Clar's Sextet Rule Research Articles

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.

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.

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.

Low Bandgap Bistetracene-Based Organic Semiconductors Exhibiting Air Stability, High Aromaticity and Mobility.

The benchmark of soluble organic semiconductors based on acenes is the 6,13-bis(triisopropylsilylethynyl)pentacene (TIPS-PEN). However TIPS-PEN still suffers from photoinduced oxidation due to its low degree of aromaticity. Increasing the aromaticity while keeping similar optical and electrochemical properties as well as a shape suitable for good hole transport can be achieved with two-dimensional polycyclic aromatic hydrocarbons (2D-PAHs). Herein, we present an efficient synthesis and characterization of bistetracene derivatives that exhibit a band gap up to 1.71 eV and an increased stability up to 21 times compared to TIPS-PEN and mobility over 0.1 cm2 V-1 s-1 in solution-processed organic field-effect transistors. Based on simple structural consideration, the high stability is attributed to the aromaticity of the bistetracene which is comparable to an anthrancene along each tetracene. According to Clar's sextet rule, the bistetracene should be best regarded as two anthracenes fused at the face bridged by two ethylenic spacers. The synthesis path paves the way towards the preparation of ambipolar and/or longer 2D-PAHs such as bispentacenes and could give rise to organic semiconductors with interesting properties.

Detection of NO2 by hexa-peri-hexabenzocoronene nanographene: A DFT study

It has been previously indicated that pristine graphene cannot detect NO 2 gas. Nanographene is a segment of graphene whose end atoms are saturated with hydrogen atoms and its properties are different from those of graphene. Herein, we investigated the reactivity, electronic sensitivity, and structural properties of hexa- peri -hexabenzocoronene (HBC) nanographene toward NO 2 gas using density functional theory calculations. It was found that the central and peripheral rings of HBC are aromatic but the middle rings are non-aromatic, following Clar's sextet rule of aromaticity. The NO 2 molecule prefers to be adsorbed on the central ring with a nitro configuration, releasing an energy of about 13.2 kJ/mol. The NO 2 molecule significantly stabilizes the LUMO level of the HBC, thereby reducing the HOMO–LUMO energy gap from 3.60 to 1.35 eV. This indicates that the HBC is converted from a semiconductor to a semimetal. It was shown that the adsorption of NO 2 gas by HBC can produce an electrical signal selectively in the presence of O 2 , H 2 , N 2 , CO 2 , and H 2 O gases. A short recovery time about 1.9 ns is predicted and the effect of density functional is investigated.

A stochastic method for asphaltene structure formulation from experimental data: avoidance of implausible structures.

This work presents a stochastic procedure designed to formulate a discrete set of molecular structures that, as a whole, adjust properly to experimental asphaltene data. This algorithm incorporates the pentane effect concept and Clar's sextet rule to the formulation process. The set of viable structures was constructed based on probability distribution functions obtained from experimental information and an isomer database containing all plausible configurations for a given number of rings, avoiding high-energy structures. This procedure was applied to a collection of experimental data from the literature. Ten sets, consisting of 5000 structures each, were obtained. Each set was then optimized. For the most accurate representation, four molecules were sufficient to properly reproduce the experimental input. The asphaltene system obtained is consistent with the reported molecular weight, number of aromatic rings and heteroatom content. Molecular dynamic simulations showed that the asphaltene representation adequately reproduced asphaltene aggregation behavior in toluene and n-heptane. In toluene, a single three-molecule aggregate was observed, and the majority of asphaltene molecules remained in a monomeric state. In n-heptane, aggregates containing up to four molecules were observed; both porous and compact aggregates were found. The asphaltene molecular representation obtained, which allows researchers to avoid inappropriate torsions in the molecule, is able to reproduce interplanar distances between aromatic cores of 4 Å or less for the aggregation state, as supported by experimental results.

Aromaticity Relocation in Perylene Derivatives upon Two-Electron Oxidation To Form Anthracene and Phenanthrene.

We prepared perylene dications 1(2+) and 2(2+) by using "capped" perylene derivatives, and for the first time, successfully obtained single crystals of a perylene dication 1(2+) that enabled us to perform its structural analysis. We realized that the substituted aryl groups on perylene control the positions of positive charges, thus the remaining electronic system satisfies Clar's sextet rule toward the highest number of localized sextets. Experimental and theoretical evidence proved that Clar's aromatic π-sextet rule could be applied even for the dicationic perylenes in a very simple way.

Unconventional, chemically stable, and soluble two-dimensional angular polycyclic aromatic hydrocarbons: from molecular design to device applications.

Polycyclic aromatic hydrocarbons (PAHs), consisting of laterally fused benzene rings, are among the most widely studied small-molecule organic semiconductors, with potential applications in organic field-effect transistors (OFETs) and organic photovoltaics (OPVs). Linear acenes, including tetracene, pentacene, and their derivatives, have received particular attention due to the synthetic flexibility in tuning their chemical structure and properties and to their high device performance. Unfortunately, longer acenes, which could exhibit even better performance, are susceptible to oxidation, photodegradation, and, in solar cells which contain fullerenes, Diels-Alder reactions. This Account highlights recent advances in the molecular design of two-dimensional (2-D) PAHs that combine device performance with environmental stability. New synthetic techniques have been developed to create stable PAHs that extend conjugation in two dimensions. The stability of these novel compounds is consistent with Clar's sextet rule as the 2-D PAHs have greater numbers of sextets in their ground-state configuration than their linear analogues. The ionization potentials (IPs) of nonlinear acenes decrease more slowly with annellation in comparison to their linear counterparts. As a result, 2-D bistetracene derivatives that are composed of eight fused benzene rings are measured to be about 200 times more stable in chlorinated organic solvents than pentacene derivatives with only five fused rings. Single crystals of the bistetracene derivatives have hole mobilities, measured in OFET configuration, up to 6.1 cm(2) V(-1) s(-1), with remarkable Ion/Ioff ratios of 10(7). The density functional theory (DFT) calculations can provide insight into the electronic structures at both molecular and material levels and to evaluate the main charge-transport parameters. The 2-D acenes with large aspect ratios and appropriate substituents have the potential to provide favorable interstack electronic interactions, and correspondingly high carrier mobilities. In stark contrast to the 1-D acenes that form mono- and bis-adducts with fullerenes, 2-D PAHs show less reactivity with fullerenes. The geometry of 2-D PAHs plays a crucial role in determining both the barrier and the adduct stability. The reactivity and stability of the 2-D PAHs with regard to Diels-Alder reactions at different reactive sites were explained via DFT calculations of the reaction kinetics and of thermodynamics of reactions and simple Hückel molecular orbital considerations. Also, because of their increased stability in the presence of fullerenes, these compounds have been successfully used in OPVs. The small-molecule semiconductors highlighted in this Account exhibit good charge-transport properties, comparable to those of traditional linear acenes, while being much more environmentally stable. These features have made these 2-D PAHs excellent molecules for fundamental research and device applications.