Comparability graphs and electronic spectra of condensed benzenoid hydrocarbons

A systematic topological approach to the search for regularities in molecular properties has been proposed on the basis of the so-called comparability graphs of isomeric classes of molecules. It is shown that the ordering of the isomeric benzenoid hydrocarbons in the comparability graphs coincides with that of the longest wavelenght in the p band of their electronic spectra.     

苯型芳烃周期表

按年代次序, 简要回顾各国学者对分子周期系的研究概况. 介绍和讨论Dias, J.R.的多环苯型芳烃周期表的结构和应用.     

A unified theory of the stability of benzenoid hydrocarbons

The spectral density operator technique is proved to be a convenient tool for derivation of approximate topological formulae for total pi-electron energy (E_pi) of benzenoid hydrocarbons (BH s). Developed mathematical formalism points out a common origin of three different measures for the stability of BH s, namely: resonance energy (RE), number of Kekule structures (K) and HOMO -LUMO separation (X_HL). In turn, a novel topological invariant corresponding to “normalized” RE is derived. Numerical calculations for a representative set of BH s demonstrate effectiveness of the present approach. Various approaches to an estimation of BH stabilities are discussed.     

On the number of benzenoid hydrocarbons

We present a new algorithm which allows a radical increase in the computer enumeration of benzenoids b(h) with h hexagons. We obtain b(h) up to h = 35. We prove that b(h) approximately const.kappa(h), prove the rigorous bounds 4.789 < or = kappa < or = 5.905, and estimate that kappa = 5.16193016(8). Finally, we provide strong numerical evidence that the generating function summation operator b(h)z(h) approximately A(z) log(1 - kappa z), estimate A(1/kappa) and predict the subleading asymptotic behavior. We also provide compelling arguments that the mean-square radius of gyration (h) of benzenoids of size h grows as h(2 nu), with nu = 0.64115(5).     

A novel nomenclature of polycyclic aromatic hydrocarbons without using graph centre

In this paper, we develop a novel adjacency matrix, He-matrix, corresponding to the dualist graph. Without using the graph center concept, we advance a novel nomenclature of polycyclic aromatic hydrocarbons. Further, we derive some distinguishing theorems about PAH molecules and present some results of our automatic derivatization and automatic classification counting of fused PAH molecules.     

Thermochemical parameters for benzenoid hydrocarbons

The heats of atomization of aromatic hydrocarbons are correlated with an incremental 5-term scheme that includes CH and CC bond energy terms, resonance energies, and two steric parameters. Regression analysis of the experimental data with respect to the proposed parameters gives reasonable values for each term. A simple method for calculating resonance energies is illustrated that agrees with the results of SCFLCAOMO calculations.     

A new yardstick for benzenoid polycyclic aromatic hydrocarbons

The newly introduced signature of benzenoids (a sequence of six real numbers Si with i = 6-1) shows the composition of the pi-electron partition by indicating the number of times all rings of the benzenoid are assigned 6, 5, 4, 3, 2, or 1 pi-electrons. It allows the introduction of a new ordering criterion for such polycyclic aromatic hydrocarbons by summing some of the terms in the signature. There is an almost perfect linear correlation between sums S6 + S5 and S4 + S3 for isomeric cata- or peri-fused benzenoids, so that one can sort such isomers according to ascending s 6 + S5 or to descending S4 + S3 sums (the resulting ordering does not differ much and agrees with that based on increasing numbers of Clar sextets and of Kekule structures). Branched cata-condensed benzenoids have higher S6 + S5 sums than isomeric nonbranched systems. For nonisomeric peri-condensed benzenoids, both sums increase with increasing numbers of benzenoid rings and decrease with the number of internal carbon atoms. Other partial sums that have been explored are S6 + S5 + S3 And S6 + S2 + S1, and the last one appears to be more generally applicable as a parameter for the complexity of benzenoids and for ordering isomeric benzenoids.     

Resonance in catacondensed benzenoid hydrocarbons

We consider resonance in cata-condensed benzenoids having six and seven fused benzene rings. The resonance relationship between the Kekule valence structures of the molecules is represented by the resonance graphs in which the vertices represent the Kekule valence structures, and the edges, the presence of the quantum chemical resonance integral involving permutation of three CC double bonds (within a single six-membered ring). The construction of the resonance graphs for large benzenoids is outlined and the properties of the derived resonance graphs are discussed. It is shown that the leading eigenvalue of the resonance graphs correlates with the resonance energy of benzenoids. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 585–600, 1997     

On dioxo derivatives of benzenoid hydrocarbons

Extending a problem occurring in connection with the stability order of the tautomers of hypericin, we examine the topological factors influencing the stability of the isomeric dioxo derivatives of benzenoid hydrocarbons, in particular the rules determining the number of Kekulé structures in them. Depending on the position of the oxo groups, the pattern of cyclic conjugation varies significantly, as does the Kekulé structure count. Some general regularities along these lines are established.     

Enumeration and classification of benzenoid hydrocarbons

The enumeration of benzenoids is studied with the aid of different modifications of a computer program. Known values for the number of cata-condensed and of all benzenoids with h (number of hexagons) up to eight are reproduced. These benzenoids are classified into (a) unbranched of different symmetries and branched cata-condensed, and (b) normal, essentially disconnected and non-Kekuléan peri-condensed. Within the normal benzenoids a more detailed classification is performed: basic benzenoids, fused, or annelated. For h = 9 an almost complete classification along the same lines was achieved.     

Perimeter topology of benzenoid polycyclic hydrocarbons

The equivalence of the perimeter topological equations derived by Dias and the 13 possible modes of hexagon adjacency in fused benzenoid systems subsequently presented by Cyvin, Gutman, and collaborators is shown. The aufbau principle for generation of all fused total resonant sextet (TRS) benzenoid hydrocarbons is proved. The precise distinction and topological properties between fused, nonfused, strain-free, strained, helical, and nonhelical benzenoid hydrocarbons are carefully delineated. The TRS benzenoid isomers have the maximum number of bay regions, and expressions for the number of bay regions that any given TRS benzenoid will have are given.     

A formula periodic table for benzenoid hydrocarbons and the aufbau and excised internal structure concepts in benzenoid enumerations

The genesis of the aufbau and excised internal structure concepts is traced. These concepts were pivotal to the first published enumerations of the strictly peri-condensed, non-Kekuléan, and essentially strain-free total resonant sextet benzenoid groups. Aperiodic table set is defined as a partially ordered set forming a two-dimensional array which complies with thetriad principle where a central element has a metric property that is the arithmetic mean of two adjacent surrounding member elements.     

Additivity of resonance energy in benzenoid hydrocarbons

A simple method is described for the calculation of resonance energies (RE ) of linear acenes based on their number of Kekulé structures. The values obtained for the first five linear acenes are used to graph–theoretically calculate RES of a wide variety of benzenoid hydrocarbons. Excellent linear relationships are found between RES and each of A-II, graph-theoretical (GT ), Hess–Schaad (HS ), and Dewar resonance energies (SCF ). These relations apply to 42 hydrocarbons and lead to the following equations: A-II = 0.084RE + 0.080 (0.9999); GT = 0.072RE + 0. 135 (0.9832); HS = 0. 106RE + 0. 169 (0.9889); and SCF = 0.316RE + 0. 166 (0.9899). Correlation coefficients are shown in parentheses. A linear relation also exists between RES and the square roots of the wavelengths of the UV spectra of hydrocarbons of the linear acenes and phene series. Least-squares analysis of the data leads to the following equation: RE = 0.412(λ)^½ ?15.479, with a correlation coefficient equal to 0.9903, in which λ is the wavelength of the β band of the UV spectra of these hydrocarbons. The method predicts no resonance energies for both open chain polyenes and the radialenes.     

Topological hamiltonian spectra of polycyclic benzenoid hydrocarbons

A general theory which points out the relations between Hückel-electron energy, the number of Kekulé structures and the HOMO-LUMO separation is presented. Some normalized topological invariants are derived from the concept of the spectral density function. A reasonably simple (three parameters) model spectral density function leads to universal relations between topological invariants that, although valid for any alternant molecule, were tested numerically for polycyclic benzenoid hydrocarbons. Some general conclusions concerning a distribution of the adjacency matrix eigenvalues are drawn.     

Resonance energy of very large benzenoid hydrocarbons

The resonance energy of conjugated benzenoid systems is expressed as contributions arising from independent conjugated circuits. The scheme has been applied to numerous very large conjugated systems. In many cases, it was possible to find regularities in the increments for the resonance energy within a family of benzenoid systems as the number of benzene rings is increased.     

On the alleged correlations between simple LCAO-MO reactivity indices and proton chemical shifts in planar,condensed, benzenoid hydrocarbons

Previous investigations into the proposed correlations between proton chemical shifts in conjugated hydrocarbons and the various LCAO-MO ‘reactivity indices’ (at the corresponding carbon atoms to which the peripheral protons are bonded), are here reassessed in the light of more-recently acquired experimental data, for the case of the planar, alternant, condensed, benzenoid hydrocarbons. A correlation coefficient of 0·73, statistically ‘significant’ at less than the ½% level, is obtained. Nevertheless, there are several unsatisfactory features of such proposed correlations (which are discussed), and, in the final analysis, no causative relation is expected between proton chemical shifts and reactivity indices in these molecules. Furthermore, the relative chemical shifts of the sterically unhindered protons in planar, alternant, benzenoid hydrocarbons can be accounted for by the ‘ring current’ effect alone, without the need to postulate a dependence of the proton chemical shifts on reactivity indices, which is in any case considered to be unlikely on physical grounds.     

On the characterization of local aromatic properties in benzenoid hydrocarbons

A generalization of the Kekulé index for composite valence structures provides a quantitative value corresponding to Clar's assessment of benzenoid character of aromatic ring systems. The idea involved is further specialized for the individual local rings in the molecules. Comparison with limited experimental data supports the validity of this approach.     

On total π-electron energy of benzenoid hydrocarbons

Hall's observation that the total π-electron energy E of benzonoid hydrocarbons is a linear functions of the number of Kukule structures is supported by theoretical arguments and extensive numerical work. A rather accurate topological formula for E is obtained.