding of polyhedral borane clusters (B _n H _n ). Because of electron deficiency, B cannot form conventional covalent bonds between adjacent pairs of atoms. Instead, it forms multicenter bonds with the valence electrons separated into external and skeletal electrons. The former forms traditional covalent bonds with ligands while the latter contributes to cage bonding. Consider a borane polyhedron, B _n H _n with n being the number of vertices. According to the Wade‐Mingos rule, 2n + 2, 2n + 4, and 2n + 8 electrons are needed to form closo, nido, and archano boranes, respectively. B₁₂H₁₂ ²⁻ is a well‐known example of a closo‐borane having an icosahedral geometry (Figure 2.22). Here, n = 12. Of the three valence electrons of B, one is involved in the covalent bonding with H while the other two are contributed to the cage bonding. Because 2n + 2 = 2 × 12 + 2 = 26 electrons are needed to stabilize the cage, B₁₂H₁₂ ²⁻ is stable as a dianion. Indeed, the electron affinities of the first and second electron are 4.56 and 0.9 eV, respectively.

If one of the B atoms in B _n H _n is replaced by a C atom, according to the Wade‐Mingos rule only one extra electron will be needed to satisfy the stability criterion. Hence, CB _{n − 1}H _n ⁻ should be a stable cluster. Indeed, this is the case and mono‐carboranes with n = 7–12 have been isolated and structurally characterized [77–80]. Pathak et al. [81] hypothesized that CB₁₁H₁₂ should also behave like a halogen atom. Using density functional theory, the authors calculated the structure and found the electron affinity of CB₁₁H₁₂ to be 5.39 eV, establishing it as a superhalogen. They also showed that MB₁₂H₁₂ (M = Li, Na, K, Rb, and Cs) clusters are superhalogens as they only need one electron to satisfy the Wade‐Mingos rule. In addition, they showed that CB₁₁H₁₂ can be used as the building blocks of hyperhalogens.

Figure 2.22 Geometry of B₁₂H₁₂²⁻.

      Source: Adapted with permission from Jena and Sun [1]. © American Chemical Society.

Al and B belong to the same column in the periodic table, yet they have different chemistry. While Al is a metal, B is not. In addition, Al is not electron deficient like B and its valence electrons are nearly free in the bulk phase. Al does not form the same range of complexes with H as B does. Consequently, Wade‐Mingos rule was known not to apply to Al. Bowen and coworkers [106] studied the possibility that small clusters of Al may have properties similar to that of B. Using the pulsed arc cluster ion source (PACIS), the authors reacted Al clusters with hydrogen and observed a vast range of previously unknown Al _n H _m clusters. In Figure 2.23 we show the mass spectra of Al₄H _m clusters, with Al₄H₆ being particularly stable. Photoelectron spectroscopy experiment revealed a large HOMO–LUMO gap of 1.9 eV, which further confirmed the unusual stability of Al₄H₆. To understand the origin of this stability, the authors computed the geometry of Al₄H₆, which consists of an Al₄ tetrahedron with four radially bonded and two bridge‐bonded H atoms. An examination of the electronic structure revealed that two bridge‐bonded H atoms and the four Al‐H pairs contribute 10 electrons. Thus, Al₄H₆ can be viewed as Al₄H₄ ²⁻, which satisfies the Wade‐Mingos 2(n + 1) rule with n = 4. Note that n = 6 is the smallest value of n for which B _n H _n clusters satisfy the Wade‐Mingos rule.

Figure 2.23 PES spectrum of Al₄H₆ anion (left panel) and mass spectra of Al₄H_m⁻. The inset shows the geometry of Al₄H₆⁻.

      Source: X. Li et al. [106]. © American Chemical Society.

Wade‐Mingos rule can also be used to rationalize the bonding in Zintl ions, which are multiply charged clusters belonging to the post‐transition metal elements in groups 13, 14, and 15. Consider, for example, Sn₁₂ ²⁻. While studying the semiconductor to metal transition, Wang and coworkers [59] observed a very simple photoelectron spectrum (PES) of Sn₁₂ ⁻, which was different from that of its isoelectronic cousin, Ge₁₂ ⁻. The optimized geometry of Sn₁₂ ⁻ was found to be a distorted cage with C_5v symmetry. Adding an extra electron resulted in closed shell Sn₁₂ ²⁻ cluster with icosahedral (I_h) symmetry (Figure 2.24). The PES of Sn₁₂ ²⁻ was found to be similar to that KSn₁₂ ⁻, which can be viewed as K⁺Sn₁₂ ²⁻. Named stannaspherene, Sn₁₂ ²⁻ has a diameter of 6.1 Å, which is large enough to accommodate a metal atom. Indeed, four years prior to the above experiment Kumar and Kawazoe [82] had predicted M@Sn₁₂ (M = Zn, Cd) to be a perfect endohedral cluster with I_h symmetry and a large HOMO–LUMO gap. Cui et al. [83] have subsequently synthesized a series of endohedral clusters with the composition M@Sn₁₂ (M = Ti, V, Cr, Fe, Co, Ni, Cu, Y, Nb, Gd, Hf, Ta, Pt, Au). Kandalam et al. [84] showed that Mn@Sn₁₂ is a stable cluster with a magnetic moment of 5 μ_B and can be regarded as a magnetic superatom. The bonding pattern of Sn₁₂ ²⁻ was found to be similar to that of B₁₂H₁₂ ²⁻ where the 12 5s² localized electron pairs in Sn₁₂ are equivalent to replacing 12 B‐H bonds [59].

      Pb₁₂ ²⁻, which is isoelectronic with Sn₁₂ ²⁻, was also found [58] to be a cage cluster whose stability can similarly be justified in terms of the Wade‐Mingos rule. Named “plumbaspherene,” Pb₁₂ ²⁻ cage has a diameter of 6.29 Å and can accommodate a metal atom inside it. This is consistent with an earlier experiment where an extremely stable AlPb₁₂ ⁺ cluster was synthesized in the gas phase. AlPb₁₂ ⁺ can be viewed as Al₃ ⁺: Pb₁₂ ²⁻ just as KSn₁₂ ⁻ was viewed as K⁺: Sn₁₂ ²⁻. Note that a series of endohedral cage compounds, M@Pb₁₂ ²⁻ (M = Ni, Pd, Pt), stabilized by K⁺ counterions, have been synthesized in solution and in crystalline form. Both of their icosahedral symmetries have been confirmed [85, 86] by X‐ray diffraction and nuclear magnetic resonance (NMR) experiments.

Figure 2.24 Optimized structure of (a) Sn₁₂⁻, (b) Sn₁₂²⁻, and (c) KSn₁₂⁻. The bond distances and cage diameters are in angstroms.

      Source: Cui et al. [59]. © American Chemical Society.

Zintl compounds composed of alkali and alkaline earth cations and Zintl anions such as Sn₅ ²⁻, Pb₅ ²⁻, Pb₉ ⁴⁻, Sb₇ ³⁻, and Bi₄ ²⁻ have been known since 1930s [19, 87]. The entry of Zintl ions into cluster science dates back to the work of Recknagel [88],