Aromaticity is one of the most important concepts in organic chemistry to understand the electronic properties of cyclic π-conjugated molecules. Over a century, different aromaticity rules have been developed and validated. For planar monocyclic conjugated polyenes (also known as [n]annulenes), they will be aromatic if they contain [4N + 2] π electrons according to Hückel's rule, or antiaromatic if they have [4N] π electrons. Topological change from a planar to a half-twisted Möbius strip will lead to [4N] ([4N + 2]) aromaticity (antiaromaticity), which is just inverse to Hückel's rule. When the molecules are excited into the first triplet excited state, the Hückel (anti)aromaticity observed in the ground state will become reversed according to Baird's rule. Strictly speaking, these basic rules are only applicable for monocyclic conjugated systems, but some polycyclic systems such as porphyrinoids may also follow these rules if there is a dominant [n]annulene-like conjugation pathway. On the other hand, all-benzenoid polycyclic aromatic hydrocarbons usually display local aromaticity with π electrons predominantly localized at certain benzene rings according to Clar's aromatic sextet rule. In recent years, some proaromatic and antiaromatic molecules with even number of paired electrons have been found to exhibit open-shell diradical character and unique optical, electronic, and magnetic activities. One of the major driving forces is their intrinsic tendency to become aromatic in the open-shell diradical/polyradical forms. A number of stable diradicaloids and linear polyradicaloids have been successfully synthesized by using thermodynamic and kinetic stabilizing strategies. Herein, our particular interest is a type of macrocyclic polyradicaloid in which multiple frontier π-electrons are antiferromagnetically coupled with each other in a cyclic mode. Formally, these free electrons may behave like normal π-electrons in the [n]annulenes, and thus, it raises questions about their possible global aromaticity and which rule they will follow. In the past 5 years, our group has synthesized a series of macrocyclic polyradicaloids and systematically investigated their global aromaticity and electronic properties. Some important findings include: (1) global (anti)aromaticity is generally observed, but there is a balance between local aromaticity and global aromaticity; (2) most of these molecules follow Hückel's rule in the singlet state and display respective (anti)aromatic characteristics; (3) in some special cases, both Hückel's rule and Baird's rule can be applicable, and a unique annulene-within-an-annulene super-ring structure was demonstrated for the first time; (4) global antiaromaticity in the transition state is also important and a slow valence tautomerization process was observed in a supercyclobutadiene tetraradicaloid. These studies demonstrate how these open-shell macrocyclic polyradicaloids adapt their geometry and spin state to reach the lowest-energy state (aromatic). In this Account, we will mainly discuss their synthesis, global aromaticity, and the fundamental structure-radical character-aromaticity-properties relationships. Various experimental methods (e.g., NMR, X-ray crystallographic analysis, and electronic absorption spectroscopy) and theoretical calculations (e.g., anisotropy of the induced current density, nucleus independent chemical shift, and isochemical shielding surface) have been used to elaborate their (anti)aromatic character. At the end, a perspective on the possible three-dimensional global aromaticity in fully conjugated cagelike diradicaloids or polyradicaloids will be also discussed.
Aromaticity is an important concept in chemistry primarily for organic compounds, but it has been extended to compounds containing transition-metal atoms. Recent findings of aromaticity and antiaromaticity in all-metal clusters have stimulated further research in describing the chemical bonding, structures and stability in transition-metal clusters and compounds on the basis of aromaticity and antiaromaticity, which are reviewed here. The presence of d-orbitals endows much more diverse chemistry, structure and chemical bonding to transition-metal clusters and compounds. One interesting feature is the existence of a new type of aromaticity-delta-aromaticity, in addition to sigma- and pi-aromaticity which are the only possible types for main-group compounds. Another striking characteristic in the chemical bonding of transition-metal systems is the multi-fold nature of aromaticity, antiaromaticity or even conflicting aromaticity. Separate sets of counting rules have been proposed for cyclic transition-metal systems to account for the three types of sigma-, pi- and delta-aromaticity/antiaromaticity. The diverse transition-metal clusters and compounds reviewed here indicate that multiple aromaticity and antiaromaticity may be much more common in chemistry than one would anticipate. It is hoped that the current review will stimulate interest in further understanding the structure and bonding, on the basis of aromaticity and antiaromaticity, of other known or unknown transition-metal systems, such as the active sites of enzymes or other biomolecules which contain transition-metal atoms and clusters.
Inverse sandwich clusters composed of a monocyclic boron ring and two capping transition metal atoms are interesting alloy cluster systems, yet their chemical bonding nature has not been sufficiently elucidated to date. We report herein on the theoretical prediction of a new example of boron-based inverse sandwich alloy clusters, V2B7−, through computational global-minimum structure searches and quantum chemical calculations. This alloy cluster has a heptatomic boron ring as well as a perpendicular V2 dimer unit that penetrates through the ring. Chemical bonding analysis suggests that the inverse sandwich cluster is governed by globally delocalized 6π and 6σ frameworks, that is, double 6π/6σ aromaticity following the (4n + 2) Hückel rule. The skeleton B−B σ bonding in the cluster is shown not to be strictly Lewis-type two-center two-electron (2c-2e) σ bonds. Rather, these are quasi-Lewis-type, roof-like 4c-2e V−B2−V σ bonds, which amount to seven in total and cover the whole surface of inverse sandwich in a truly three-dimensional manner. Theoretical evidence is revealed for a 2c-2e Lewis σ single bond within the V2 dimer. Direct metal–metal bonding is scarce in inverse sandwich alloy clusters. The present inverse sandwich alloy cluster also offers a new type of electronic transmutation in physical chemistry, which helps establish an intriguing chemical analogy between inverse sandwich clusters and planar hypercoordinate molecular wheels.
Significance Antiaromaticity is associated with extra thermodynamic instability and makes the synthesis and isolation of antiaromatic molecules particularly challenging. Craig-type (anti)aromaticity, with a reversal to Hückel rule, describes a planar molecule with π-conjugated systems involving pπ–dπ interaction. To synthesize Craig antiaromatic compound is challengeable as it contains a set of properties that initially seems mutually incompatible: 1) antiaromaticity destabilization; 2) a planar structure with [4n + 2] π electrons; and 3) pπ–dπ interaction with phase shift in d orbital. In this work, we report the first synthesis of the Craig-type antiaromatic compounds via the deprotonation-induced reduction process and the Craig antiaromaticity along with the driving force of realization of Craig-type antiaromatic compounds was evidenced both experimentally and theoretically.
Planar tetracoordinate silicon, germanium, tin, and lead (ptSi/Ge/Sn/Pb) species are scarce and exotic. Here, we report a series of penta-atomic ptSi/Ge/Sn/Pb XB2Bi2 (X = Si, Ge, Sn, Pb) clusters with 20 valence electrons (VEs). Ternary XB2Bi2 (X = Si, Ge, Sn, Pb) clusters possess beautiful fan-shaped structures, with a Bi–B–B–Bi chain surrounding the central X core. The unbiased density functional theory (DFT) searches and high-level CCSD(T) calculations reveal that these ptSi/Ge/Sn/Pb species are the global minima on their potential energy surfaces. Born–Oppenheimer molecular dynamics (BOMD) simulations indicate that XB2Bi2 (X = Si, Ge, Sn, Pb) clusters are robust. Bonding analyses indicate that 20 VEs are perfect for the ptX XB2Bi2 (X = Si, Ge, Sn, Pb): two lone pairs of Bi atoms; one 5c–2e π, and three σ bonds (two Bi–X 2c–2e and one B–X–B 3c–2e bonds) between the ligands and X atom; three 2c–2e σ bonds and one delocalized 4c–2e π bond between the ligands. The ptSi/Ge/Sn/Pb XB2Bi2 (X = Si, Ge, Sn, Pb) clusters possess 2π/2σ double aromaticity, according to the (4n + 2) Hückel rule.
Purine stretches, sequences of adenine (A) and guanine (G) in DNA, play critical roles in binding regulatory protein factors and influence gene expression by affecting DNA folding. This study investigates the relationship between purine stretches and cancer development, considering the aromaticity of purines, quantified by methods like Hückel's rule and NICS calculations, and the importance of the flanking sequence context. A pronounced avoidance of long purine stretches by typical cancer mutations was observed in public data on the intergenic regions of cancer patients, suggesting a role of intergenic sequences in chromatin reorganization and gene regulation. A statistically significant shortening of purine stretches in cancerous tumors (<i>p</i> value < 0.0001) was found. The insights into the aromatic nature of purines and their stacking energies explain the role of purine stretches in DNA structure, contributing to their role in cancer progression. This research lays the groundwork for understanding the nature of purine stretches, emphasizing their importance in gene regulation and chromatin restructuring, and offers potential avenues for novel cancer therapies and insights into cancer etiology.
Hückel's rule
In organic chemistry, Hückel's rule is a rule that help to determine if a molecule has the properties of an aromatic compound. It is named after chemist Erich Hückel, who formulated it in 1931. A well known compound that fulfills the rule is Benzene.
It states that: A compound to be aromatic, it must contain 4n+2 π delocalized electrons above or below the plane of the molecule and the molecule is supposed to be cyclic or planar.
Example:
- Say benzene,
It has 3 π bonds.
i.e. 6 π electrons.
According to this rule,
- 4n+2 π e- = 6 π e-
4n+2 = 6
4n=4
∴ n = 1 which belong to Z(0,1,2,...)
The paper deals with quantifying aromaticity in π-electron networks by unsophisticated MO techniques. The focus is placed on local aromaticity measures associated with individual benzenoid rings. We revised the ring aromaticity index due to Cioslowski et al (2007) by including explicitly net charges and electron unpairing effects. Our previously introduced quasi-correlated tight-binding (QCTB) approximation serves here as an easily available tool for taking account of π-electron correlations. The latter crucially influence the behavior of large and even small conjugated π-structures with a nontrivial topology. Numerical applications of Hückel and QCTB models to measuring local aromaticity are reported for various structural classes (polycyclic aromatic hydrocarbons (PAHs), graphene nanoflakes, and others). We analytically investigate the aromaticity in conjugated monocycles CNHN (neutral and charged ones). Furthermore, in the same manner several PAH structures (oligocenes, pyrene, perylene, etc.) are considered in their charged states, and the results are compared with those of related quinoid-type systems, such as p-diphenoquinodimethane. It is shown that, unlike usual PAHs, quinodimethane structures tend to increase their aromaticity in dicationic (dianionic) form. In our studies of nanographene aromaticity we find a decrease of the local aromaticity as we move to a center of graphene structures, that is in a sharp contrast to the predictions of NICS (nucleus independent chemical shift), a rather criticized approach. A particular emphasis is being put on measuring local aromaticity in highly correlated π-systems. Typical non-Kekule hydrocarbons (e.g., triangulene radical and polyradicals), are also studied within QCTB by which characteristic difficulties caused by the occurrence of many non-bonding π-MOs, are simply obviated.
The Hückel Hamiltonian is an incredibly simple tight-binding model known for its ability to capture qualitative physics phenomena arising from electron interactions in molecules and materials. Part of its simplicity arises from using only two types of empirically fit physics-motivated parameters: the first describes the orbital energies on each atom and the second describes electronic interactions and bonding between atoms. By replacing these empirical parameters with machine-learned dynamic values, we vastly increase the accuracy of the extended Hückel model. The dynamic values are generated with a deep neural network, which is trained to reproduce orbital energies and densities derived from density functional theory. The resulting model retains interpretability, while the deep neural network parameterization is smooth and accurate and reproduces insightful features of the original empirical parameterization. Altogether, this work shows the promise of utilizing machine learning to formulate simple, accurate, and dynamically parameterized physics models.
Normally, aromaticity is qualitatively assessed using an electron counting rule for cyclic conjugated rings. The best known is the Hückel 4n+2 rule (n=0,1, etc) for inferring diatropic aromatic ring currents in singlet-state π-conjugated cyclic molecules‡ and a counter 4n rule which infers an antiaromatic paratropic ring current for the system.
Aromaticity, in general, can promote a given reaction by stabilizing a transition state or a product via a mobility of π electrons in a cyclic structure. Similarly, such a promotion could be also achieved by destabilizing an antiaromatic reactant. However, both aromaticity and transition states cannot be directly measured in experiment. Thus, computational chemistry has been becoming a key tool to understand the aromaticity-driven reaction mechanisms. In this review, we will analyze the relationship between aromaticity and reaction mechanism to highlight the importance of density functional theory calculations and present it according to an approach via either aromatizing a transition state/product or destabilizing a reactant by antiaromaticity. Specifically, we will start with a particularly challenging example of dinitrogen activation followed by other small-molecule activation, C-F bond activation, rearrangement, as well as metathesis reactions. In addition, antiaromaticity-promoted dihydrogen activation, CO2 capture, and oxygen reduction reactions will be also briefly discussed. Finally, caution must be cast as the magnitude of the aromaticity in the transition states is not particularly high in most cases. Thus, a proof of an adequate electron delocalization rather than a complete ring current is recommended to support the relatively weak aromaticity in these transition states.
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