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Figure 2.28 Equilibrium geometries of (a) neutral and (b) anionic Mn[BC₅(CN)₆]₂ cluster.

      Source: Adapted with permission from Giri et al. [94]. © Royal Society of Chemistry.

      2.3.2 Dianions

Unusual stability of Mn[BC₅(CN)₆]₂ ⁻ suggests that if Mn is replaced by Cr, one extra electron will be needed to satisfy the octet, aromaticity, and 18‐electron rule, simultaneously. Thus, Cr[BC₅(CN)₆]₂ ²⁻ should be a stable cluster. Giri et al. [94] calculated the second electron affinity of Cr[BC₅(CN)₆]₂ ²⁻ to be 2.58 eV, which is substantially larger than the 0.9 eV value of B₁₂H₁₂ ²⁻. Molecular dynamics simulation of Cr[BC₅(CN)₆]₂ ²⁻ at 300 K confirmed that it is thermally stable. From the snapshots of the geometries taken at different time intervals in Figure 2.29, we see that there is very little change in its geometry.

Another example of an ultra‐stable dianion designed by satisfying multiple electron‐counting rules is B₁₂(CN)₁₂ ²⁻ where the H atoms of B₁₂H₁₂ ²⁻ are replaced by CN molecules. Recall that CN needs an extra electron to satisfy the octet rule. Thus, B₁₂(CN)₁₂ ²⁻ satisfies both the octet and Wade‐Mingos rules. Zhao et al. [99] found the optimized geometry of B₁₂(CN)₁₂ ²⁻ to be a perfect icosahedron (see Figure 2.30) with the second electron bound by 5.3 eV. This colossal stability of B₁₂(CN)₁₂ ²⁻ has been recently verified experimentally by Mayer et al. [100] and the measured electron affinity of 5.55 eV agrees well with predicted value. To date, B₁₂(CN)₁₂ ²⁻ is the most stable dianion known in the gas phase.

Figure 2.29 Molecular dynamics simulation of Cr[BC₅(CN)₆]₂²⁻ cluster.

      Source: Giri et al. [94]. © Royal Society of Chemistry.

Figure 2.30 Geometry of B₁₂(CN)₁₂²⁻ with I_h symmetry.

      Source: Jena and Sun [1]. © American Chemical Society.

Dianions of organic molecules such as C₆H₆ and C₈H₈ can also be stabilized by replacing H with BO and CN superhalogens and two of the carbon atoms by boron. The resulting B₂C₄X₆ ²⁻ (X = H, BO, CN) clusters satisfy both the aromaticity rule and octet rule. Chen et al. [54] computed the geometries of neutral, monoanion, and dianions of B₂C₄X₆ (X = H, BO₂, CN) clusters. These are given in Figure 2.31; the electron affinity and vertical detachment energies associated with the addition of the first and second electron are given in Table 2.3. Note that the dianions of all molecules are stable, once H is replaced by CN and BO. Similarly, TiC₁₂(CN)₁₂ ²⁻ that satisfies both the 18‐electron rule and aromaticity rule is also stable with the second electron bound by 0.76 eV.

Figure 2.31 Optimized geometries of (a) B₂C₄H₆^0,1−,2−, (b) B₂C₄(BO)₆^0,1−,2−, (c) B₂C₄(CN)₆^0,1−,2−, (d) C₈(CN)₆^0,1−,2−, (e) C₈H₈^0,1−,2−, (f) C₈(BO)₈^0,1−,2−, and (g) C₈(CN)₈^0,1−,2− clusters. Gray, pink, brown, and red spheres stand for C, N, B, and O atoms, respectively.

      Source: Chen et al. [54]. © American Chemical Society.

Table 2.3 First and second electron affinity (EAs) and vertical detachment energy (VDEs) of the studied aromatic molecules.

Clusters	FVDE	FEA	SVDE	SEA
B2C4H6	2.01	1.90	−2.68	−3.27
B2C4(BO)6	6.93	6.11	1.71	1.58
B2C4(CN)6	5.47	5.38	1.59	1.12
C8(CN)6	5.41	5.19	0.83	0.81
C8H8	1.47	0.82	−3.35	−3.49
C8(BO)8	5.03	4.53	1.70	1.21
C8(CN)8	5.00	4.64	1.54	1.21

      FEA, first electron affinity; SEA, second electron affinity; and SVDE, second vertical detachment energy.

      In some cases, the ligands can play a significant role that can even dominate over the electron‐counting rule. Consider, for example, manganocene, Mn(C₅H₅)₂. It has 17 electrons with Mn contributing 7 electrons due to its 3d ⁵ 4s ² configuration and each C₅H₅ contributing 5 electrons. Thus, Mn(C₅H₅)₂ ⁻ should be very

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