I discuss the symmetry of fullerenes, viruses and geodesic domes within a unified framework of icosadeltahedral representation of these objects. The icosadeltahedral symmetry is explained in details by examination of all of these structures. Using Euler’s theorem on polyhedra, it is shown how to calculate the number of vertices, edges, and faces in domes, and number of atoms, bonds and pentagon...

An algorithm has been developed for the construction of planar graphs for two series of IPR fullerenes of the general formula C50þ 10n and C60þ 12n (n 1⁄4 1, 2, 3,. . .) maintaining 5and 6-fold rotational symmetry, respectively. Some important utilities of these graphs have been shown. Simple rules have then been developed for factorising these graphs in order to obtain the eigenvalues correspo...

Conjugated rigid rod molecules are extensively studied for their optical and semiconducting properties. Since their size is suitable for the inclusion in SWNTs, they are optimal candidates molecules to obtain hybrid systems emitting in the visible spectral range [1]. Such hybrids systems are called peapods where the nanotube is the “pod” and the inserted molecule the “pea”. Successful encapsula...

A computer code and algorithm are developed for the computer perception of molecular symmetry. The code generates and uses the Euclidian distance matrices of molecular structures to generate the permutationinversion group of the molecule. The permutation-inversion group is constructed as the automorphism group of the Euclidian distance matrix. Applications to several molecular structures and fu...

Internet Electron. J. Mol. Des. 2003, 1, 000–000 Abstract Motivation. The periodic table (PT) of the elements suggests that hydrogen could be the origin of everything. The construction principle is an evolutionary process that is formally similar to those of Darwin and Oparin. The PT of fullerenes suggests that C60 could be the origin of fullerenes and C30 could be considered as the element zer...

We investigate the size-dependent dielectric response of carbon fullerenes with up to 3840 atoms in the framework of the linear response theory. Our results suggest a significant polarizability enhancement due to quantum size effects with respect to classical or semiclassical calculations. The accuracy of our results, based on a parametrized Hamiltonian, is verified by ab initio time dependent ...

We investigate high-order harmonic generation in a sequence of icosahedral fullerenes using the extension of the so-called three-step or Lewenstein model to the molecular case. The high harmonic spectra obtained at midinfrared wavelengths show modulations in the plateau region. These modulations are due to the coherent superposition of the contributions from the atomic centers in the molecule t...

Decay and fusion as two different mechanisms of stability loss for the (C 20) 2 cluster dimer ABSTRACT The thermal stability of the (C 20) 2 cluster dimer consisting of two C 20 fullerenes is examined using a tight-binding approach. Molecular dynamics simulations of the (C 20) 2 dimer at temperatures T = 2000-3500 K show that the finite lifetime τ of this metastable system is determined by two ...

Carbon the 6th element in the periodic tables has always remains a fascinating material to the researcher and technologist. Diamond, graphite, fullerenes, carbon nanotubes and newly dis‐ covered graphene are the most studied allotropes of the carbon family. The significance of the these material can be understand as the discovery of fullerene and graphene has been awarded noble prizes in the ye...

The van der Waals coefficients between quasispherical nanostructures can be modeled accurately and analytically by those of classical solid spheres (for nanoclusters) or spherical shells (for fullerenes) of uniform valence electron density, with the true static dipole polarizability. Here, we derive analytically and confirm numerically from this model the size dependencies of the van der Waals ...