Superatoms. Группа авторов
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al. [36] studied the stability of crystals composed of (CH3)4N+ cation and B(CN)4 − anion. Note that both molecules satisfy the octet rule. The authors found [(CH3)4N+][B(CN)4 −] to be a stable charge‐transfer transparent salt with a band gap of 6.5 eV and having a diverse range of structural phases. In Figure 2.16 we show the geometry of the isolated [(CH3)4N+][B(CN)4 −] cluster and the optimized geometry of the [(CH3)4N+][Al13 −] crystal having body‐centered cubic structure and Td symmetry. The band gap of the crystal phase is close to that of the HOMO–LUMO gap of the isolated cluster, implying that the electronic structure of the crystal is guided by the properties of the individual cluster building blocks.
Figure 2.15 (a)–(e) are the globally optimized geometries for M(CN)40,1−,2− (M = Be, Mg, Ca, Zn, and Cd) clusters, respectively. Gray, pink, light green, dark green, purple, light blue, and dark blue spheres stand for C, N, Be, Mg, Ca, Zn, and Cd atoms, respectively. The charges on selected atoms are also given.
Source: Chen et al. [54]. © American Chemical Society.
In spite of the success of the octet rule accounting for the stability of clusters composed of light elements, like the jellium model, it has limitations; stable clusters exist even though they do not satisfy the octet rule. These include, for example, NO (which has an odd number of valence electrons), BH3 and BF3 (which are electron deficient), and PCl5, SF4, and SF6 (which are electron rich).
Figure 2.16 (a) Isolated (CH3)4N+Al13− cluster. (b) Optimized body‐centered‐cubic phase of (CH3)4N+Al13− crystal with Td symmetry (same as the molecular point‐group of the respective ions). (c) Total energy and lattice parameter (lattice constants a, b, and c in Å, interaxial angles α, β, and γ in degrees, and volume in Å3) fluctuations during the ab initio molecular dynamics simulation. (d) Snapshot of the structure obtained from the ab initio molecular dynamics (AIMD) simulation for 10 ps after 4 ps to allow the system to reach thermal equilibrium.
Source: Huang et al. [36]. © American Chemical Society.
2.2.3 18‐Electron Rule
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 MAu120,1−,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.
2.2.4 32‐Electron Rule
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 D6d 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