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Views: 3 Author: Site Editor Publish Time: 2023-05-03 Origin: Site

The combinatorial topology (i.e. carbon atoms and bonds between them, neglecting their positions and distances) of closed-shell **fullerenes** with simple spherical mean surfaces (orientable, genus zero) can be expressed as convex A polyhedron; more precisely, its one-dimensional skeleton, consisting of its vertices and edges. A Schlegel graph is the projection of the skeleton onto a face of the polyhedron through a point outside the face; so that all other vertices are projected into the face.The Schlegel graphs of closed fullerenes are planar and 3-regular (or "cubic"; meaning all vertices have degree 3).Closed fullerenes with spherical shells must have at least some pentagonal or heptagonal cycles.More precisely, if all faces have 5 or 6 sides, according to Euler's polyhedron formula V−E+F=2 (where V, E, F are the number of vertices, edges and faces), must be is even and must have exactly 12 pentagons and V/2−10 hexagons.A similar restriction exists if the fullerene has a heptagonal (seven atoms) cycle.Open fullerenes, such as carbon nanotubes and graphene, can be composed entirely of hexagonal rings.Theoretically, long nanotubes connected at both ends to form closed ring-like sheets could also consist entirely of hexagons.

**Bind**

Since each carbon atom is bonded to only three adjacent carbon atoms instead of the usual four, it is customary to describe these bonds as a mixture of single and double covalent bonds.Carbohybridization in C60 has been reported as sp2.01.The bonding state can be analyzed by Raman spectroscopy, infrared spectroscopy, and X-ray photoelectron spectroscopy.

**Package**

Additional atoms, ions, clusters, or small molecules can become trapped inside the fullerene, forming clathrates called intercalated fullerenes.An unusual example is the egg-shaped fullerene84, which violates the isolated Pentagon rule,found evidence of end-Permian meteor impacts by analyzing noble gases trapped in fullerenes.

**Research**

In the early 2000s, the chemical and physical properties of fullerenes were a hot topic in research and development.Popular Science discusses the possible use of fullerenes (graphene) in armor.Heat resistance and superconductivity are some of the more studied properties in the field of nanotechnology.Many calculations have been done using ab initio quantum methods applied to fullerenes.IR, Raman and UV spectra can be obtained by DFT and TD-DFT methods.The results of this calculation can be compared with experimental results.Fullerenes are unusual reactants in many organic reactions, such as the Binger reaction discovered in 1993.

**Aromaticity**

Researchers have been able to increase the reactivity of fullerenes by attaching reactive groups to their surfaces.Buckminsterfullerene does not exhibit "superaromaticity": that is, the electrons in the hexagonal rings are not delocalized across the molecule.Spherical fullerenes of n carbon atoms have n pi-bonding electrons and can be freely delocalized.These should try to delocalize over the entire molecule.The quantum mechanics of this arrangement should be like a shell of the well-known quantum mechanical structure of a single atom, with a stable filled shell n = 2, 8, 18, 32, 50, 72, 98, 128, etc. (i.e. twice perfect squares), but this series does not include 60.The 2(N + 1)2 spherical aromaticity rule (N integer) is a three-dimensional analog of the Hückel rule.10+ cations satisfy this rule and should be aromatic.This has been shown to be the case using quantum chemical models, which show the presence of strong diamagnetic ball currents in the cations result, C.60 in water tends to absorb two more electrons and become an anion 60 Attempts to form loose metal bonds.

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