Related papers: Some open mathematical problems on fullerenes
It is well known since 2010 that fullerene C60 is widespread through the interstellar space. Also, it is well known that graphene is a source material for synthesizing fullerene. Here, we simply assume the occurrence of graphene in space.…
Graphene - a monolayer of carbon atoms densely packed into a hexagonal lattice - has one of the strongest possible atomic bonds and can be viewed as a robust atomic-scale scaffold, to which other chemical species can be attached without…
We introduce a new cohomology theory for planar trivalent graphs with perfect matchings. The graded Euler characteristic of the cohomology is a one variable polynomial called the 2-factor polynomial that, if nonzero when evaluated at one,…
In 1985, "During experiments aimed at understanding the mechanisms by which long-chain carbon molecules are formed in interstellar space and circumstellar shells", Harry Kroto and his collaborators serendipitously discovered a new form of…
The chapter is devoted to chemical uniqueness of graphene. In view of molecular theory, the latter is a consequence of benzenoid packing of carbon atoms, based on three neighbors to each carbon atom leaving the atom fourth valence electron…
A great efficacy of molecular quantum chemistry applied to basic graphene problems has been recently demonstrated by the authors when studying the formation of peculiar composites between carbon nanotubes and graphene as well as considering…
A unified theory of orthogonal polynomials of a discrete variable is presented through the eigenvalue problem of hermitian matrices of finite or infinite dimensions. It can be considered as a matrix version of exactly solvable Schr\"odinger…
Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of…
Most {\em ab initio} calculations on fullerene molecules have been carried out based on the paradigm of the H\"uckel model. This is consistent with the restricted nature of the independent-particle model underlying such calculations, even…
Fullerenes, including \ce{C60} and \ce{C70}, have been detected in various astronomical environments. Understanding how their structures evolve over time is essential for gaining insights into their life cycle and making further…
Small cationic fullerene fragments, produced by electron impact ionization of C60, were mass-selected and accumulated in cryogenic Ne matrixes. Optical absorption spectroscopy of these fragments with up to 18 carbon atoms revealed linear…
The recent discovery of graphene has sparked significant interest, which has so far been focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particle. However, the structure of…
Two dimensional layers of graphene are currently drawing a great attention in fundamental and applied nanoscience. Graphene consists of interconnected hexagons of carbon atoms as in graphite. This article presents for the first time the…
Two-dimensional (2D) carbon allotropes have received considerable attention due to their unique properties and potential applications in several fields, including electronics, catalysis, energy storage, and sensing. Following the…
The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown's…
We apply here the principle of affine symmetry to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organisational…
Transformation of graphene flakes to fullerenes assisted by Ni clusters is investigated using molecular dynamics simulations. The bond-order potential for Ni-C systems is developed. The potential reproduces the experimental and…
Block designs are combinatorial structures in which each pair of a set of varieties appears together in a fixed number of blocks. Complete graphs are graphs in which every pair of vertices are adjacent. We present some new constructions of…
Catacondensed benzenoids (those benzenoids having no carbon atom belonging to three hexagonal rings) form the simplest class of polycyclic aromatic hydrocarbons (PAH). They have a long history of study and are of wide chemical importance.…
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…