Clar's Aromatic Sextet Theory Research Articles

Magnetic shielding paints an accurate and easy-to-visualize portrait of aromaticity.

Chemists are trained to recognize aromaticity semi-intuitively, using pictures of resonance structures and Frost-Musulin diagrams, or simple electron-counting rules such as Hückel's 4n + 2/4n rule. To quantify aromaticity one can use various aromaticity indices, each of which is a number reflecting some experimentally measured or calculated molecular property, or some feature of the molecular wavefunction, which often has no visual interpretation or may not have direct chemical relevance. We show that computed isotropic magnetic shielding isosurfaces and contour plots provide a feature-rich picture of aromaticity and chemical bonding which is both quantitative and easy-to-visualize and interpret. These isosurfaces and contour plots make good chemical sense as at atomic positions they are pinned to the nuclear shieldings which are experimentally measurable through chemical shifts. As examples we discuss the archetypal aromatic and antiaromatic molecules of benzene and square cyclobutadiene, followed by modern visual interpretations of Clar's aromatic sextet theory, the aromaticity of corannulene and heteroaromaticity.

Detailed Visualization of Aromaticity Using Isotropic Magnetic Shielding.

For many years, Clar's aromatic sextet theory has served as a qualitative method for assessing the aromatic character of polycyclic aromatic hydrocarbons. A new approach, based on the calculation of isotropic magnetic shielding (IMS) contour plots, is shown to provide a feature-rich picture of aromaticity that is both quantitative yet still easily interpreted. Chemists are visual creatures who are adept at discerning reactivity and chemical behavior from molecular structures. To quote Roald Hoffmann, "People like pictures. Chemists live off them." Thus, the detailed image analysis we present simultaneously provides quantitative assessment of electronic structure, which is still easy-to-understand through visual inspection, embedded in an aesthetically appealing and intuitive picture that draws the reader in. We provide novel computed IMS contour plots for a representative selection of aromatic molecules. Where Clar's static drawings capture only a partial sketch of the electronic properties of a molecule, IMS contour plots present a detailed, global landscape of a molecule that sums all possible resonance structures. This novel analysis allows us to correct certain drawbacks of Clar's analysis with respect to polycyclic aromatics and quantitatively assess the bonding and electronic structure of acene hydrocarbons.

Detailed Visualization of Aromaticity Using Isotropic Magnetic Shielding

AbstractFor many years, Clar's aromatic sextet theory has served as a qualitative method for assessing the aromatic character of polycyclic aromatic hydrocarbons. A new approach, based on the calculation of isotropic magnetic shielding (IMS) contour plots, is shown to provide a feature‐rich picture of aromaticity that is both quantitative yet still easily interpreted. Chemists are visual creatures who are adept at discerning reactivity and chemical behavior from molecular structures. To quote Roald Hoffmann, “People like pictures. Chemists live off them.” Thus, the detailed image analysis we present simultaneously provides quantitative assessment of electronic structure, which is still easy‐to‐understand through visual inspection, embedded in an aesthetically appealing and intuitive picture that draws the reader in. We provide novel computed IMS contour plots for a representative selection of aromatic molecules. Where Clar's static drawings capture only a partial sketch of the electronic properties of a molecule, IMS contour plots present a detailed, global landscape of a molecule that sums all possible resonance structures. This novel analysis allows us to correct certain drawbacks of Clar's analysis with respect to polycyclic aromatics and quantitatively assess the bonding and electronic structure of acene hydrocarbons.

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.

A Pedestrian Approach to the Aromaticity of Graphene and Nanographene: Significance of Huckel’s (4n+2)π Electron Rule

In an attempt to describe and rationalize the elusive aromatic properties of graphene by first-principles calculations in a simple and transparent way, we have constructed numerous judicially chosen real-space models of various sizes and symmetries, which lead to the aromaticity pattern of infinite graphene by a process of “spatial” evolution through successive peripheral additions, characterized by fundamental periodicities related to the traditional Huckel (4n+2)π electron rule. In accord with the early expectations of Pauling, we have found that the electronic and aromatic properties of infinite graphene result from the superposition of two complementary primary aromatic configurations, in which full and empty rings are interchanged. The primary pattern consists of a hexagonal superlattice in which each fully aromatic ring is surrounded by six nonaromatic rings, in full agreement with the empirical Clar aromatic sextet theory. We have found that, for finite nanographene(s), aromaticity patterns change ...

Antidot-dependent bandgap and Clar sextets in graphene antidot lattices

By using first-principles calculations, the bandgap of two types of graphene antidot lattices (GALs) with triangular lattice, anthrancene-removed GALs and phenanthrene-removed GALs, have been studied. One third of either GALs are semiconductors as lattice parameter varies, while the lattice parameters corresponding to semiconductors are different in the two GALs, indicating the bandgap opening of GALs depends on the antidot configuration as well as lattice parameter. The bandgap opening or not is interpreted with Clar's aromatic sextet theory. A nonzero bandgap appears in phenanthrene-removed GALs, only when the number of Clar sextets exceeds one third of the total number of hexagons in the unit cell. However, due to a long zigzag edge existing in anthrancene-removed GALs, the bandgap can be open without meeting the condition. Our results suggest that the antidot configuration is a non negligible factor on the bandgap of graphene antidot lattices.

DFT Prediction of Multitopic N-Heterocyclic Carbenes Using Clar’s Aromatic Sextet Theory

Existence of several multitopic N-heterocyclic carbene (NHC) ligands with up to four carbene centers have been predicted on the basis of Clar's aromatic sextet theory. Assessment on stability and reactivity of NHCs was made by quantifying aromaticity, aromatic stabilization energy (E(aroma)), strength of carbene lone pair, proton affinity, and CuCl binding energy. On NICS(0) and HOMA scales of aromaticity, several NHCs showed high aromaticity, while E(aroma) (17.2-19.4 kcal/mol) indicated substantial stability for the N-heterocycle. Homodesmotic reactions suggested that heat of formation of most of the newly designed carbenes is very close to that of the existing bis-NHCs. Designing a multitopic ligand through branching via C(sp3) linkage was very effective as it improved the stability of the carbene. Electrostatic potential minimum (V(min)) at the carbene lone pair suggested that annelation of heterocycle to a benzenoid ring or branching through C(sp3) linkage can only marginally influence the electron donating power of the ligand. Hence, all multitopic NHCs showed proton affinity (252.3-267.4 kcal/mol) and CuCl binding energy (62.9-66.6 kcal/mol) very close to those of 1,3-dimethylimidazolidine-2-ylidene (1). It has also been demonstrated that branched multitopic 3-dimensional NHCs are attractive for designing metal-organic framework with narrow (1-1.5 nm) cage/pore size.

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.

Advances of Clar's Aromatic Sextet Theory and Randic´'s Conjugated Circuit Model

Advances of Clar's Aromatic Sextet Theory and Randic´'s Conjugated Circuit Model

Cyclic conjugation in benzo-annelated coronenes

The cyclic conjugation in benzo-annelated coronenes is studied by means of the energy effect (ef) and π-electron content (EC) of the six-membered rings. Some peculiarities of the π-electron structure of benzo-coronenes, inferred by the Clar aromatic sextet theory, could be tested and verified. A regularity that earlier was discovered in the case of perylene congeners is now shown to hold also for benzo-annelated coronenes: Benzenoid rings that are annelated linearly with regard to the central hexagon H0 of coronene decrease the intensity of cyclic conjugation in H0 and this effect is proportional to the number of linearly annelated rings. A very good linear correlation exists between the ef- and EC-values.

Pictorial representation and validation of Clar's aromatic sextet theory using molecular electrostatic potentials

Topographical features of the molecular electrostatic potential (MESP) of a series of polycyclic aromatic benzenoid hydrocarbons have been analyzed at B3LYP/6-31+G(d,p) and MP2/6-31+G(d,p) levels of theory to study the relationship between π-electron distribution and Clar's aromatic sextet theory. For all the molecules, MESP isosurface plots provided an unambiguous visual representation of Clar's aromatic sextet theory. For molecules represented using a single dominant Clar structure, a complete agreement of Clar's theory was observed. For benzenoid structures showing more than one Clar structure, MESP isosurface lobes reflected the merger of possible Clar structures, and even in such cases, the most dominant configuration was clearly obtained in the MESP topography. The MESP at the ring critical point (Vrcp) of the π-electron cloud of every ring was found to be a good local measure of aromaticity. A hydrogenation scheme was introduced to calculate the aromatic stabilization energy (Earoma) of the peripheral rings. Earoma and Vrcp showed a good linear correlation. Furthermore, a linear correlation of Vrcp with the widely used geometric index of aromaticity, HOMA, was obtained. Thus, for a visual representation as well as rationalization of Clar's theory, MESP serves as an important descriptor of the π-regions, and Vrcp values give further insight into this theory by quantifying the local aromaticity of each ring in the polycyclic aromatic system. The theoretical results presented herein fully support the ideas of Clar's empirical sextet theory—a theory mainly based on experimental findings of the local reactivity of condensed aromatic systems.

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.

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.

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.

K-resonant benzenoid systems and k-cycle resonant graphs.

A benzenoid system (or hexagonal system) H is said to be k-resonant if, for 1 < or = t < or = k, any t disjoint hexagons of H are mutually resonant; that is, there is a Kekule structure (or perfect matching) K of H such that each of the k hexagons is an K-alternating hexagon. A connected graph G is said to be k-cycle resonant if, for 1 < or = t < or = k, any t disjoint cycles in G are mutually resonant. The concept of k-resonant benzenoid systems is closely related to Clar's aromatic sextet theory, and the concept of k-cycle resonant graphs is a natural generalization of k-resonant benzenoid systems. Some necessary and sufficient conditions for a benzenoid system (respectively a graph) to be k-resonant (respectively k-cycle resonant) have been established. In this paper, we will give a survey on investigations of k-resonant benzenoid systems and k-cycle resonant graphs.

Clar's Aromatic Sextet Theory Revisited via Molecular Electrostatic Potential Topography

Full characterization of the molecular electrostatic potential (MESP) topography of the π-regions of 12 polycyclic benzenoid hydrocarbons (PBHs) is carried out. Benzene is endowed with the most perfect circular distribution of π-delocalization, and the hexagonal rings of other systems possess varying degrees of lesser π-delocalization. The topographical features describe Clar's aromatic sextet theory very well and simplify the aromatic characterization of each ring of a PBH system. The concepts such as “aromatic dilution” observed for polyacene series and the “empty ring” in triphenylene, perylene, and coronene are clearly brought out from this study. The positions of (3, +3) critical points (CPs) are always observed very close to shorter bonds, providing valuable hints at how the π-electrons are shared among the carbons. Further, average values of the MESP at CPs calculated for each ring ( ) and for the whole molecule ( ) bear linear correlation with the local aromaticity values estimated by Li and Jiang and the hardness values reported by Zhou and Parr for the global aromaticity, respectively. Thus the mapping of the MESP topography provides an elaborate characterization of the π-regions of PBH systems and a description of the intimately connected aromaticity.

A Clar-Type Regularity for Dianions of Benzenoid Hydrocarbons

Phenanthreno-annelated anthracenes as well as their dianions are studied by means of molecular-orbital theory (at the AM1 level). The charge distribution in the dianions is highly non-uniform: the anthracene fragment bears roughly 50% more negative charge than the phenanthrene fragment(s). These findings point at the possibility to apply the concepts of Clar aromatic sextet theory to benzenoid dianions. Within the framework of this Clar-type model, phenanthreno-annelated anthracene dianions may be viewed as charged analogs of all-benzenoid hydrocarbons.

Topological Properties of Circumcoronenes

Abstract The regular-hexagon-shaped benzenoid hydrocarbons: B1 = benzene (C6H6), B2 = coronene (C24H12), B3 = circumcoronene (C54H18), B4 = circumcircumcoronene (C150H30), etc. possess unique topological properties. General expressions for the most important of such properties (number of fun-damental structural invariants, number of Kekule and Clar structures, number of aromatic sextets, Wiener and Szeged indices, spectral moments) are given, including a number of results that are communicated here for the first time. Cyclic conjugation in circumcoronenes is analyzed by means of its energy-effect, and found to agree with the predictions of Clar's aromatic sextet theory only in the case of B1 and B2.