Stability and aromaticity of nH(2)@B(12)N(12) (n=1-12) clusters

The inscribed polygon method is consistent with Hückel’s 4n + 2 rule and helps to learn whether the given cyclic compound is aromatic or not. The compound is stable and aromatic if every bonding molecular orbital (MO) is completely filled with a pair of electrons. However, if the non-bonding or antibonding orbitals are filled with electrons, the compound is unstable and not aromatic. Consider the Frost circle diagrams for cycloalkenes containing 4 to 8 carbons.

Like benzene, cyclobutadiene and cyclooctatetraene are cyclic compounds with alternate single and double bonds. However, their chemical behavior differs from benzene, as they are unstable and not aromatic. So, what are the structural characteristics of unsaturated compounds categorized as aromatic?
For the first time, Eric Hückel, a German chemical physicist, derived a set of structural features for a compound to be classified as aromatic. This is now known as Hückel’s rule or the 4n + 2 rule.

Aromatic compounds can be identified or analyzed using proton NMR and carbon‐13 NMR. Typically, aromatic hydrogens or hydrogens directly bonded to the aromatic rings are strongly deshielded by the aromatic ring current. Therefore, they absorb in the range of 6.5–8.0 ppm in proton NMR spectra. For instance, aromatic hydrogens directly bonded to the benzene ring absorb at 7.3 ppm. However, aromatic hydrogens of larger rings absorb farther upfield or downfield than the ideal range. Consider...

According to the molecular orbital (MO) model, benzene has a planar structure with a regular hexagon of six sp2 hybridized carbons. As shown in Figure 1, each carbon is bonded to three other atoms with C–C–C and H–C–C bond angles of 120°. The C–H bond length is 109 pm, and the C–C bond length is 139 pm which is midway between the single bond length of sp3 hybridized carbons (154 pm) and sp2 hybridized carbons (133 pm).

In aromatic compounds, such as benzene, the circulation of (4n + 2) π-electrons sets up a diamagnetic or diatropic ring current around the perimeter of the molecule. This current induces a magnetic field that opposes the external field inside the ring and reinforces it on the outside. The protons in benzene are deshielded and exhibit high chemical shifts in the range 6.5–8.5 ppm. The shielding effect at the center of the ring is evident in complex aromatic molecules, such as annulenes. In...

Simple unsubstituted benzene has six aromatic protons, all chemically equivalent. Therefore, benzene exhibits only a singlet peak at δ 7.3 ppm in the 1H NMR spectrum. The observed shift is far downfield because the aromatic ring current strongly deshields the protons. Any substitution on the benzene ring makes the aromatic protons nonequivalent, and the protons split each other. The peak is, therefore, no longer a singlet and the splitting pattern and their associated coupling constants depend...