Clar's Sextet Research Articles

π‐Extended 4,5‐Fused Bis‐Fluorene: Highly Open‐Shell Compounds and their Cationic Tetrathiafulvalene Derivatives

AbstractThe synthesis of diradical organic compounds has garnered significant attention due to their thermally accessible spin inversion and optoelectronic properties. Yet, preparing such stable structures with high open‐shell behavior remains challenging. Herein, we report the synthesis and properties of four π‐extended, fused fluorene derivatives with high diradical character, taking advantage of a molecular design where the closed‐shell does not include any Clar sextet, comparatively to a maximum of 5 in the corresponding open‐shell state. This led to an unusual open‐shell triplet ground state with an outstanding singlet‐triplet energy difference (ΔEST) of ca. 19 kcal/mol, one of the highest values reported to date for an all‐carbon conjugated scaffold. Incorporation of dithiafulvene units at each end of the molecule (at the five‐membered rings) furnishes extended tetrathiafulvalenes (TTFs) undergoing reversible oxidations to the radical cation and diradical dication. The various pro‐aromatic structures presented herein show highly localized spin density and a limited conjugation due to the confined π‐electrons in the aromatic cycles, as supported by 1H NMR, UV/Visible, EPR spectroscopy and DFT calculations.

π-Extended 4,5-Fused Bis-Fluorene: Highly Open-Shell Compounds and their Cationic Tetrathiafulvalene Derivatives.

The synthesis of diradical organic compounds has garnered significant attention due to their thermally accessible spin inversion and optoelectronic properties. Yet, preparing such stable structures with high open-shell behavior remains challenging. Herein, we report the synthesis and properties of four π-extended, fused fluorene derivatives with high diradical character, taking advantage of a molecular design where the closed-shell does not include any Clar sextet, comparatively to a maximum of 5 in the corresponding open-shell state. This led to an unusual open-shell triplet ground state with an outstanding singlet-triplet energy difference (ΔEST) of ca. 19 kcal/mol, one of the highest values reported to date for an all-carbon conjugated scaffold. Incorporation of dithiafulvene units at each end of the molecule (at the five-membered rings) furnishes extended tetrathiafulvalenes (TTFs) undergoing reversible oxidations to the radical cation and diradical dication. The various pro-aromatic structures presented herein show highly localized spin density and a limited conjugation due to the confined π-electrons in the aromatic cycles, as supported by 1H NMR, UV/Visible, EPR spectroscopy and DFT calculations.

A new graph theory to unravel the bulk-boundary correspondence of graphene nanoribbons

We developed a new graph theory rooted in Clar's sextet rule to unravel the bulk-boundary correspondence of graphene. This methodology is specifically focused on the topological invariant and the chiral winding number, which enables the chemical rationalization of edge and boundary states in one-dimensional graphene nanoribbon (GNR) materials. The Clar structure derived from facile Lewis structures facilitates direct prediction of free radical distribution along edges and boundaries of GNRs across various geometric configurations. We then extend this graph theoretical framework to include metallic GNRs, demonstrating its power in several paradigms where conventional topological theories show limitations. Upon reducing the topological parameters and hence the complexity, the new approach provides a visual comprehension for the electronic topology and hence conductivity of GNR, greatly simplifying the formulation of design principles for future application of graphene interconnects.

Evaluation of Molecular Fragmentation in Polycyclic Aromatic Hydrocarbons by Time-of-Flight Secondary Ion Mass Spectrometry

In time-of-flight secondary ion mass spectrometry (TOF-SIMS), ionized molecules and molecular fragments (secondary ions) are generated in collisions of high-energy ions (primary ions) with a solid sample surface. Mass spectra of the emitted secondary ions are typically used to identify molecular species and to determine their spatial distribution on the sample surface. Here, we extend this application in a TOF-SIMS study of a series of polycyclic aromatic hydrocarbons (PAHs) where we focus on the fragmentation of these molecules, with the purpose of better understanding the fragmentation patterns of heavy aromatic molecules in petroleum. For all PAHs, the collision process generated (i) a series of smaller cation fragments and (ii) cations close in size to the original PAH (molecular cations). Stark differences are measured for various PAHs regarding the abundance of smaller fragments versus molecular cations. Observation of hydrogen-deficient (H-deficient) cation fragments indicates the formation of polyynes and allenes. For PAHs producing higher fractions of small cation fragments, these ions are surprisingly hydrogen rich (H-rich). The H/C ratio of fragments does not scale with the fraction of Clar sextet carbon, nor with energies of low-lying electronic transitions. Free radical cation fragments tend to be suppressed. For sufficiently large fragments, aromatic cations appear to be formed and include some free radical aromatics. There is ample production of molecular ions with loss of a single carbon atom or a methine group, which corresponds to the reduction of a 6-membered aromatic ring to a 5-membered ring. There is some enhancement of free radical molecular cations due to the corresponding formation of neutral polyynes. Fragment anions are also produced with a strong preference for very H-deficient carbon clusters, in some cases being the same as carbon cluster anions observed in space. Comparisons of PAH TOF-SIMS spectra with those of asphaltenes are discussed in detail.

4nπ Stable Multitasking Azapentacene: Acidochromism, Hole Mobility, and Visible Light Photoresponse.

Herein, we describe the synthesis, characterization, and optoelectronic investigation of a stable 4nπ dihydrotetraazapentacene derivative. The neutral dihydrotetraazapentacene contains a 24π-conjugated N-heteroacene core with two phenyl pendants appended thereof. The exceptional stability of this formally antiaromatic π-system is attributed to the fused dihydropyrazine ring, which has ethenamine (enamine) conjugations, and hence, the π-electrons delocalize over the nearly planar azapentacene core to endow with a global aromatic characteristic. The embedded dihydropyrazine also offers an additional Clar's sextet with enhanced aromaticity. The present dihydrotetraazapentacene can be considered as a multitasking N-heteroacene, which showed photoresponsive nature under visible light illumination, acidochromism in solution, and p-type charge transport with an appreciable field-effect hole mobility of 0.02 cm2 V-1 s-1 and a bulk p-type mobility of 0.98 × 10-4 cm2 V-1 s-1 in the space charge-limited regime of operation measured in the hole-only device. Nucleus-independent chemical shift calculation, anisotropy of the induced current density plot, and anisotropic mobility calculation were performed to support the experimental findings.

A C 54 B 2 Polycyclic π-System with Bilayer Assembly and Multi-Redox Activity

A C ₅₄ B ₂ Polycyclic π-System with Bilayer Assembly and Multi-Redox Activity

Clar and Fries structures for fullerenes

Fries and Clar numbers are qualitative indicators of stability in conjugated π systems. For a given Kekulé structure, call any hexagon that contains three double bonds benzenoid. The Fries number is the maximum number of benzenoid hexagons, whereas the Clar number is the maximum number of independent benzenoid hexagons, in each case taken over all Kekulé structures. A Kekulé structure that realises the Fries (Clar) number is a Fries (Clar) structure. For benzenoids, it is not known whether every Fries structure is also a Clar structure. For fullerenes Cn, it is known that some Clar structures in large examples correspond to no Fries structure. We show that Fries structures that are not Clar occur early: examples where some Fries structure is not Clar start at C34, and examples where no Fries structure is Clar start at C48. Hence, it is unsafe to use fullerene Fries structures as routes to Clar number. However, Fries structures often describe the neutral fullerene better than a Clar structure, e.g. in rationalising bond lengths in the experimental isomer of C60. Conversely, an extension of Clar sextet theory suggests the notion of anionic Clar number for fullerene anions, where both pentagons and hexagons may support sextets.

Activity origin of boron doped carbon cluster for thermal catalytic oxidation: Coupling effects of dopants and edges

Catalytic oxidation plays important roles in energy conversion and environment protection. Boron-doped crystalline carbocatalyst has been demonstrated effective; however, the application potential of boron-doped amorphous carbocatalyst remains to be explored. For amorphous carbon material, finite-sized carbon clusters are the basic structural units, which exhibit unique activity due to edge and size effect. Herein, using sulfur dioxide (SO2) and carbon monoxide (CO) oxidation as probe thermal-catalysis reactions, we found the distribution and reactivity of active sites in boron-doped carbon clusters are simultaneously determined by dopants and edges. According to comparisons of oxygen (O2) chemisorption energy at different sites of symmetric and non-symmetric carbon cluster, the most active site is found to be the edge carbon atom with high electron donation ability, which can be accurately identified by electrophilic Fukui function. More importantly, the reactivity of boron-doped cluster is simultaneously influenced by doping configuration and the type of edge, based on which -O-B-O- configuration embedded into K-region edge (isolated carbon–carbon double bonds that do not belong to Clar sextet) is predicted to exhibit the highest reactivity among various boron doping configurations. This work clarifies unique activity origin of heteroatom-doped amorphous carbon materials, providing new insights into designing high-performance carbocatalysts.

Quantitative Resonance Theory Based on the Clar Sextet Model.

Despite its great explanatory power in understanding the chemistry of polycyclic aromatic hydrocarbons (PAHs) and related systems, the Clar sextet rule still remains an intuitive and qualitative model with notable exceptions in some cases. Here we develop a quantitative theory of chemical resonance based on semilocalized Clar-type resonance structures (named the Clar resonators) consisting of variable numbers of Clar sextets and C═C bonds. The constructed wave functions of the Clar resonators are used to expand the actual wave function of the π-conjugated system obtained from a DFT or Hartree-Fock calculation. The resultant weights and one-electron energies of the Clar resonators can serve as a quantitative measure of the importance of these resonators. Implementing the theory in our open-source python code EzReson and applying it to over a thousand PAH molecules of different sizes and shapes, we show that the weight of the Clar resonators increases exponentially with increasing number of sextets and that their energy decreases linearly with the latter, thus confirming the general validity of the Clar rule. On the basis of such a large-scale resonance analysis, we propose three extended Clar rules, along with a unified quantitative model, that are able to evaluate the importance of all Clar resonators and the ring aromaticity for PAHs. Using the present theories, we uncover the essential role that the minor Clar resonators may play in correctly understanding the resonance stabilization and local aromaticity of rings, which was totally overlooked in the original Clar model.

Assessment of the Performance of the Bond Resonance Energy, Circuit Resonance Energy, Magnetic Resonance Energy, Ring Currents, and Aromaticity of Anthracene, Biphenylene, Phenalenyl, and p-Terphenyl.

This paper contributes to the further understanding of bond resonance energy (BRE), circuit resonance energy (CRE), and ring currents (RC = I) as indices for the measure of local ring aromaticity and topological resonance energy (TRE) and magnetic resonance energy (MRE) as indices for the measure of global molecular aromaticity. Calculations of ring currents in the 3-ring polycyclic hydrocarbons of anthracene, biphenylene, phenalenyl, and p-terphenyl are demonstrated. This comparative study provides new molecular insights. A number of shortcut techniques are briefly illustrated. p-Terphenyl is a benzenoid total resonant sextet (TRS) and biphenylene is shown to be a nonbenzenoid TRS, i.e., both obey Clar's sextet principle. p-Terphenyl has only ring circuits, whereas anthracene, biphenylene, and phenalenyl have ring circuits and larger circuits engulfing the ring circuits. The perimeter circuits of anthracene, biphenylene, and phenalenyl engulf all other circuits, thus leading to the definition of MRE. By these several aromatic indices, the monocation, monoanion, and monoradical of phenalenyl are equally aromatic. The agreement in the prediction of local ring aromaticity between the three indices of m-BRE, t-BRE, and CRE is evaluated.

Optoelectronic Properties of Polycyclic Benzenoid Hydrocarbons of Various Sizes and Shapes for Donor‐π‐Acceptor Systems: A DFT Study

AbstractThe zigzag and armchair‐edged benzenoid polycyclic aromatic hydrocarbons (PAHs) possessing circular, parallelogram, rectangular and triangular shapes have been studied for a systematic evaluation of their optoelectronic properties for the design of donor‐π‐acceptor (D‐π‐A) systems using M06L/6‐31+G(d) level of density functional theory (DFT). Molecular electrostatic potential (MESP) analysis of the PAHs is done to characterize their electron distribution while the time‐dependent DFT (TD‐DFT) analysis was used for the absorption spectral analysis. MESP analysis showed Clar's sextet like electronic arrangement in armchair‐edged systems whereas zigzag‐edged ones showed significant electron localization towards the edges. The absorption spectra revealed a linear trend in absorption maximum (λmax) for most of the armchair‐edged systems with respect to the number of π‐electrons. MESP based assessment of the electron rich/deficient features of PAH systems led to the design of PAH‐π‐PAH type D‐π‐A systems wherein a conjugated diene moiety functions as the π‐spacer. The D‐π‐A behaviour of these systems significantly enhanced with the introduction of electron donating functional group NMe2 on donor PAH and electron withdrawing group COOH on the acceptor PAH. The MESP features, frontier molecular orbital (FMO) distribution, and absorption spectral features supported the strong D‐π‐A character of functionalized PAH‐π‐PAH. Among the different shapes studied, the rectangular PAH moiety showed the most efficient tuning of HOMO‐LUMO gap. The optical and electronic properties of PAH, PAH‐π‐PAH and functionalized PAH‐π‐PAH systems suggest the high tunable character of these properties with respect to the size and shape of the PAH.

Hydrogen bonding interactions can decrease clar sextet character in acridone pigments.

Computed nucleus-independent chemical shifts (NICS), contour plots of isotropic magnetic shielding (IMS), and gauge-including magnetically induced current (GIMIC) plots suggest that polarization of the π-system of acridones may perturb the numbers and positions of Clar sextet rings. Decreasing numbers of Clar sextets are connected to experimental observations of a narrowing HOMO-LUMO gap and increased charge mobility in solid-state assemblies of quinacridone and epindolidione.

Interplay Between Planar and Spherical Aromaticity: Shielding Cone Behavior in Dual Planar-Planar, Planar-Spherical and Spherical-Spherical Aromatics.

The shielding cone concept is one of the most characteristic aspects of planar aromatic species. Herein, we explored how two neighbor aromatic moieties behave as dual planar-planar, planar-spherical, and spherical-spherical species given by biphenyl, [PhCB11 H11 ]- , and [CB11 H11 ]2 2- , respectively. Our results show two separate aromatic regimes given by Clar's sextet and spherical aromatic states, with independent shielding cones sharing shielding regions of moderate strength, which can be extended for networks involving multiple independent aromatic states.

Clar Rules the Electronic Properties of 2D π-Conjugated Frameworks: Mind the Gap.

The key electronic properties of a family of 2D frameworks structurally convergent with holey graphenes were studied. The bandgap of these materials decreases monotonically with size, showing a common trend with anthracenes and kekulenes. This was rationalized by Clar's sextet rule, which reveals a direct relationship between the molecular systems and the 2D frameworks. In addition, a detailed benchmark against experimental data showcased the high quality of the models, which reproduce accurately available electronic properties. Overall, it was shown that DFT can be used to screen and understand the intrinsic bandgaps and electrochemistry potentials for technological applications prior to the synthesis of π-conjugated porous materials.

Tuning the UV spectrum of PAHs by means of different N-doping types taking pyrene as paradigmatic example: categorization via valence bond theory and high-level computational approaches.

Tuning of the electronic spectra of carbon dots by means of inserting heteroatoms into the π-conjugated polycyclic aromatic hydrocarbon (PAH) system is a popular tool to achieve a broad range of absorption and emission frequencies. Especially nitrogen atoms have been used successfully for that purpose. Despite the significant progress achieved with these procedures, the prediction of specific shifts in the UV-vis spectra and the understanding of the electronic transitions is still a challenging task. In this work, high-level quantum chemical methods based on multireference (MR) and single-reference (SR) methods have been used to predict the effect of different nitrogen doping patterns inserted into the prototypical PAH pyrene on its absorption spectrum. Furthermore, a simple classification scheme based on valence bond (VB) theory and the Clar sextet rule in combination with the harmonic oscillator measure of aromaticity (HOMA) index was applied to arrange the different doping structures into groups and rationalize their electronic properties. The results show a wide variety of mostly redshifts in the spectra as compared to the pristine pyrene case. The most interesting doping structures with the largest red shifts leading to absorption energies below one eV could be readily explained by the occurrence of diradical VB structures in combination with Clar sextets. Moreover, analysis of the electronic transitions computed with MR methods showed that several of the low-lying excited states possess double-excitation character, which cannot be realized by the popular SR methods and, thus, are simply absent in the calculated spectra.

Theoretical Insight into Configurational Selectivity of Functionalized Single-Walled Carbon Nanotubes Based on the Clar Sextet Theory

Based on Clar’s theory of the aromatic sextet, finite-length models of single-walled carbon nanotubes (SWNTs) have been utilized to study the configurational selectivity of modified SWNTs via covalent functionalization with organic substitutions by density functional theory calculations. After considering near-armchair, near-zigzag, and zigzag SWNTs with distinct chiralities, it is found that the parameter R of semiconducting SWNTs plays a significant role in determining the stability difference of functionalized SWNTs; that is, SWNTs with R = 2 exhibit better configurational selectivity than those with R = 1 when binding the same substituent to the sidewall of SWNTs. Except for the zigzag (7,0) and (10,0) SWNTs with R = 1, the most favorable addition site in the considered SWNTs corresponds to the double bond in their Clar unit cells. The methyl-SWNT radicals with different R values exhibit distinct localizations of the unpaired spin, which is supposed to make a major contribution to the diversity of adducts. The addition sites with the largest spin density lead to the most stable adducts in modifications with small substituents for (6,4), (6,5), (9,1), (8,0), and (11,0) SWNTs, but the correlation tends to disappear for substituents with the increased alkyl chain or bulkiness. Particularly, the bulkiness of alkyl groups is more influential than the alkyl chain length. The degree of bond length change at addition sites is mainly affected by structures of SWNTs, and bulky substituents prefer addition positions in favor of releasing the steric repulsion between substituents. Bond angle changes around addition sites reveal that the extent of sp2 distortion depends on addition sites, and para adducts exhibit much larger sp2 distortion than ortho adducts, resulting in more ideal sp3 carbons. In addition, the increase in the alkyl chain and bulkiness of substituents can weaken the formed C–C bonds between the substituent and SWNT; especially, bulky substituents make the strength of covalent C–C bonds much weaker.

Edge Effects in Benzenoid and Total Resonant Sextet Benzenoid Hydrocarbons and Clar's Sextet Principle.

Because the effect of a benzenoid perimeter edge on a sextet pattern is of paramount importance, trends in the degree of sextet aromaticity are determined. The spectacular structural isomorphism between the total set of benzenoid hydrocarbons and its strain-free total resonant sextet (TRS) subset as described herein is an unequivocal demonstration of the validity of the Clar sextet principle. Aromaticity and the Clar's sextet principle are intricately related which form the basis of this isomorphism. Hexagons on the edge of a polycyclic benzenoid hydrocarbon tend to have higher spin density, have a higher probability of sextet residence, be more reactive to substitution reactions, and have a perimeter topology described by four distinct parameters by means of a very simple relation. It is shown that because the location of Clar sextets in TRS benzenoids is totally fixed, the relative order of ring aromaticity of the peripheral benzene hexagons can be predicted from their topology. Using Bosanac and Gutman's energy effect ( ef) and Aihara's bond resonance energy, we show for the first time that the relative order of decreasing ring aromaticity for perimeter edge hexagons in any specific TRS benzenoid is quarto > trio > duo > solo > empty. TRS benzenoid hydrocarbons are those isomers in benzenoids having their number of formula carbons divisible by six and a maximum number of perimeter bay regions (ηo) given by η0(TRS) = (1/2) NH(sextet) - 3 + F. NH(sextet) is the number of formula hydrogens and F is the number of perimeter fjords (triplet of adjacent bay regions); for strain-free TRS benzenoids, F = 0.

Formation of boron nitride islands in the graphene nanoflakes: A DFT study

Abstract We have applied density functional calculations to investigate the formation of boron nitride islands in the triangular and hexagonal graphene nanoflakes (GNFs). Based on the calculated reaction energies, BN doping of GNFs is found to be endothermic. The variation of reaction energies indicates that BN doping of the GNFs follow previously proposed ‘hexagon filling’’ rule. Based on the calculated NICS indexes, aromaticity inside these molecules can be explained within the framework of the Clar's Sextet Theory. In the case of BN-doped hexagonal and triangular GNFs, NICS(1) index shows aromaticity and nonaromaticity for the borazine like substructures, respectively. Moreover, the substitution of one BN unit in the 1,2 azaborine like rings leads to the increase of aromaticity and nonaromaticity in hexagonal and triangular GNFs, respectively. Based on our results, the BN doped hexagonal GNFs not only lose electrons somewhat more easily to form positive ions, but also obtain electrons more easily to form anions.

Energetic Analysis of Conjugated Hydrocarbons Using the Interacting Quantum Atoms Method.

A number of aromatic, antiaromatic, and nonaromatic organic molecules was analyzed in terms of the contributions to the electronic energy defined in the quantum theory of atoms in molecules and the interacting quantum atoms method. Regularities were found in the exchange and electrostatic interatomic energies showing trends that are closely related to those of the delocalization indices defined in the theory. In particular, the CC interaction energies between bonded atoms allow to rationalize the energetic stabilization associated with the bond length alternation in conjugated polyenes. This approach also provides support to Clar's sextet rules devised for aromatic systems. In addition, the H⋯H bonding found in some of the aromatic molecules studied was of an attractive nature, according to the stabilizing exchange interaction between the bonded H atoms. © 2017 Wiley Periodicals, Inc.

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.