A theorem on the fullerenes with no adjacent pentagons

Overview of VSEPR Theory

sp3d and sp3d 2 Hybridization

Cyclohexane does not exist in a planar form due to the high angle and torsional strain it would experience in the planar structure. Instead, it adopts non-planar chair and boat conformations.
The chair form is the most stable and derives its name from its resemblance to the “easy chair.” In the chair conformation, two carbon atoms are arranged out-of-plane — one above and one below, minimizing the torsional strain. In the chair form, the bond angle is very close to the ideal tetrahedral value,...

Neutral hydrocarbons like cyclopentadiene with an odd number of carbon atoms and one intervening CH2 group in the ring are not aromatic. Cyclopentadiene with 4 π electrons does not satisfy the 4n + 2 π electron rule. Additionally, the intervening CH2 group is sp3 hybridized and lacks a vacant p orbital, thereby interrupting the overlap of p orbitals in a continuous manner and preventing the delocalization of π electrons throughout the ring.
Due to the absence of continuous overlap of p...

Heterocyclic aromatic compounds are cyclic compounds that are aromatic and have one or more heteroatoms—atoms other than carbon, in the ring. Depending upon the number of atoms present in the ring, they can be either five or six-membered. Examples of five-membered heterocyclic aromatic compounds include pyrrole, furan, thiophene, and imidazole. Pyrrole consists of one nitrogen atom having one lone pair of electrons. Furan and thiophene have one oxygen and one sulfur heteroatom, respectively.

Cycloheptatriene is a neutral monocyclic unsaturated hydrocarbon that consists of an odd number of carbon atoms and an intervening sp3 carbon in the ring. The three double bonds in the ring correspond to 6 π electrons, which is a Huckel number, and therefore satisfies the criteria of 4n + 2 π electrons. However, the intervening sp3 carbon disrupts the continuous overlap of p orbitals. As a result, cycloheptatriene is not aromatic.
Removing one hydrogen from the intervening CH2 group with both...