LITMIR.BIZ

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      Source: Dognon et al. [60]. © John Wiley & Sons.

      2.2.5 Aromaticity Rule

Aromaticity rule was developed by Huckel [12, 13, 69] to account for the stability of planar conjugated molecules such as C₆H₆. Based on a molecular orbital theory, it was shown that planar conjugated monocyclic polyene that has (4n + 2) (n = 0, 1, 2, . . . ) π or nonbonding electrons will be aromatic and stable. For benzene, n = 1. Because of the high stability, the aromatic molecules have low electron affinities, which seldom exceed 1.17 eV. Indeed, the electron affinity of C₆H₆ is −1.29 eV [70]. Jena and coworkers [71, 72] showed that the aromaticity rule can be used to design superatoms with electron affinities that can even exceed the electron affinity of Cl. This is accomplished by replacing H atoms in C₆H₆ by more electronegative atoms as well as by changing composition of the hexagonal core. In Figures 2.19 and 2.20, we show the globally optimized geometries of C₆H_{6 − x} F _x and BC₅H_{6 − x} F _x (x = 1–6) computed by Driver and Jena [73] using density functional theory. The corresponding electron affinities are given in Table 2.2. Note that the electron affinities of C₆H_{6 − x} F _x and BC₅H_{6 − x} F _x steadily increase with x. The computed electron affinity, 0.75 eV of C₆F₆ agree well with the experimental value of 0.86 ± 0.03 eV [74, 75]. Realizing that the electron affinity of C₅H₅, which lacks one electron to be aromatic, is +1.80 eV, Jena and coworkers replaced one of the C atoms in C₆H₆ by a B atom. The resulting BC₅H₆ lacks one electron to be aromatic, and its electronic affinity of 2.31 eV is indeed high. Further replacement of H atoms by F atoms allows the electron affinity to rise systematically, reaching a value of 3.24 eV for BC₅F₆. Thus, an aromatic molecule can mimic the chemistry of a halogen atom by suitable tailoring of its core and/or the ligand atoms.

Figure 2.19 Ground state geometries of neutral and anionic C₆H_{6 − x}F_x. The gray, white, and blue spheres correspond to carbon, hydrogen, and fluorine, respectively.

      Source: Driver and Jena [73]. © John Wiley & Sons.

The aromaticity rule has been extended to inorganic systems, providing further opportunities to design a new class of superatoms. One of these is an all‐metal cluster, MAl₄ ⁻ (M = Li, Na, Cu). Using experiment and ab initio calculations, Li et al. [76] compared the measured photoelectron spectra with theory. The computed geometries of the MAl₄ ⁻ clusters (see Figure 2.21) are found to be pyramidal with the metal atom M at the apex carrying +1 charge and interacting with a square Al₄ ²⁻ moiety. Note that the geometry of an isolated Al₄ ²⁻ is also a square, although it is unstable against spontaneous emission of the second electron. The HOMO of MAl₄ ⁻, as well as that of Al₄ ²⁻, was found to be doubly occupied and composed of a delocalized π orbital, with other molecular orbitals being either σ‐type or lone pairs. The presence of two valence electrons is characteristic of Huckel aromaticity, with n = 0.

Figure 2.20 Ground state geometries of neutral and anionic C₅BH_{6 − x}F_x. The gray, white, pink, and blue spheres correspond to carbon, hydrogen, boron, and fluorine, respectively.

      Source: Driver and Jena [73]. © John Wiley & Sons.

Table 2.2 Electron affinities (in eV) of ground state molecules.

x	C6H6 − x F x	BC5H6 − x F x	C6H6 − x (BO2) x	BC5H6 − x (BO2) x	C6H6 − x (CN) x
0	−1.29	2.31	−1.15	2.31	−1.29
1	−0.93	2.28	−0.75	2.78	0.09
2	−0.62	2.56	−0.38	2.72	1.06
3	−0.42	2.93	0.79	3.24	1.70
4	0.01	2.91	1.22	3.12	2.44
5	0.45	3.15	1.67	3.93	3.11
6	0.75	3.24	1.80	3.65	3.49

Figure 2.21 Left panel: photoelectron spectra at 355 nm (3.496 eV) for (a) LiAl₄⁻, (b) NaAl₄⁻, and (c) CuAl₄⁻ and at 266 nm (4.661 eV) for (d) LiAl₄⁻, (e) NaAl₄⁻, (f) CuAl₄⁻, and (g) square planar Al₄^2– cluster. Right panel: optimized structures of LiAl₄⁻, NaAl₄⁻, Al₄²⁻ [at the CCSD(T)/6‐311+G* level of theory], and CuAl₄⁻.

      Source: Li et al. [76]. © American Association for the Advancement of Science.

      2.2.6 Wade‐Mingos Rule

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