Benzenoid Molecules Research Articles

Unveiling Three Interconvertible Redox States of Boraphenalene.

Neutral 1-boraphenalene displays the isoelectronic structure of the phenalenyl carbocation and is expected to behave as an attractive organoboron multi-redox system. However, the isolation of new redox states have remained elusive even though the preparation of neutral boron(III)-containing phenalene compounds have been extensively studied. Herein, we have adopted an N-heterocyclic carbene ligand stabilization approach to achieve the first isolation of the stable and ambipolar 1-boraphenalenyl radical 1•. The 1-boraphenalenyl cation 1+ and anion 1- have also been electrochemically observed and chemically isolated, representing new redox forms of boraphenalene for the study of non-Kekulé polynuclear benzenoid molecules. Experimental and theoretical investigations suggest that the interconvertible three-redox-state species undergo reversible electronic structure modifications, which primarily take place on the polycyclic framework of the molecules, exhibiting atypical behavior compared to known donor-stabilized organoboron compounds. Initial reactivity studies, aromaticity evaluations, and photophysical studies show redox-state-dependent trends. While 1+ is luminescent in both the solution and solid states, 1• exhibits boron-centered reactivity and 1- undergoes substitution chemistry on the boraphenalenyl skeleton and serves as a single-electron transfer reductant.

Two-dimensional coronene fractal structures: topological entropy measures, energetics, NMR and ESR spectroscopic patterns and existence of isentropic structures

Molecular fractals are geometric patterns that appear self-similar across all length scales and are constructed by repeating a single unit on a regular basis. The benzenoid compounds are found to have a natural pattern that helps to analyse and explore the potential attributes of these molecular fractals. Here, we focus on coronene-based fractals where coronene is a benzenoid molecule with a symmetric graphite-like structure and challenging synthesis methods. Topological molecular descriptors are obtained in order to provide structure-activity relations for the physico-chemical properties. We obtain these descriptors for the molecular fractals that are constructed by repeating a fixed unit of coronene on different stages systematically. The structural characterisation of the two-dimensional coronene fractals in various tessellations is presented through a wide range of degree-based topological indices. The entropy measures of these significant frameworks are also computed for estimating their potential attributes, and the comparison of their values among various degree-based indices is performed, which shows the existence of isentropic structures. We have developed machine learning techniques for robust computations of the enthalpies, NMR and ESR spectroscopic patterns of coronene fractals.

Hosoya Polynomial for Subdivided Caterpillar Graphs.

Computing Hosoya polynomial for a graph associated with a chemical compound plays a vital role in the field of chemistry. From Hosoya polynomial, it is easy to compute the Weiner index(Weiner number) and Hyper Weiner index of the underlying molecular structure. The Wiener number enables the identifying of three basic features of molecular topology: branching, cyclicity, and centricity (or centrality) and their specific patterns, which are well reflected by the physicochemical properties of chemical compounds. Caterpillar trees are used in chemical graph theory to represent the structure of benzenoid hydrocarbons molecules. In this representation, one forms a caterpillar in which each edge corresponds to a 6-carbon ring in the molecular structure, and two edges are incident at a vertex whenever the corresponding rings belong to a sequence of rings connected end-to-end in the structure. Due to the importance of Caterpillar trees, it is interesting to compute the Hosoya polynomial and the related indices. The Hosoya polynomial of a graph G is defined as H(G;x) = Σd(G)K=0 d(G.k)xk. In order to compute the Hosoya polynomial, we need to find its coefficient d(G.k) which is the number of pairs of vertices of G which are at distance k. We classify the ordered pair of vertices which are at distance , 2 ≤ m ≤ (n + 1)k in the form of sets. Then finding the cardinality of these sets and adding them up will give us the value of coefficient d(G.m) . Finally, using the values of coefficients in the definition, we get the Hosoya polynomial of uniform subdivision of caterpillar graph. In this work, we compute the closed formula of Hosoya polynomial for subdivided caterpillar trees. This helps us to compute the Weiner index and hyper-Weiner index of uniform subdivision of caterpillar graph. Caterpillar trees are among the important and general classes of trees. Thorn rods and thorn stars are the important subclasses of caterpillar trees. The idea of the present research article is to provide a road map to those researchers who are interested in studying the Hosoya polynomial for different trees.

Aromaticity of Nonplanar Fully Benzenoid Hydrocarbons.

The Clar aromatic sextet theory can provide a qualitative description of the dominant modes of cyclic π-electron conjugation in benzenoid molecules and of the relative stability among a series of isomeric benzenoid systems. In a series of nonplanar fully benzenoid hydrocarbons, the predictions of the Clar theory were tested by means of several different theoretical approaches: topological resonance energy (TRE), energy effect (ef), harmonic oscillator model of aromaticity (HOMA) index, six center delocalization index (SCI), and nucleus-independent chemical shifts (NICS). To assess deviations from planarity in the examined molecules, four different planarity descriptors were employed. It was shown how the planarity indices can be used to quantify the effect of nonplanarity on the local and global aromaticity of the studied systems.

Strain in strain-free benzenoid hydrocarbons: the case of fibonacenes

In a recent paper (Radenkovic et al. Chem Phys Lett 625:69–72, 2015), a new method for quantifying the strain energy in benzenoid molecules, resulting from the repulsion between the bay H-atoms was elaborated. In this work, we present a modified procedure, capable of estimating the strain energy in a single-step calculation. Strain energies were obtained at the B3LYP/def2-TZVP level of density functional theory. It was found that in benzenoid molecules with a single bay region, the strain energy is essentially constant, equal to around 7.3 kJ/mol. On the other hand, in the case of the first four members of the fibonacene series, the strain energy is found to be linearly proportional to the number of bay regions.

Strain in strain-free benzenoid hydrocarbons: The case of phenanthrene

Benzenoid molecules possessing bays are traditionally considered as ‘strain-free’. Yet, repulsion between the two bay H-atoms affects the length of the near-lying carbon–carbon bonds. A method is developed to estimate the energy of this strain. In the case of phenanthrene its value was found to be about 7kJ/mol.

A case of breakdown of the Pauling bond order concept

According to the Pauling bond orders, the lengths of the rung carbon–carbon bonds along the central hexagonal chain in chevron-type benzenoid molecules are monotonically changed. The calculated bond lengths obtained at the B3LYP/6-311G(d,p) level of theory show that this regularity holds only for the first few members of the chevron homologous series. In the case of higher members of the series, the predictions of the Pauling bond orders are false. This indicates that the Pauling bond orders are not generally applicable for the prediction of bond lengths.

Testing the Clar theory: Cyclic conjugation in some benzo- and naphthaleno-annelated ovalenes

Cyclic conjugation (assessed by its energy effect) is studied in benzo- and naphthaleno-annelated ovalenes, in which annelation is in positions d and o. These benzenoid species possess a large number of Clar aromatic sextet formulas, making the application of Clar theory difficult and ambiguous. Some predictions based on Clar formulas are not in agreement with the calculated energy effects. This indicates that Clar theory is not universally applicable, even in the case of fully conjugated benzenoid molecules.

Investigation of correlation between impact sensitivities and bond dissociation energies in benzenoid nitro compounds

The geometries of ten benzenoid energetic materials are fully optimized by employing B3LYP and B3P86 methods with the 6–31G** basis set. Bond dissociation energies (BDEs) for the removal of the NO2 group in benzenoid molecules are calculated at the same level. The calculation results show that the insertion of an electron withdrawing group increases the stability of the molecules, while the insertion of an electron donating group reduces the stability of the molecules. In addition, the relationship between the impact sensitivities and the weakest BDE values is examined. There exists a good linear correlation between the impact sensitivity and the ratio of the BDE value to the molecular total energy.

A test of Clar aromatic sextet theory

The Clar aromatic sextet theory predicts that the intensity of cyclic conjugation in chevron-type benzenoid hydrocarbons monotonically decreases along the central chain. This regularity has been tested by means of several independent theoretical methods (by the energy effects of the respective six-membered rings, as well as by their HOMA, NICS, and SCI values, calculated at the B3LYP/6-311G(d,p) level of DFT theory). Our results show that the predictions of Clar theory are correct only for the first few members of the chevron homologous series, and are violated at the higher members. This indicates that Clar theory is not universally applicable, even in the case of fully conjugated benzenoid molecules.

Tandem extraction strategy for separation of metallic and semiconducting SWCNTs using condensed benzenoid molecules: effects of molecular morphology and solvent

Separation of metallic and semiconducting single-walled carbon nanotubes (SWCNTs) is of great importance for SWCNT-based nano-electronics. We propose a tandem extraction strategy for efficient separation of different types of SWCNTs. This strategy is based on chiral angle discriminated adsorption of soluble condensed benzenoid aromatic molecules on SWCNTs, which induce different dispersibility of SWCNTs in various organic solvents. The proposed tandem extraction strategy involves two extraction steps, in which the first step extracts metallic SWCNTs with large chiral angles and the subsequent step enriches large chiral angle semiconducting SWCNTs. This separation strategy is tested on a series of condensed benzenoid aromatic molecules. Both experimental and theoretical results show that the separation efficiency is strongly dependent on the molecular morphology, i.e. higher aspect ratio gives better separation results. The separation efficiency is also dependent on the SWCNT diameter and the solvent properties. This tandem extraction strategy may also be applied to other available noncovalent separation reagents to improve their separation efficiency.

Partitioning of π-electrons in rings of diaza-derivatives of acenes

A few years ago, a method was proposed for assessing the ?-electron content (EC) of rings in heteroatom-containing benzenoid molecules. In this work, the effect of two nitrogen atoms at the opposite sides of a linear benzenoid molecule on the partitioning of its ?-electrons was investigated. The results obtained can be explained by means of resonance-theoretical arguments.

Ring signatures for benzenoids with up to seven rings, Part 1: Catacondensed systems

AbstractWe revisited the π‐electron ring partitions in catacondensed benzenoids and re‐examined structural regularities reported for the ring partitions in these compounds, seeking the origin of the observed regularities. We examined the distribution of the π‐electron ring partitions by counting the contributions arising from benzene rings having different assigned numbers of π‐electrons. This has led to a better insight into the underlying structure of the π‐electron ring partitions and also to a novel and unique π‐electron “signature” of individual rings in benzenoid hydrocarbons. The physical interpretation of the local π‐electron ring partition represents the local π‐electron density of benzenoid molecules, and is not an alternative index of local aromaticity as one may erroneously assume. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

An upper bound on the independence number of benzenoid systems

Recently, the graph theoretic independence number has been linked to fullerene stability [S. Fajtlowicz, C. Larson, Graph-theoretic independence as a predictor of fullerene stability, Chem. Phys. Lett. 377 (2003) 485–490; S. Fajtlowicz, Fullerene Expanders, A list of Conjectures of Minuteman, Available from S. Fajtlowicz: math0@bayou.uh.edu]. In particular, stable fullerenes seem to minimize their independence numbers. A large piece of evidence for this hypothesis comes from the fact that stable benzenoids—close relatives of fullerenes—do minimize their independence numbers [S. Fajtlowicz, “Pony Express”—Graffiti's conjectures about carcinogenic and stable benzenoids, 〈 http://www.math.uh.edu/∼siemion/pony.html 〉 ]. In this paper, an upper bound on the independence number of benzenoids is introduced and proven—giving a limit on how large the independence ratio for benzenoids can be. In conclusion, this bound on independence is correlated to an upper bound on the number of unpaired sites a benzenoid system has with respect to a maximum matching, which is precisely the number of zero eigenvalues in the spectrum of the adjacency matrix (due to a conjecture of Graffiti and its proof by Sachs [S. Fajtlowicz, “Pony Express”—Graffiti's conjectures about carcinogenic and stable benzenoids, 〈 http://www.math.uh.edu/∼siemion/pony.html 〉 ; H. Sachs, P. John, S. Fajtlowicz, On Maximum Matchings and Eigenvalues of Benzenoid Graphs, preprint—MATCH]). Thus, since zero eigenvalues and unpaired sites are indicative of instability (reactivity), we get a simple but intuitive bound on how reactive a benzenoid molecule can be.

NOTE ON THE Y-RULE IN CLAR THEORY

The recently proposed Y-rule for constructing Clar-type aromatic sextet formulas for benzenoid molecules is examined, and the limits of its applicability are established. According to the Y-rule, the π-electron configuration of a benzenoid hydrocarbon is best represented by the Clar-type formula(s) in which all internal carbon atoms (the so-called Y-carbon atoms) are covered by aromatic sextets. The Y-rule is, by definition, applicable only to perifusenes (because catafusenes do not possess internal carbon atoms). We show that the rule is not applicable to all perifusenes, and that in some case it leads to numerous “best” Clar-type formulas.

Relating resonance energy with the Zhang-Zhang polynomial

The Zhang-Zhang polynomial ?(x) is a recently conceived tool in the mathematical apparatus of theoretical chemistry. It combines (in a quantitative manner) the Kekul?- and Clar-structure-based features of benzenoid molecules. It is shown that the topological resonance energy (TRE) can be accurately approximated as TRE ? a??(x)+ b where x?0.5, by which fact a significant insight is gained into the structure-dependence of TRE of benzenoid molecules.

Relating Total π-Electron Energy and Resonance Energy of Benzenoid Molecules with Kekulé- and Clar-Structure-Based Parameters

Within classes of isomeric benzenoid hydrocarbons various Kekule- and Clar-structure-based parameters (Kekule structure count, Clar cover count, Herndon number, Zhang–Zhang polynomial) are all mutually correlated. This explains why both the total π-electron energy (E), the Dewar resonance energy (DRE), and the topological resonance energy (TRE) are well correlated with all these parameters. Nevertheless, there exists an optimal value of the variable of the Zhang–Zhang polynomial for which it yields the best results. This optimal value is negative-valued for E, around zero for TRE, and positive-valued for DRE. A somewhat surprising result is that TRE and DRE considerably differ in their dependence on Kekule- and Clar-structure-based parameters.

Vindicating the Pauling-bond-order concept

In the Pauling-bond-order concept, it is assumed that all Kekulé structures of a benzenoid molecule contribute equally to the π-electron contents of the carbon–carbon bonds. We modified the Pauling-bond-order: (a) by increasing the weight of a Kekulé structure proportional to the number of Fries-type hexagons and (b) by increasing the weights of the Kekulé structures that are compatible with Clar aromatic sextet formulas. Improvements in reproducing experimental carbon–carbon bond lengths are insignificant, implying that equal weighting of Kekulé structures is more justified than one could anticipate.

A DIFFERENCE BETWEEN THE π-ELECTRON PROPERTIES OF CATAFUSENES AND PERIFUSENES

It is shown that there is a remarkable difference between the Kekulé- and Clar-structure-dependence of the total π-electron energy (E) of catafusenes and perifusenes (catacondensed and pericondensed benzenoid molecules). Within classes of isomeric catafusenes the main parameter determining E is the Kekulé structure count whereas the influence of Clar-structure-based features is negligible. Within classes of isomeric perifusenes, Clar-structure-based features, in addition to the Kekulé structures, exhibit a significant effect on E. The present analysis is performed by using the mathematical formalism of the Zhang-Zhang polynomial [whose details are found in the recent paper: Gutman, Furtula, Balaban, Polycyclic Aromatic Compounds 26 (2006) 17–35].

A Kekulé structure basis for phenylenes

By means of Kekulé structures and, in particular, their count K, many properties of benzenoid molecules can be rationalized. The analogous properties of non-benzenoid polycyclic conjugated molecules require the consideration of some, but not all, Kekulé structures, whose number is the precisely defined and long time known ‘algebraic structure count’ ASC. In the general case it is not known how to construct a Kekulé structure basis for non-benzenoid molecules, consisting of ASC Kekulé structures, ASC≤ K. We now offer a solution of this problem for phenylenes and point out some applications.