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0.28 eV [101]. Furthermore, Mn(C5H5)2 − should be unstable against electron emission not only because it is a 19‐electron system but also because the two extra electrons will repel. This is indeed the case. However, if H is replaced by CN or BO, the corresponding Mn[C5(BO)5]2 and Mn[C5(CN)5]2 2− are superhalogens with electron affinities of 4.85 and 4.78 eV, respectively. In addition, Mn[C5(BO)5]2 2− and Mn[C5(CN)5]2 2−, which are 19‐electron systems, are stable with a second electron affinity of 0.38 and 0.7 eV, respectively.
2.3.3 Trianions
Unlike the studies of dianions, work on trianions is rather scarce. One of the early studies of the trianions was due to Compton and coworkers who reported the mass spectra of (C60)2(CN)5 3− and (C60)2(CN)7 3− [102]. Note that observation of species in mass spectra does not necessarily mean that the trianions are stable, but simply that they exist only within experimental conditions. Many metastable multiply charged ions are observed due to repulsive Coulomb barrier. Indeed, (C60)2(CN)5 3− is metastable against autodetachment of the third electron. Cederbaum and coworkers [103] examined the stability of a number of trianions and found that the best candidate, B(C2CO2)3 3−, is thermodynamically unstable against electron emission by −0.4 eV.
Following the discovery of colossal stability of the B12(CN)12 2−, Zhao et al. [104] calculated the optimized geometry and total energy of BeB11(CN)12 in neutral, monoanion, dianion, and trianion form. Note that with Be replacing a B atom, an additional electron will be required to satisfy the Wade‐Mingos rule and the octet rule, simultaneously. In Figure 2.32 we show the geometry, thermal stability at 800K, and electronic structure of BeB11(CN)12 3−, which is stable against auto‐ejection of the third electron by 2.65 eV. When CN is replaced by BO or SCN, the third electron affinities of the resulting trianions BeB11(BO)12 3− and BeB11(SCN)12 3− are, respectively, 1.30 and 0.59 eV.
Figure 2.32 BeB11(CN)123− (a) geometry, (b) AIMD simulation as a function of temperature and total energy fluctuation, (c) Raman and infra‐red (IR) simulation spectra, (d) natural bond orbital (NBO) charge distribution, and (e) energy diagram and frontier orbitals.
Source: Zaho et al. [104]. © John Wiley & Sons.
2.3.4 Tetra‐Anions and Beyond
Recently Hong and Jena [105] developed a universal model to examine the stability of multiply charged anions capable of carrying more than three extra electrons by tailoring their proximity to the closed shell as well as the size and the electron affinity of the terminal groups. They discovered several thermodynamically stable tetra‐ and penta‐anions containing as few as 50 and 80 atoms, respectively. The starting point is to realize that the extra electrons in a stable multiply charged cluster must reside in a set of bound states. Assuming a spherical potential well with a given depth V and radius r, the number of bound states depends on a positive coefficient a where V ≥ a/r 2. The larger the coefficient a, the greater are the number of bound states. A deeper or wider potential well can hold more bound states.
To form a stable tetra‐anion, the authors chose two stable dianions. Recall that M(CN)4 2− (M = Mg, Ca, Sr, Ba) and BeB11(CN)12 3− are known to be very stable dianion and trianion, respectively. By removing a CN− from BeB11(CN)12 3−, Hong and Jena combined BeB11(CN)11 2− with a series of M(CN)4 2− clusters and optimized the resulting geometries (Figure 2.33). BeB11(CN)11M(CN)4 4− (M = Ca, Sr, Ba) clusters were found to be stable with the fourth electron bound by 0.79, 0.20, and 0.25 eV, respectively. Similarly, the fourth electron affinity of Be2B22(CN)23 4− was found to be 1.48 eV. A similar procedure led to the discovery of Be2B22(CN)23Ca(CN)4 5− penta‐ion with a fifth electron affinity of 30 meV. The level of theory used to predict the composition, geometry, and electron affinity of the above tetra‐ and penta‐anions is same as that was used to predict the electron affinity of B12(CN)12 2−. As mentioned above, this prediction has now been experimentally verified. Thus, we believe that the predicted stable tetra‐ and penta‐anions can be found and the synergy between theory and experiment can lead to the focused discovery of other multiply charged anions, potentially opening a new chapter in materials chemistry.
Figure 2.33 (a) Evaluation of the size (r = 9.09 Å) needed for a stable tetra‐anion using the estimated a4 and the maximal V (15.85 eV) of the known trianions (in green). The red dashed line is the estimated threshold line for tetra‐anions. The green solid line is the threshold line for trianions. (b) Demonstration of using the known multiply charged clusters with proper sizes to form new clusters with higher negative charge states. To form the penta‐anion, certain CN− terminal group, as indicated under shades, needs to be knocked off. (c) Evaluation of the size (r = 11.04 Å) needed for a stable penta‐anion using the estimated a5 and the maximal V (19.86 eV) of the newly found tetra‐anions (in red). The purple dashed line is the estimated threshold line for penta‐anions. Boron is in pink, beryllium in light yellow, carbon in gray, nitrogen in blue, calcium in dark yellow, strontium in green yellow, and barium in brown.
Source: Fang and Jena [105]. © John Wiley & Sons.
2.4 Conclusions
In this chapter we have focused on the design of superatoms, which are atomic clusters of specific size and composition and whose chemistry mimics that of the atoms in the periodic table. The concept of superatoms is that their free electrons occupy a new set of orbitals that are defined by the entire group of atoms in the cluster, instead of by each atom separately. If these superatomic orbitals have the same symmetry as that of the atoms, one can think of a new class of materials with superatoms as the building blocks. Because of their specific size, cluster‐assembled materials may have properties different from those of the corresponding atom‐assembled materials. A classic example is C60 fullerene‐based material vs diamond and graphite. All are made of only carbon atoms but their properties are very different because of the way carbon atoms are arranged.
The central question is how to design these superatoms so that they are stable and maintain their structure when assembled. We discussed various electron‐counting rules that have been used for nearly a century to explain the stability of atoms and the compounds they form. Just as superatomic orbitals mimic atomic orbitals, it is expected the same electron‐counting rules that apply to atoms may also apply to superatoms. Indeed, we demonstrated how the octet rule for low atomic number species, the 18‐electron rule for transition metals, the 32‐electron rule for rare earth metals, the Wade‐Mingos rule for boron‐based