Chemistry; Computer Applications in Chemistry; Mathematics Applications in Chemistry; Theoretical and Computational Chemistry; Nanotechnology and Computer Graphics
ABSTRACT:
§1 presents literature data and the authors own results on nanostructure building, and semiempirical and strain energy calculations. Novel dimeric and oligomeric structures predicted to appear via the coalescence of C60 molecules and the cages that could result by loss of carbon atoms from the starting molecules are the main subjects. §2 presents one of the most intensively studied carbon allotropes namely the polyhex torus. Original methods of construction and tiling modification, nomenclature and correspondence to other nomenclatures are presented. Criteria for metallic and aromatic character properties are tabulated. Rules to identify identical polyhex toroidal graphs within families of chiral embedding isomers are formulated in terms of the net dimensions. Resonance energy of polyhex tori is evaluated in the context of a generalized Clar theory of aromaticity. §3 introduces Distinct Walled Tori, so called to indicate the varying number of atoms on the inner and outer walls, respectively. The energetics and aromaticity for various types of DWTs derived from armchair nanotubes or conical domains are presented. Diameter doubling of single-walled carbon nanotubes and zigzag nanotubes are also discussed. §4 defines some of the most discussed counting polynomials and the more recently proposed Omega and Cluj polynomials. Some theorems in the two latter named polynomials are discussed and demonstrated. Hosoya, Cluj, and Omega polynomials are detailed and used in the topological characterization and stability prediction of nanostructures: spherical, tubular, and toroidal. A factorization procedure, for describing the chiral polyhex tori in terms of Omega polynomial is presented. §5 deals with the study of planar and 3D surfaces by various polygonal faces. Operations on maps and geometrical-topological transformation of a parent covering, are systematically introduced, from the simplest, through to composites, and up to generalized operations, which enable the embedding of various coverings in any surface. General analytical relations among the parameters of transformed and parent maps are presented. Molecular realizations of the proposed operations or sequences of operations are illustrated. Stone-Wales edge-rotations are presented as possible routes of isomerization, enabling changes in the nanostructure tessellation. §6 offers a detailed discussion on the aromatic character of fullerenes, with classical and non-classical covering. It is shown that aromatic character is a multi-conditional molecular property which can be dependent upon energetics, electronic structure, magnetic response, geometric characteristics, or chemical behaviour. It is shown that having a varied aromaticity criteria results in a random ordering of molecules. Generalized perfect Clar structures, with the 2-factor designed as corannulenic or corazulenic disjoint flowers have been proven. Sequences of classical or single generalized map operations were used to obtain these coverings. As a structural/geometric parameter of aromaticity, the HOMA index enabled an evaluation of local aromatic character of the featured supra-faces and thus generated evidence for several dominant Kekule valence structures. The described operations and structures are believed to be helpful in the process of molecular structure elucidation and in guiding researchers in finding novel nanostructured materials. §7 discusses triply periodic nanostructures and associated units which, by a self-assembly process, provide architectures of negative curvature, also known as schwarzites. A short introduction to the theory of triply periodic minimal surfaces is offered. Unit blocks built up by opening map operations could model the junctions of carbon nanotubes; these can be synthesized by nanowelding, that is, crossing tubes in an electron beam. Junctions are rationalized according to the building operation. A gallery of junctions and triply periodic architectures is offered in the appendices.
