A fullerene F, is a 3-regular (or cubic) polyhedral carbon molecule for which the n vertices the carbons atoms are arranged in 12 pentagons and (n/210) hexagons. Only a finite number of fullerenes are expected to be, up to scale, isometrically embeddable into a hypercube. Looking for the list of such fullerenes, we first check the embeddability of all fullerenes F, for n < 60 and of all prefera...

Fullerenes, a new form of carbon, were discovered in 1985 [1] in graphite vaporization under inert gas at low pressure. Fullerenes have many properties different from either diamond or graphite. Potential applications include superconductors, sensors, catalysts, optical and electronic devices, polymer composites, high-energy fuels and biological and medical materials. But wide application of fu...

In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C60 fullerenes, and a carbon atom and two C60 fullerenes. We model the van der Waals forces between the fullerenes by the Lennard-Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes ar...

We present a comparison of the bond polarizabilities for carbon-carbon bonds in hydrocarbons and fullerenes, using two different models for the fullerene Raman spectrum and the results of Raman measurements on ethane and ethylene. We find that the polarizabilities for single bonds in fullerenes and hydrocarbons compare well, while the double bonds in fullerenes have greater polarizability than ...

This report reviews the thermally activated delayed fluorescence (TADF) displayed by fullerenes. From the analysis of the steady-state data, time-resolved data, or by a combination of both, it is possible to determine several important photophysical parameters of fullerenes. Herein we also cover the development of temperature and oxygen sensors based on the TADF effect exhibited by fullerene C(...

fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. this study considers the symmetry of small fullerenes cage c24 and c28‎. ‎using pm3 program for c24 and c28 fullerenes, oh and td symmetry were confirmed, respectively‎. ‎ the mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of th...

The possible formation of a “cluster molecule” (C20)2 from two single C20 fullerenes is studied by the tight-binding method. Several (C20)2 isomers in which C20 fullerenes are bound by strong covalent forces and retain their identity are found; actually, these C20 fullerenes play the role of “atoms” in the “cluster molecule”. The so-called open-[2+2] isomer has a minimum energy. Its formation p...

We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes - fullgen - and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers ...

New strapped porphyrin-based hosts with different π-conjugated moieties and linkers have been prepared and their ability to bind with fullerenes was studied in dilute solution. We found that the ability of these hosts to bind with fullerenes strongly depends on their chemical nature and more precisely on the substitution pattern of the porphyrin deck. As expected, the more electron-rich hosts c...