Motivation. Novel carbon allotropes, with finite molecular structure, including spherical fullerenes are nowadays currently produced and investigated. These compounds have beautiful architectures and show unusual properties that are very promising for the development of nanotechnologies. The Kekulé structure count and permanent of the adjacency matrix are computed for these molecules. Method. A...

It is known that silicon fullerenes cannot maintain perfect cage structures like carbon fullerenes. Previous density-functional theory calculations have shown that even with encapsulated species, nearly all endohedral silicon fullerenes exhibit highly puckered cage structures in comparison with their carbon counterparts. In this work, we present theoretical evidences that the tetrahedral fuller...

Strutinsky shell corrections for the Cesium-coated fullerenes were investigated. The single particle levels of electrons are obtained using the spherical mean-field potential of a shifted Wood-Saxon type. The parameters of the potential are adjusted to reproduce the experimental ionization energies of the Cs(N) clusters and the magic numbers observed in their photo-ionization spectra of the C60...

Using the first principle methods, we proposed a series of three-chain boron cages B6n+14 (n = 1-12) which are mainly built by fusing three boron semi-double-rings. Their simple geometric structures (approximate D3 or C3 symmetry) facilitate their bottom-up syntheses from the hexagonal B7 and the double-chain boron clusters, such as B2, B4, B6, B8H2, B10H2, B12H2, and the double ring B20. The s...

Here we identify a novel class of biological membrane ion channel blockers called single-walled carbon nanotubes (SWNTs). SWNTs with diameter distributions peaked at approximately 0.9 and 1.3 nm, C60 fullerenes, multi wall nanotubes (MWNTs), and hyperfullerenes (nano-"onions") were synthesized by several techniques and applied to diverse channel types heterologously expressed in mammalian cells...

The notion of Isoperimetric Quotient (IQ) of a polyhedron has been already introduced by Polya. It is a measure that tells us how spherical is a given polyhedron. If we are given a polyhedral graph it can be drawn in a variety of ways in 3D space. As the coordinates of vertices belonging to the same face may not be co-planar the usual deenition of IQ fails. Therefore, a method based on a proper...

The stability of He@C60 and Ne@C60 is discussed in the context of a spherical model where the carbon atoms are smeared out into a uniform shell. The electronic properties of the sixty π electrons together with those of the central atom are treated in the Thomas-Fermi approximation. Simple electrostatic reasoning elucidates the nature of the radial stability of the complex. A method to include n...

Amphiphilic poly(phenylquinoline)-block-polystyrene rod-coil diblock copolymers were observed to self-organize into robust, micrometer-scale, spherical, vesicular, cylindrical, and lamellar aggregates from solution. These diverse aggregate morphologies were seen at each composition, but their size scale decreased with a decreasing fraction of the rigid-rod block. Compared to coil-coil block cop...

In this paper, we introduce two combinatorial operations and a knot-theoretical approach for generation and description of fullerene architectures. The ‘Spherical rotating–vertex bifurcation’ operation applied to original fullerene polyhedra can lead to leapfrog fullerenes. However, the ‘Spherical stretching–vertex bifurcation’ operation applied to fullerene generates a family of related polyhe...