Search Results (5)

Columnar phases consisting of a group of carbon toroidal molecules (C₁₂₀, C₁₉₂, C₂₅₂, C₂₈₈) are studied numerically. Each nanotorus was previously doped with an iron atom. This made it possible to use an external magnetic field as a tool for influencing both an individual molecule and a linear fragment of the columnar phase. A high-precision scheme for calculating the dynamics of large molecules with a rigid frame structure is proposed to solve the problem. The group dynamics of nanotori clusters under the influence of an external magnetic field has been studied using classical molecular dynamics methods. The influence of the molecular cluster size, temperature, magnetic moment of the molecule, and magnetic field direction on the collective behavior of iron-doped toroidal molecules with different contents of carbon atoms is analyzed. Molecular dynamics calculations showed that systems of nanotori doped with a single iron atom retain a columnar structure both in the absence and in the presence of an external magnetic field. The columnar fragment behaves as a stable linear association of molecules even at sufficiently high values of magnetic induction, performing a coordinated collective orbital rotation around a common center of mass on a nanosecond time scale. Full article

Supramolecular interaction of carbon nanotori in a columnar phase is described using the methods of classical molecular dynamics. The collective behavior and dynamic properties of toroidal molecules arising under the action of the van der Waals forces are studied. The conditions under which columnar structures based on molecular tori become unstable and rearrange into another structure are investigated. The reasons for the appearance of two types of directed rotational motion from the chaotic motion of molecules are discussed. Full article

There are three different approaches for constructing nanotori in the literature: one with three parameters suggested by Altshuler, another with four parameters used mostly in chemistry and physics after the discovery of fullerene molecules, and one with three parameters used in interconnecting networks of computer science known under the name generalized honeycomb tori. Altshuler showed that his method gives all non-isomorphic nanotori, but this was not known for the other two constructions. Here, we show that these three approaches are equivalent and give explicit formulas that convert parameters of one construction into the parameters of the other two constructions. As a consequence, we obtain that the other two approaches also construct all nanotori. The four parameters construction is mainly used in chemistry and physics to describe carbon nanotori molecules. Some properties of the nanotori can be predicted from these four parameters. We characterize when two different quadruples define isomorphic nanotori. Even more, we give an explicit form of all isomorphic nanotori (defined with four parameters). As a consequence, infinitely many 4-tuples correspond to each nanotorus; this is due to redundancy of having an “extra” parameter, which is not a case with the other two constructions. This result significantly narrows the realm of search of the molecule with desired properties. The equivalence of these three constructions can be used for evaluating different graph measures as topological indices, etc. Full article

A Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [d_ij], where for i≠j, dij is the Euclidean distance between the nuclei i and j. In this matrix d_ii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. The aim of this paper is to compute the automorphism group of the Euclidean graph of a carbon nanotorus. We prove that this group is a semidirect product of a dihedral group by a group of order 2. Full article

The PI polynomial of a molecular graph is defined to be the sum X^{|E(G)|−N(e)} + |V(G)|(|V(G)|+1)/2 − |E(G)| over all edges of G, where N(e) is the number of edges parallel to e. In this paper, the PI polynomial of the phenylenic nanotubes and nanotori are computed. Several open questions are also included. Full article