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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.