Aromatic Sextet Research Articles

Oxidation Unzipping of Stable Nanographenes into Joint Spin-Rich Fragments

When an all-benzenoid nanographene is linearly unzipped into oxygen-joined fragments, the oxidized benzenoid rings (aromatic sextets) selectively adopt the low-spin (DeltaS = 0) or high-spin conformation (DeltaS = 1) to yield the thermally most stable isomer. The selection of the conformation depends simply on the position of the aromatic sextets: the inner ones prefer the high-spin conformation, whereas the peripheral ones prefer the low-spin conformation. Therefore, the resulting most stable isomer has a total spin whose value equals the number of inner aromatic sextets (n(i)) along the oxidizing line. The nanographene fragments contained in this isomer have a ferromagnetic spin coupling. Due to the tautomerization between the high-spin and low-spin conformations, there also exist other possible isomers with higher energies and with spins at ground state ranging from 0 to (n(i) - 1). The rich geometrically correlated spins and the adjustable energy gaps indicate great potential of the graphene oxides in spintronic devices.

Clar Theory for Molecular Benzenoids

Eric Clar's ideas concerning "aromatic sextets" are extended to a quantitative format in terms of a polynomial called the "Clar 2-nomial", along with related derivative quantities. The quantification is successfully tested to make correlations with a selection of numerical data, including resonance energies, bond lengths, and NICS ring-aromaticity values.

First-principles investigations on the functionalization of chiral and non-chiral carbon nanotubes by Diels–Alder cycloaddition reactions

Functionalization of single-walled carbon nanotubes through cycloaddition reactions constitutes an effective route to obtain novel nanostructured materials with interesting properties. In this paper, we perform density functional theory calculations on Diels-Alder reactions at the sidewall of armchair, zigzag and chiral nanotubes by applying finite-length models of carbon nanotubes based on Clar's theory of the aromatic sextet. The analysis of binding energies and molecular orbitals suggests a prevalence of local factors, related to the structural and electronic properties at the coordinating site, in controlling the overall energetics of cycloaddition reactions. Our results can be expected to have strong implications in the development of rational strategies for the functionalization of carbon nanotubes of any stereochemistry.

Electronic properties and stability of graphene nanoribbons: An interpretation based on Clar sextet theory

The electronic structure and the stability of hydrogen-terminated graphene nanoribbons (GNRs) are evaluated by means of gradient-corrected density functional theory calculations and rationalized by application of Clar’s theory of the aromatic sextet. Our results show that the electronic properties of GNRs are deeply related to the description of the bonding pattern provided from the valence bond picture obtained by application of Clar’s theory. This finding applies either to zigzag-, armchair- and chiral-terminated GNRs and can be expected to have strong impact in the interpretation of experiments and on the design of devices based on nanostructured graphene materials.

Comparing the stability of tribenzo[b,n,pqr]perylene and tribenzo[b,k,pqr]perylene

Two isomeric benzenoid hydrocarbons – tribenzo[b,n,pqr]perylene and tribenzo[b,k,pqr]perylene played a crucial role in the formulation of the Clar aromatic sextet theory. The basic assumption of this theory is that tribenzo[b,n,pqr]perylene is more stable than tribenzo[b,k,pqr]perylene because the former has five, whereas the latter only four aromatic sextets. We now approach this stability problem from a different direction. By means of a recently developed molecular-orbital-based method it is possible to estimate the energy effects of individual cycles, as well as pairs, triplets, etc. of cycles in polycyclic conjugated molecules. From these energy-effects one can better understand which structural details are responsible for the thermodynamic stability of the underlying molecule. In particular, it is possible to rationalize (in a quantitative manner) the causes of differences in the thermodynamic stability of isomers. Our analysis corroborates the conclusion of Clar theory, but points out a number of hitherto overlooked structure-stability connections.

TESTING THE Y–RULE IN CLAR THEORY

A recently proposed modification of the basic postulates of the Clar aromatic sextet theory, called the Y–rule, is tested on a suitably chosen homologous series of benzenoid hydrocarbons. For these benzenoid systems the original Clar theory predicts a significantly different distribution of π-electrons than the Y–rule. It was found that both the π-electron contents of rings as well as their energy effects agree with the predictions of the original Clar theory, failing to corroborate the Y–rule.

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.

The Regioselectivity of Addition to Carbon Nanotube Segments

Calculations (AM1) demonstrate that Clar's valence bond model predicts the long-range reactivity patterns of hydrogenation of carbon nanotube (CNT) segments. CNT segments behave as other polycyclic aromatic hydrocarbons--hydrogenation of double bonds is energetically preferred over hydrogenation of aromatic sextets. The frontier molecular orbitals of CNT segments have greatest amplitude at the double bonds, suggesting that Clar's model also predicts kinetic reactivity.

Polycyclic Aromatic Hydrocarbons of Asphaltenes Analyzed by Molecular Orbital Calculations with Optical Spectroscopy

The number and geometry of the rings in polycyclic aromatic hydrocarbons (PAHs) in petroleum asphaltene has remained unresolved for many years. Many sophisticated imaging and spectroscopic methods have been utilized to narrow the list of candidate structures for asphaltene PAHs. Here, we exploit a canonical property of petroleum asphaltenes, their color, along with their fluorescence emission properties. These universal spectral properties are analyzed through the lens of molecular orbital (MO) calculations, thereby providing quantitative bounds on asphaltene PAH systems. Energetic considerations mandate that these fused aromatic ring systems are predominantly aromatic sextet carbon (within the Clar representation) but not entirely sextet carbon. Matching the ubiquitous asphaltene spectral data with MO calculations shows that asphaltene ring systems predominantly consist of 4−10 rings. PAHs with 6−8 rings are most predominant in petroleum asphaltenes. Not surprisingly, polydispersity is implied in this an...

Unimodularity of the Clar number problem

We study the generalization to bipartite and 2-connected plane graphs of the Clar number, an optimization model proposed by Clar [E. Clar, The Aromatic Sextet, John Wiley & Sons, London, 1972] to compute indices of benzenoid hydrocarbons. Hansen and Zheng [P. Hansen, M. Zheng, The Clar number of a benzenoid hydrocarbon and linear programming, J. Math. Chem. 15 (1994) 93–107] formulated the Clar problem as an integer program and conjectured that solving the linear programming relaxation always yields integral solutions. We establish their conjecture by proving that the constraint matrix of the Clar integer program is always unimodular. Interestingly, in general these matrices are not totally unimodular. Similar results hold for the Fries number, an alternative index for benzenoids proposed earlier by Fries [K. Fries, Uber Byclische Verbindungen und ihren Vergleich mit dem Naphtalin, Ann. Chem. 454 (1927) 121–324].

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.

Clar theory and resonance energy

A mathematical model, referred here as the Zhang–Zhang polynomial ζ( x), that embraces all the main concepts encountered in the Clar aromatic sextet theory of benzenoid hydrocarbons, was recently put forward by Zhang and Zhang. We now show that ζ( x) is related to resonance energy, and that ln ζ( x) and RE are best correlated when x ≈ 1. This indicates that ζ(1) could be viewed as a (novel) structure-descriptor, playing a role analogous to the Kekulé structure count in Kekulé-structure-based theories. Some basic properties of ζ(1) are established.

On the ordering of benzenoid chains and cyclo-polyphenacenes with respect to their numbers of Clar aromatic sextets

Based on Clar aromatic sextet theory [Clar, The Aromatic Serxtet (Wiley, New York, 1972)] and the concept of sextet polynomial introduced by Hosoya and Yamaguchi [Mathematical Concepts in Organic Chemistry (Springer, Berlin, 1986)], we define a new ordering of benzenoid systems. For two isomeric benzenoid systems B1 and B2, we say B1>B2 if each coefficient of sextet polynomial of B1 is no less than the corresponding coefficient of sextet polynomial of B2. In this paper, we consider the ordering of the benzenoid chains. The maximal and second maximal benzenoid chains as well as the minimal, the second minimal up to the fourth minimal benzenoid chains are determined. Furthermore, under this ordering, we determine the maximal and second maximal cyclo-polyphenacenes as well as the minimal, the second minimal, and up to the seventh minimal cyclo-polyphenacenes.

π-ELECTRON CONTENTS OF RINGS IN THE DOUBLE-HEXAGONAL-CHAIN HOMOLOGOUS SERIES (PYRENE, ANTHANTHRENE AND OTHER ACENOACENES)

Recently three methods for calculating the π-electron content of rings of benzenoid hydrocarbons were put forward: one based on the consideration of Kekuléstructural formulas, and the other two based on an analogous treatment of the Clar aromatic sextet formulas. These three methods are applied to the homologous series consisting of two condensed acene chains (whose first members are pyrene, anthanthrene, peri-naphthacenonaphthacene, …), leading to basically identical results. In contrast to acenes (in which the partition of π-electrons into rings is uniform), in the double-hexagonal-chain species the partition of π-electrons is highly non-uniform. The electron content monotonically decreases, in opposite directions, along the two acene chains, being maximal in the least annelated rings. Some other generally valid regularities in the π-electron properties of the double–hexagonal–chain benzenoids are also pointed out.

The Agreement between Clar Structures and Nucleus-Independent Chemical Shift Values in Pericondensed Benzenoid Polycyclic Aromatic Hydrocarbons: An Application of the Y-Rule

In the present study, we verify theoretically the performance of a previously introduced qualitative simple rule for aromaticity, the Y-rule, which determines the relative aromaticity of each hexagonal ring in pericondensed benzenoid polycyclic aromatic hydrocarbons (peri-PAHs). The Y-rule extends the sextet−double bond description of Clar's model for peri-PAHs by predicting, in an easy way, the most likely location and total number of aromatic sextets in the structure. The final π-electronic distribution thus obtained corresponds to the superposition of the most important Clar structures. The problem of the number and location of aromatic sextets in peri-PAHs involves the very concept of aromaticity. The π-electronic distribution obtained by the Clar sextet principle (or model) as determined by the Y-rule is compared with the π-electronic distribution obtained from nucleus-independent chemical shift (NICS) calculations for various series of benzenoid peri-PAHs. The NICS values were used to assess the relative aromaticities of the individual rings in the peri-PAH compounds. We found that the simple heuristic Y-rule predicts for all the calculated systems the same relative aromaticities given by the NICS calculations, and for the case of peri-systems with very high symmetry (like the compact peri-PAHs) it reinforces the picture derived from the NICS calculations. In these cases, the NICS results can be complex due to symmetry. The advantages of the qualitative Y-rule are that it is of particular importance for the case of large peri-PAHs, it takes only a few minutes to be applied following a very easy methodology, and it provides a quick answer about the aromaticity and location of the resonant sextets in peri-PAH compounds without having to carry out theoretical quantum chemistry calculations that take time and that can be costly depending on the size of the system.

On the distribution of π-electrons in large polycyclic aromatic hydrocarbons

On the recently recorded-high resolution STM images of large polycyclic aromatic hydrocarbons (PAHs), submolecularly resolved patterns are observed, that differentiate between parts of the molecules in which, according to the Clar aromatic sextet theory, the ‘full’ and the ‘empty’ rings are located. This phenomenon has been explained by the shape of the frontier orbitals of the PAHs, usually by the HOMO or LUMO. We now put forward a simple theoretical model of the distribution of π-electrons in PAHs, that results in patterns remarkably similar to those observed in the STM images. A possible explanation for this coincidence is offered.

The Most Stable Class of Benzenoid Hydrocarbons — New Topological Correlations of Strain‐Free Total Resonant Sextet Benzenoids.

While briefly reviewing how the concepts of strictly pericondensed, strain-free, Clar's aromatic sextet, and symmetry are interconnected in the topological correspondence between strictly pericondensed and total resonant sextet (TRS) benzenoid hydrocarbons, new structural correlations in isomer numbers, symmetry distributions, and empty rings between various strain-free TRS benzenoids made up of only fused hexagonal rings are presented. These correlations are made evident by the Formula Periodic Table for Total Resonant Sextet Benzenoid Hydrocarbons [Table PAH6(sextet)] and application of the leapfrog operation. A new perimeter topology relationship for fused strain-free TRS benzenoids is derived. This work represents a contribution toward understanding formula/structure relationships of benzenoid hydrocarbons.

A CLASSICAL VALENCE BOND VIEW OF CYLINDER-SHAPED AND FULLY BENZENOID-LIKE POLYARENES (POLYCYCLIC AROMATIC HYDROCARBONS) OF LARGE SIZE

This note first defines a class of cylindrical polyarenes polycyclic aromatic hydrocarbons (PAHs) C2(m+ 1)nH2n, for which the periphery is acenic. From this class the leapfrog algorithm derives the second class of cylindrical PAHs C6nmH4n, where the periphery is phenacenic. One further application of this algorithm to the second class leads to the third class of cylindrical PAHs C12nmH8n, where the less regular periphery has 2n capes (i.e., hexagons exposed on four adjacent sides to the external “sea” of space). Each molecule in the second and third classes is totally covered by aromatic sextets, that is, appears related to a fully benzenoid hydrocarbon (FBH). The Pauling bond order, and several new indices derived from the Pauling bond order and Clar sextet counts are calculated for the three classes with increasing numbers of carbons. This calculation suggests that a typical cylindrical PAH becomes more graphite-like than a typical flat FBH.

The most stable class of benzenoid hydrocarbons-new topological correlations of strain-free total resonant sextet benzenoids.

While briefly reviewing how the concepts of strictly pericondensed, strain-free, Clar's aromatic sextet, and symmetry are interconnected in the topological correspondence between strictly pericondensed and total resonant sextet (TRS) benzenoid hydrocarbons, new structural correlations in isomer numbers, symmetry distributions, and empty rings between various strain-free TRS benzenoids made up of only fused hexagonal rings are presented. These correlations are made evident by the Formula Periodic Table for Total Resonant Sextet Benzenoid Hydrocarbons [Table PAH6(sextet)] and application of the leapfrog operation. A new perimeter topology relationship for fused strain-free TRS benzenoids is derived. This work represents a contribution toward understanding formula/structure relationships of benzenoid hydrocarbons.

Clar Formulas: How to Draw and How not to Draw Formulas of Polycyclic Aromatic Hydrocarbons

Historically, the aromatic sextet originates with Crocker (2), Armit and Robinson (3), and Hückel (4). The inscribed circle for denoting an aromatic sextet was introduced by Armit and Robinson, but it was Clar who defined how the sextet was to be used in polycyclic aromatic compounds. However, in some papers a mistaken form of Clar formulas is found. The present note stipulates that such mistakes should be corrected before their acceptance in respectable scientific journals, including this Journal.