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Many different celestial objects emit an infrared sprectrum which has been attributed to infrared fluorescence from a family of highly vibrationally excited benzenoid hydrocarbons referred to as polycyclic aromatic hydrocarbons (PAHs). The most intense emitters contain between 20 to 50 carbon atoms, although larger species also contribute to the emission. This assignment is based on a rough resemblance...
A Valence Bond theory of delocalization predicts that Xn aggregates of atoms or groups X are generally unstable when X is able to form strongly bound dimers X2 (e.g. H2), while Xn may be stable if the X2 bond is weak (e.g. Li2). According to this theory, the π systems of aromatic hydrocarbons are expected to be unstable in a regular geometry and to be more stable in an alternated one. To verify this...
Clear theoretical evidence is presented to show that the π-electron systems of benzenoid aromatic molecules are described well in terms of localized, non-orthogonal, singly-occupied orbitals. The characteristic properties of molecules such as benzene or naphthalene arise from a profoundly quantum mechanical phenomenon, namely the mode of coupling of the electron spins, rather than from any supposed...
Because the π-networks of benzenoid hydrocarbons are the classical prototypical example of delocalized bonding, they provide a crucial test for chemical-bonding theories. Here there is revealed a systematic organization for valence-bond views to describe such π-bonding. With an initiation near the ab initio realm a sequence of semiempirical valence-bond models is identified and characterized. The...
The formalism of scaling relations between the reduced topological invariants is reviewed. First, the basic concepts of the chemical graph theory, the known approximate formulae for the total π-electron energy and the size extensivity of topological invariants are outlined. The scaling properties of the reduced topological invariants are introduced and the accuracy of various scaling functions is...
After a brief discussion of the notion of molecular topology and the analogy principle as related to topology/reactivity relationships more recent developments in the field of reactivity indices for polynuclear benzenoid hydrocarbons are reviewed. Reaction mechanisms and correlations of reactivity indices with rates of electrophilic substitution and Diels-Alder reactions, thermally induced polymerization,...
The formulas for all benzenoid hydrocarbons are found in Table PAH6 which has x,y-coordinates of (ds, NIc). Recursive construction of this table was accomplished using an aufbau principle. This table complies to a sextet rule analogous to the octet rule for the periodic table of elements, and ds is analogous to the outer-shell...
A survey of relevant papers is given, and five simple and simply handleable algorithms of low complexity based on results contained in these papers are described (without proofs): Algorithms A and C enable the number of Kekulé structures and Pauling's bond orders to be determined and the characteristic polynomial and the eigenspaces (eigenvalues, eigenvectors) to be calculated for all benzenoid...
The existence of Kekulé structures in a benzenoid system is the first fundamental problem in the topological theory of benzenoid systems. It was considered as one of the most difficult open problems in this theory. Many investigations have been made in order to find necessary and sufficient conditions for the existence of Kekulé structures in a benzenoid system. Some fairly simple conditions which...
The present paper is a review of the P-V path method. The concept of the P-V path was proposed by Gordon and Davison in 1952. In the last few years this method has been greatly developed and has become one of the important approaches for investigating Kekulé structures of benzenoid hydrocarbons. The superiority of this method is its simplicity and visualization. According to the properties of the...
This chapter presents rapid ways to determine whether or not a given benzenoid system possesses a Kekulé structure. Two simple were discovered by Sachs and the present author, respectively. Both algorithms operate by deleting vertices and edges from the benzenoid system examined. Emphasis is given to the algorithm proposed by the present author. The algorithm seems to be the simplest of the presently...
The enumeration of Kekulé structures for rectangle-shaped benzenoids is treated. Combinatorial formulas for K (the Kekulé structure count) are derived by several methods. The oblate rectangles, Rj(m, n), with fixed values of m are treated most extensively and used to exemplify different procedures based on the method of fragmentation (chopping, summation), a fully computerized method (fitting of polynominal...
Several illustrations of the Clar's aromatic sextet theory for the electronic properties of benzenoid hydrocarbons are demonstrated. It is shown how various techniques and concepts of the graph theory are useful for realizing and formulating not only this purely empirical theory but also the mathematical beauty of the structural formula of aromatic hydrocarbons. It is proposed that the sextet polynomial...
Gutman trees (also known as caterpillar trees and benzenoid trees) are demonstrated to be elegant storage devices of information on graph-theoretical properties of many mathematical objects including benzenoid graphs, rook boards, king polyomino graphs, Clar graphs, and Young diagrams. The notion of a “restricted” equivalence relation is considered to relate these graphs. The uses of caterpillars...
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