Aromaticity in spin-polarized systems: Can rings be simultaneously alpha aromatic and beta antiaromatic?

Spin population determines whether antiaromaticity can increase or decrease radical stability

Aromaticity, as a classical and fundamental concept in chemistry, can enhance thermodynamic stability. In sharp contrast, a previous study showed that antiaromaticity rather than aromaticity can enhance the radical stability of α-methyl heterocyclic compounds. Here, we demonstrate a similar antiaromaticity-promoted radical stability when the methyl group is replaced by five-membered (alkyl)(amino)cyclics (AACs). More interestingly, when an AAC is fused with an antiaromatic ring, the radical stability could be either reduced or enhanced, depending on the spin population. Specifically, when the spin density is populated on an incoming antiaromatic 1,4-dihydro-1,4-diborinine moiety, the radical stability is enhanced whereas when the spin density is maintained on the original five-membered ring, the radical stability is reduced. Our findings highlight the importance of spin density in tuning the radical stability, inviting experimental chemists' verification.

Unraveling the enigma of Craig-type Möbius-aromatic osmium compounds

Nuclear magnetic resonance (NMR) chemical shifts and the magnetically induced current density (MICD) susceptibility of four osmium containing molecules have been calculated at the density functional theory (DFT) level using three relativistic levels of theory. The calculations were performed at the quasi-relativistic level using an effective core potential (ECP) for Os, at the all-electron scalar exact two-component (X2C) relativistic level, and at the relativistic X2C level including spin-orbit coupling (SO-X2C). In earlier studies, the osmapentalene (1) and the osmapentalynes (2 and 3) were considered Craig-type Möbius aromatic and it was suggested that the analogous osmium compound (4) is Craig-type Möbius antiaromatic. Here, the ring-current strengths were obtained with the gauge including magnetically induced currents (GIMIC) method by integrating the MICD susceptibility passing through planes that intersect chemical bonds and by line integration of the induced magnetic field using Ampère-Maxwell's law. The ring-current calculations suggest that 1, 2 and 3 are weakly aromatic and that 4 is nonaromatic. The accuracy of the MICD susceptibility was assessed by comparing calculated NMR chemical shifts to available experimental data. Visualization of the MICD susceptibility shows that the ring current does not pass from one side of the molecular plane to the other, which means that the MICD susceptibility of the studied molecules does not exhibit any Möbius topology as one would expect for Craig-type Möbius aromatic and for Craig-type Möbius antiaromatic molecules. Thus, molecules 1-3 are not Craig-type Möbius aromatic and molecule 4 is not Craig-type Möbius antiaromatic as previously suggested. Calculations of the 1H NMR and 13C NMR chemical shifts of atoms near the Os atom show the importance of including spin-orbit effects. Overall, our study revisits the understanding of the aromaticity of organometallic molecules containing transition metals.

The n,π* States of Heteroaromatics: When are They the Lowest Excited States and in What Way Can They Be Aromatic or Antiaromatic?

Heteroaromatic molecules are found in areas ranging from biochemistry to photovoltaics. We analyze the n,π* excited states of 6π-electron heteroaromatics with in-plane lone pairs (nσ, herein n) and use qualitative theory and quantum chemical computations, starting at Mandado's 2n + 1 rule for aromaticity of separate spins. After excitation of an electron from n to π*, a (4n + 2)π-electron species has 2n + 2 πα-electrons and 2n + 1 πβ-electrons (or vice versa) and becomes πα-antiaromatic and πβ-aromatic. Yet, the antiaromatic πα- and aromatic πβ-components seldom cancel, leading to residuals with aromatic or antiaromatic character. We explore vertically excited triplet n,π* states (3n,π*), which are most readily analyzed, but also singlet n,π* states (1n,π*), and explain which compounds have n,π* states with aromatic residuals as their lowest excited states (e.g., pyrazine and the phenyl anion). If the πβ-electron population becomes more (less) uniformly distributed upon excitation, the system will have an (anti)aromatic residual. Among isomers, the one that has the most aromatic residual in 3n,π* is often of the lowest energy in this state. Five-membered ring heteroaromatics with one or two N, O, and/or S atoms never have n,π* states as their first excited states (T1 and S1), while this is nearly always the case for six-membered ring heteroaromatics with electropositive heteroatoms and/or highly symmetric (D2h) diheteroaromatics. For the complete compound set, there is a modest correlation between the (anti)aromatic character of the n,π* state and the energy gap between the lowest n,π* and π,π* states (R2 = 0.42), while it is stronger for monosubstituted pyrazines (R2 = 0.84).

Stabilization of the Neutral [25]Hexaphyrin(1.0.1.0.1.0) Radical by Hetero-Bimetal-Coordination

Stabilization of hexaphyrin(1.0.1.0.1.0) (named "rosarin") in its 25π radical state is achieved using a hetero-bimetal-coordination strategy. The antiaromatic BF2 complex B-1 was first synthesized, and then rhodium ion was inserted into B-1 to produce the BF2/Rh(CO)2 mixed complex Rh-B-1 as a highly air-stable radical. The structures of B-1 and Rh-B-1 were determined by single-crystal X-ray diffractions, and the antiaromatic or radical character was identified by various spectroscopy evidence and theoretical calculations. Rh-B-1 exhibits excellent redox properties, enabling amphoteric aromatic-antiaromatic conversion to their 24/26π states. Compared to the 24/26π conjugation systems on the same skeleton, Rh-B-1 has the narrowest electrochemical and optical band gaps, with the longest absorption band at 1010 nm. The ring-current analysis reveals intense paratropic currents for B-1 and co-existing diatropic-paratropic currents for Rh-B-1. This hetero-bimetal-coordination system provides a novel platform for organic radical stabilization on porphyrinoids, showing the prospect of modulating ligand oxidation states through rational coordination design.

Unveiling the quantum secrets of triel metal triangles: a tale of stability, aromaticity, and relativistic effects

Low lying electronic states of Al3-, Ga3-, In3-, and Tl3- have been characterized using high level multiconfigurational quasi degenerate perturbation theory on the multiconfigurational self-consistent field. Among these species, the singlet states emerge as the predominant energy minima, displaying remarkable stability. However, within the Tl3- series, our investigation leads to the identification of the high-spin , as the most stable spin state, a result corroborated by previous experimental detection via photoelectron spectroscopy. Similarly, we have also identified the singlet state of In3- as the signal detected previously experimentally. By applying Mandado's rules and an array of aromaticity indicators, it is conclusively demonstrated that both the singlet and quintet states exhibit multiple-fold aromaticity, while the triplets exhibit conflicting aromaticity. Furthermore, this investigation highlights the significant impact of relativistic effects, as they enhance the stability of the state relative to its singlet counterpart. These findings shed new light on the electronic structures and properties of these ions, offering valuable insights into their chemical behavior and potential applications.

Cyclo[n]carbons and catenanes from different perspectives: disentangling the molecular thread

All-carbon atomic rings, cyclo[n]carbons, have recently attracted vivid attention of experimentalists and theoreticians. Among them, cyclo[18]carbon is the most studied system. In this paper, we summarize and review various properties of cyclo[n]carbons, emphasising the aspects of their aromaticity/antiaromaticity. In the first part, the trends in bonding patterns and selected aromaticity indices with the increasing size of the rings are discussed. In the second part we explore the properties of catenane models based on interlocked cyclo[18]carbon rings from different perspectives and investigate their behaviour under the action of external force using computational experiments.

Magnetic Antiaromaticity─Paratropicity─Does Not Necessarily Imply Instability

Magnetically induced ring currents are a conventional tool for the characterization of aromaticity. Dia- and paratropic currents are thought to be associated with stabilization (aromaticity) and destabilization (antiaromaticity), respectively. In the present work, I have questioned the validity of the paratropic currents as a measure of antiaromaticity among monocyclic hydrocarbons. I have shown that while reduced/oxidized radical ions of hydrocarbons sustain strong paratropic currents, they often gain extra stabilization via cyclic conjugation compared to their acyclic counterparts.

Excited-State (Anti)Aromaticity Explains Why Azulene Disobeys Kasha's Rule

Fluorescence exclusively occurs from the lowest excited state of a given multiplicity according to Kasha's rule. However, this rule is not obeyed by a handful of anti-Kasha fluorophores whose underlying mechanism is still understood merely on a phenomenological basis. This lack of understanding prevents the rational design and property-tuning of anti-Kasha fluorophores. Here, we propose a model explaining the photophysical properties of an archetypal anti-Kasha fluorophore, azulene, based on its ground- and excited-state (anti)aromaticity. We derived our model from a detailed analysis of the electronic structure of the ground singlet, first excited triplet, and quintet states and of the first and second excited singlet states using the perturbational molecular orbital theory and quantum-chemical aromaticity indices. Our model reveals that the anti-Kasha properties of azulene and its derivatives result from (i) the contrasting (anti)aromaticity of its first and second singlet excited states (S1 and S2, respectively) and (ii) an easily accessible antiaromaticity relief pathway of the S1 state. This explanation of the fundamental cause of anti-Kasha behavior may pave the way for new classes of anti-Kasha fluorophores and materials with long-lived, high-energy excited states.

Aromaticity: Quo Vadis

Aromaticity is one of the most deeply rooted concepts in chemistry. But why, if two-thirds of existing compounds can be classified as aromatic, is there no consensus on what aromaticity is? σ-, π-, δ-, spherical, Möbius, or all-metal aromaticity… why are so many attributes needed to specify a property? Is aromaticity a dubious concept? This perspective aims to reflect where the aromaticity community is and where it is going.

Aromaticity of Singlet and Triplet Boron Disk-like Clusters: A Test for Electron Counting Aromaticity Rules

Boron clusters are polyhedral boron-containing structures that have unique features and properties. The disk-like boron clusters are among the most fascinating boron cluster forms. These clusters have a molecular orbital (MO) distribution similar to the one derived from the simple particle-on-a-disk model. In this model, the MOs come in pairs except for m = 0. Disk-like boron clusters in their singlet ground state are aromatic when they reach a closed-shell structure. One could expect that disk-like aromatic boron clusters in the singlet state, when acquiring or releasing two electrons, may also be aromatic in the lowest-lying triplet state. We use magnetically induced current densities and bond current strengths to analyze the aromatic character of a series of disk-like boron clusters. Our results show that, with the exception of triplet ³B₁₉^-, the disk-like boron clusters follow Hückel and Baird's rules if one considers the different MOs grouped by their symmetry. We also found that if the lowest-lying triplet state in disk-like boron clusters is aromatic, this triplet state is the ground state for this species.

Electronic structure, stability, and aromaticity of M2B6 (M = Mg, Ca, Sr, and Ba): an interplay between spin pairing and electron delocalization

It has been shown in previous studies that the Be₂B₆ complex exhibits a triplet ground state with double aromaticity. In this work, the stability, electronic structure, and aromaticity of the homologous series M₂B₆ (M = Mg, Ca, Sr and Ba) were examined and compared to those of Be₂B₆. At the CCSD(T)/def2-TZVP//B3LYP/def2-TZVP level of theory, the target molecules were found to be more stable in the singlet than in the triplet spin state. Magnetically induced current densities and multicentre delocalization index (MCI) were employed to assess the aromatic character of the studied complexes. Both employed methods agree that M₂B₆ (M = Mg, Ca, Sr and Ba) are π aromatic and σ nonaromatic in the singlet ground state, and double aromatic in the triplet state. It was demonstrated that the electron counting rules of aromaticity cannot be used to correctly predict the aromaticity and relative stability of the examined molecules in different spin states.

Periodoannulenes: A Generalized Annulene-within-an-Annulene Paradigm for Combined σ and π Ring Currents

Periodoannulene molecules and ions C_xI_x^q in planar geometry offer examples of systems with the potential for outer σ and inner π ring-current double aromaticity, given a sufficient overlap of tangential p_σ-orbital manifolds on the large atoms of the outer cycle. Previous theoretical work indicated concentric diatropic currents in the dication C₆I₆²⁺. Ab initio ipsocentric calculations support an account in terms of frontier-orbital selection rules for current contributions in C₆I₆²⁺ (and radical C₆I₆⁺, implicated in recent experimental work on the oxidation of periodobenzene). A σ/π analogue of the annulene-within-an-annulene model is applied here to periodo systems based on cyclooctatetraene. Model species C₈I₈^q with charges q = 0, +1, +2, +4, -2 and structures constrained to a planar D_4h symmetry exhibit maps with all combinations of σ/π con- and counter-rotation, comprising global σ ring currents on the iodine perimeter and central π ring currents on the carbocycle. All can be rationalized by the separate application of the tropicity selection rules to the two subsystems, whether in singlet or triplet states.

Tetrahedral Pt10- Cluster with Unique Beta Aromaticity and Superatomic Feature in Mimicking Methane

Utilizing a customized metal cluster source in tandem with a flow tube reactor and a reflectron time-of-flight mass spectrometer, we have obtained well-resolved pure metal clusters Pt_n^- and observed their gas-phase reactions with a few small gas molecules. Interestingly, the remarkable inertness of Pt₁₀^- was repeatedly observed in different reactions. Meanwhile, we have determined the structure of Pt₁₀^- within a regular tetrahedron. Considering that Pt possesses 5d⁹6s¹ electron configuration, the tetrahedral Pt₁₀^- exhibits unexpected stability at neither a magic number of valence electrons nor a shell closure of geometric structure. Comprehensive theoretical calculations unveil the stability of Pt₁₀^- is significantly associated with the all-metal aromaticity. In addition to the classical total aromaticity, which is mainly due to 6s electrons, there is unique beta-aromaticity ascribed to spin-polarized beta 5d electrons pertaining to singly occupied multicenter bonds. Further, we demonstrate the superatomic feature of such a transition metal cluster Pt₁₀^-, as Pt₆@Pt₄^-, in mimicking methane.

Probing the Origin of Adaptive Aromaticity in 16-Valence-Electron Metallapentalenes

Species with adaptive aromaticity are aromatic in the ground and lowest-lying triplet excited states and they have normally intermediate singlet-triplet gaps. Few examples of compounds with adaptive aromaticity are known to date, including 16-valence-electron (16e) metallapentalenes. A sweeping search could be conducted to discover new members of this group, but efficient designs with an explicit strategy would facilitate the quest for new members of this elusive family. Density functional theory calculations and aromaticity evaluations have been performed to reveal the nature of triplet-state aromaticity in 16e metallapentalenes. Our results show that coordination of strong σ- or π-donor ligands helps achieving adaptive aromaticity of 16e metallapentalenes by means of a spin delocalization mechanism. These results have important implications for understanding the unusual properties of the organometallic adaptive aromatics, leading the way to efficient design of new compounds with tunable singlet-triplet gaps.

How do the Hückel and Baird Rules Fade away in Annulenes?

Two of the most popular rules to characterize the aromaticity of molecules are those due to Hückel and Baird, which govern the aromaticity of singlet and triplet states. In this work, we study how these rules fade away as the ring structure increases and an optimal overlap between p orbitals is no longer possible due to geometrical restrictions. To this end, we study the lowest-lying singlet and triplet states of neutral annulenes with an even number of carbon atoms between four and eighteen. First of all, we analyze these rules from the Hückel molecular orbital method and, afterwards, we perform a geometry optimization of the annulenes with several density functional approximations in order to analyze the effect that the distortions from planarity produce on the aromaticity of annulenes. Finally, we analyze the performance of three density functional approximations that employ different percentages of Hartree-Fock exchange (B3LYP, CAM-B3LYP and M06-2X) and Hartree-Fock. Our results reveal that functionals with a low percentage of Hartree-Fock exchange at long ranges suffer from severe delocalization errors that result in wrong geometrical structures and the overestimation of the aromatic character of annulenes.

All-metal Baird aromaticity

We have proven that Baird's rule can also be applied to a series of all-metal species with both σ- and π-aromaticity.

Singlet and triplet states of the sandwich-type Be2B6 and Be2B7+ clusters. A test for the electron counting rules of aromaticity

The studied complexes exhibit double aromaticity in their triplet states in line with the predictions of Hückel and Baird's rules.

Baird's Rule in Substituted Fulvene Derivatives: An Information-Theoretic Study on Triplet-State Aromaticity and Antiaromaticity

Originated from the cyclic delocalization of electrons resulting in extra stability and instability, aromaticity and antiaromaticity are important chemical concepts whose appreciation and quantification are still much of recent interest in the literature. Employing information-theoretic quantities can provide us with more insights and better understanding about them, as we have previously demonstrated. In this work, we examine the triplet-state aromaticity and antiaromaticity, which are governed by Baird's 4n rule, instead of Hückel's 4n + 2 rule for the singlet state. To this end, we have made use of 4 different aromaticity indexes and 8 information-theoretic quantities, examined a total of 22 substituted fulvene derivatives, and compared the results both in singlet and triplet states. It is found that cross-correlations of these two categories of molecular property descriptors enable us to better understand the nature and propensity of aromaticity and antiaromaticity for the triplet state. Our results have not only demonstrated the existence and validity of Baird's rule but also shown that Hückel's rule and Baird's rule indeed share the same theoretical foundation because with these cross-correlation patterns we are able to distinguish them from each other simultaneously in both singlet and triplet states. Our results should provide new insights into the nature of aromaticity and antiaromaticity in the triplet state and pave the road toward new ways to quantify this pair of important chemical concepts.

Triplet state homoaromaticity: concept, computational validation and experimental relevance

Conjugation through space can give rise to aromaticity in the lowest excited triplet state, with impact for photochemistry.

Cyclic conjugation that occurs through-space and leads to aromatic properties is called homoaromaticity. Here we formulate the homoaromaticity concept for the triplet excited state (T₁) based on Baird's 4n rule and validate it through extensive quantum-chemical calculations on a range of different species (neutral, cationic and anionic). By comparison to well-known ground state homoaromatic molecules we reveal that five of the investigated compounds show strong T₁ homoaromaticity, four show weak homoaromaticity and two are non-aromatic. Two of the compounds have previously been identified as excited state intermediates in photochemical reactions and our calculations indicate that they are also homoaromatic in the first singlet excited state. Homoaromaticity should therefore have broad implications in photochemistry. We further demonstrate this by computational design of a photomechanical “lever” that is powered by relief of homoantiaromatic destabilization in the first singlet excited state.

A new architecture for high spin organics based on Baird's rule of 4n electron triplet aromatics

This work reports triplet aromatic high spin ground states of cyclopentadienyl cation polyads as alternative to high spin polyradicals or polycarbenes.

Recent developments and future prospects of all-metal aromatic compounds

The usefulness of aromaticity/antiaromaticity concepts to foresee structural stability patterns and salient features of the electronic structure of small inorganic and all-metal rings has been put forward. A critical revision of the advances made in the theoretical methods to assess the aromaticity/antiaromaticity of these compounds has also been made. In particular, the performance of local versus non-local indices has been reviewed. Finally, the passivation of these rings has been put forward as a key issue in order to prevent them from collapsing into larger aggregates and to provide them protection against the environment.

The Electronic Structure of the Al3(-) Anion: Is it Aromatic?

Multiconfigurational high-level electronic structure calculations show that the Al3(-) ring-like cluster anion has three close low-lying electronic states of different spin, all of them having strong multiconfigurational character. The aromaticity of the cluster has, therefore, been studied by means of total electron delocalization and normalized multicenter electron delocalization indices evaluated from the multiconfigurational wave functions of each state. The lowest-lying singlet and triplet states are found to be highly aromatic, whereas the next lowest-lying state, the quintet state, has much less, though non-negligible, aromatic character.

The excited state antiaromatic benzene ring: a molecular Mr Hyde?

The antiaromatic character of benzene in its first ππ* excited triplet state (T1) was deduced more than four decades ago by Baird using perturbation molecular orbital (PMO) theory [J. Am. Chem. Soc. 1972, 94, 4941], and since then it has been confirmed through a range of high-level quantum chemical calculations. With focus on benzene we now first review theoretical and computational studies that examine and confirm Baird's rule on reversal in the electron count for aromaticity and antiaromaticity of annulenes in their lowest triplet states as compared to Hückel's rule for the ground state (S0). We also note that the rule according to quantum chemical calculations can be extended to the lowest singlet excited state (S1) of benzene. Importantly, Baird, as well as Aihara [Bull. Chem. Soc. Jpn. 1978, 51, 1788], early put forth that the destabilization and excited state antiaromaticity of the benzene ring should be reflected in its photochemical reactivity, yet, today these conclusions are often overlooked. Thus, in the second part of the article we review photochemical reactions of a series of benzene derivatives that to various extents should stem from the excited state antiaromatic character of the benzene ring. We argue that benzene can be viewed as a molecular "Dr Jekyll and Mr Hyde" with its largely unknown excited state antiaromaticity representing its "Mr Hyde" character. The recognition of the "Jekyll and Hyde" split personality feature of the benzene ring can likely be useful in a range of different areas.

Borazine: spin blocker or not?

Spin-blocker capacity of borazine is investigated formeta-BB,meta-NN andpara-BN structures highlighting the correlation between magnetic properties and aromaticity.

Tunable aromaticity in bicalicenes

By transferring electron charge from cyclopropene to cyclopentadiene rings the aromaticity of bicalicenes may be controlled chemically or electrically.

An efficient generalized polyelectron population analysis in orbital spaces: the hole-expansion methodology

We present relations leading to an efficient generalized population analysis in orbital spaces of usual delocalized molecular orbital wave functions. Besides the calculation of the diagonal elements of the reduced density matrices of any order, one can also calculate efficiently the probabilities (or, in general, the weights) of various occupation schemes of local electronic structures, by using generalized density operators referring to both electrons and electron holes. Within this population analysis, correlated molecular orbital wave functions can be used, and there are no restrictions to the number of the analyzed electrons and electron holes. It is based on the hole-expansion methodology, according to which a given electronic population is expanded in terms involving only electron holes, which as shown, can be calculated very efficiently; usual difficulties arising from the necessity to handle extremely large local determinantal basis sets are avoided, without introducing approximations. Although an emphasis is given for populations in the basis of orthogonal orbital spaces (providing probabilities), the case of nonorthogonal ones is also considered in order to show the connection of the generalized populations and the traditional weights obtained from valence-bond wave functions. Physically meaningful populations can be obtained by using natural orbitals, such as the natural atomic orbitals (NAOs) (orthogonal orbitals) or the pre-NAO's (nonorthogonal orbitals); numerical applications for pyrrole molecule are presented in the basis of these natural orbitals.