Zhang–Zhang Polynomials of Multiple Zigzag Chains Revisited: A Connection with the John–Sachs Theorem

Multiple zigzag chains Zm,n of length n and width m constitute an important class of regular graphene flakes of rectangular shape. The physical and chemical properties of these basic pericondensed benzenoids can be related to their various topological invariants, conveniently encoded as the coefficients of a combinatorial polynomial, usually referred to as the ZZ polynomial of multiple zigzag chains Zm,n. The current study reports a novel method for determination of these ZZ polynomials based on a hypothesized extension to John–Sachs theorem, used previously to enumerate Kekulé structures of various benzenoid hydrocarbons. We show that the ZZ polynomial of the Zm,n multiple zigzag chain can be conveniently expressed as a determinant of a Toeplitz (or almost Toeplitz) matrix of size m2×m2 consisting of simple hypergeometric polynomials. The presented analysis can be extended to generalized multiple zigzag chains Zkm,n, i.e., derivatives of Zm,n with a single attached polyacene chain of length k. All presented formulas are accompanied by formal proofs. The developed theoretical machinery is applied for predicting aromaticity distribution patterns in large and infinite multiple zigzag chains Zm,n and for computing the distribution of spin densities in biradical states of finite multiple zigzag chains Zm,n.     

π‐Electron currents in larger fully aromatic benzenoids

Recently, we have reported on calculation of π‐electron ring currents in several smaller fully benzenoid hydrocarbons having up to eight fused benzene rings and five Clar π‐aromatic sextets. In contrast to early HMO ring current calculations and more recent ab initio calculations of π‐electron density, our current calculations are based on a graph theoretical model in which contributions to ring currents comes from currents associated with individual conjugated circuits. In this contribution, we consider several larger fully benzenoid hydrocarbons having from 9 to 13 fused rings and from six or seven π‐aromatic sextets. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

正规苯型烃的命名及对称性分类

正规苯型烃的命名及对称性分类贾金萍王爱坤（河北科技大学）何文辰（河北工业大学，天津３００１３０）关键词本型烃正规苯型烃苯型烃（稠环芳烃）是一系列苯环稠接而成的化合物，是介于苯与石墨间的多种有机化合物的统称。如能在氢气氛中将石墨裂解就有可能得到各种苯型...     

Wiener Index of Hexagonal Systems

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. Hexagonal systems (HS's) are a special type of plane graphs in which all faces are bounded by hexagons. These provide a graph representation of benzenoid hydrocarbons and thus find applications in chemistry. The paper outlines the results known for W of the HS: method for computation of W, expressions relating W with the structure of the respective HS, results on HS's extremal w.r.t. W, and on integers that cannot be the W-values of HS's. A few open problems are mentioned. The chemical applications of the results presented are explained in detail.     

On the Anti-forcing Number of Benzenoids

The anti-forcing number is introduced as the smallest number of edges that have to be removed that any benzenoid remains with a single Kekulé structure. Similarly, the anti- Kekulé number is discussed as the smallest number of edges that have to be removed that any benzenoid remains connected but without any Kekulé structure. These concepts have been exemplified on damaged benzenoid parallelograms.     

On the anti-Kekulé number and anti-forcing number of cata-condensed benzenoids

Previously introduced concepts the anti-Kekulé number and anti-forcing number (Vukicevic et al., J. Math. chem., in press) are applied to cata-condensed benzenoids. It is shown that all cata-benzenoids have anti-Kekulé number either 2 or 3 and both classes are characterized. The explicit formula for anti-forcing number of chain (unbranched) cata-benzenoids is given. It is also shown that anti-forcing number of any cata-benzenoid goes up to h/2 where h is the number of hexagons in a cata-benzenoid.      

Conjugated circuits currents in hexabenzocoronene and its derivatives formed by joining proximal carbons

We report on calculated CC bond currents for a dozen derivatives of hexabenzocoroenene in which one or more proximal carbon atoms at the molecular periphery have been bridged. The approach that we use is graph‐theoretical in nature, following our outline of this method in 2003, which is based on finding all conjugated circuits in all Kekulé valence structures of these molecules. To the π‐electrons having 4n + 2 π‐electrons are assigned anticlockwise π‐electron currents and to conjugated circuits having 4n π‐electrons are assigned π‐electron currents. One may summarize the results reported in this work by stating that CC bond currents in the compounds considered decrease on going from peripheral rings to the central ring of the molecule, and also that CC bond currents decrease by insertion of bridges to proximal peripheral benzenoid rings. © 2012 Wiley Periodicals, Inc.     

Novel PI Indices of Hexagonal Chains

Problems don't hung on trees. Formulation of a good problem is often the most important part of a (theoretical) research. New problems usually arise when you try to solve old problems. Ivan Gutman, June 27, 1995.The Padmakar–Ivan (PI) index of hexagonal chains (i.e., the molecular graphs of unbranched catacondensed benzenoid hydrocarbons) is examined. The index PI is a graph invariant defined as the summation of the sums of edges of n _eu and n _ev over all the edges of connected graph G, where n _eu is the number of edges of G lying closer to u than to v and n _ev is the number of edges of G lying closer to v than to u. An efficient calculation of formula for PI for hexagonal chains are put forward.     

Biomimetic Total Synthesis of Cyanosporaside Aglycons from a Single Enediyne Precursor through Site‐Selective p‐Benzyne Hydrochlorination

The cyanosporasides A–F are a collection of monochlorinated benzenoid derivatives isolated from the marine actinomycetes Salinispora and Streptomyces sp. All derivatives feature one of two types of cyanocyclopenta[a]indene frameworks, which are regioisomeric in the position of a single chlorine atom. It is proposed that these chloro‐substituted benzenoids are formed biosynthetically through the cycloaromatization of a bicyclic nine‐membered enediyne precursor. Herein, we report the synthesis of such a bicyclic precursor, its spontaneous transannulation into a p‐benzyne, and its differential 1,4 hydrochlorination reactivity under either organochlorine or chloride‐salt conditions. Our bioinspired approach culminated in the first regiodivergent total synthesis of the aglycons A/F and B/C, as well as cyanosporasides D and E. In addition, empirical insights into the site selectivity of a natural‐like p‐benzyne, calculated to be a ground‐state triplet diradical, to hydrogen, chlorine, and chloride sources are revealed.