Many-body conjugated-circuit computations

Aromaticity of Carbon Nanotubes

Carbon nanotubes are composed of cylindrical graphite sheets. Both nanotubes and graphite sheets are benzenoid derivatives composed of sp2 carbon atoms arranged in a hexagonal pattern. Therefore both systems are aromatic. The extent of the aromatic character of a molecule G (here benzenoids) can be explained in terms of the number of possible Kekulé structures in G. In this work the Kekulé structures in carbon nanotubes and the corresponding, rectangular, graphite-sheets the tubes might originate from, were enumerated. It was shown that (2,2), (3,3), and (4,4) carbon nanotubes are more aromatic than the corresponding, rectangular, planar structures. This explains why it might be more difficult to saturate nanotubes by addition reactions than the respective, "narrow", graphite sheets.

An Alternative Strategy for Count and Storage of Kekulé and Longer Range Resonance Valence Bond Structures

In this paper, we suggest a simple representation for notation of Kekulé valence bond (KVB) structures and longer range resonance valence bond (RVB) structures, which is called "the adjacency bonding array". In this representation, only an N component one-dimensional array is needed for inscribing each KVB or longer range RVB structure for an N-carbon system. Based on the adjacency bonding arrays, we develop very efficient algorithms for the systematic search of KVB and RVB structures as well as evaluation of the basis set overlap and Hamiltonian matrices.

Table of Periodic Properties of Fullerenes Based on Structural Parameters

The periodic table (PT) of the elements suggests that hydrogen could be the origin of everything else. The construction principle is an evolutionary process that is formally similar to those of Darwin and Oparin. The Kekulé structure count and permanence of the adjacency matrix of fullerenes are related to structural parameters involving the presence of contiguous pentagons p, q and r. Let p be the number of edges common to two pentagons, q the number of vertices common to three pentagons, and r the number of pairs of nonadjacent pentagon edges shared between two other pentagons. Principal component analysis (PCA) of the structural parameters and cluster analysis (CA) of the fullerenes permit classifying them and agree. A PT of the fullerenes is built based on the structural parameters, PCA and CA. The periodic law does not have the rank of the laws of physics. (1) The properties of the fullerenes are not repeated; only, and perhaps, their chemical character. (2) The order relationships are repeated, although with exceptions. The proposed statement is the following: The relationships that any fullerene p has with its neighbor p + 1 are approximately repeated for each period.

Nanotubes: number of Kekulé structures and aromaticity

Carbon nanotubes (CNTs) are composed of cylindrical graphite sheets consisting of sp(2) carbons. Due to their structure CNTs are considered to be aromatic systems. In this work the number of Kekulé structures (K) in "armchair" CNTs was estimated by using the transfer matrix technique. All Kekulé structures of the cyclic variants of naphthalene and benzo[c]phenanthrene have been generated and the basic patterns have been obtained. From this information the elements of the transfer matrix were derived. The results obtained indicate that K (and the resonance energy) is greater if tubulenes are extended in the vertical than in the horizontal direction. Tubulenes are therefore more stabile than cyclic strips. An illustration, obtained by using scanning probe microscope, has been attached to affirm the existence of thin CNTs.