The role of the long-range exchange corrections in the description of electron delocalization in aromatic species

Helical polycyclic hydrocarbons with open-shell singlet ground states and ambipolar redox behaviors

Organic π-conjugated polycyclic hydrocarbons (PHs) with an open-shell diradical character are attracting increasing interest due to their promising applications in organic electronics and spintronics. However, most of the open-shell PHs synthesized thus far are based on planar π-conjugated molecules. Herein, we report the synthesis and characterization of two new quinodimethane-embedded expanded helicenes H1 and H2. The helical structures of both molecules were revealed using X-ray crystallographic analysis. It was elucidated in detailed experimental and theoretical studies that they possess an open-shell singlet biradical structure in the ground state and show a small energy gap and amphoteric redox behavior. Both compounds can also be easily oxidized or reduced into relatively stable charged species. The dianions of H1 and H2 exhibit similar electronic structures to the respective isoelectronic structures of their all-benzenoid helical analogues according to NMR measurements and theoretical calculations. Moreover, the structures of the dication and dianion of H2 were identified by X-ray crystallographic analysis, revealing the effect of electron transfer on their backbones and aromaticity. This study thus opens up new avenues for both helical polycyclic π-systems and diradicaloids.

New Perspectives on Delocalization Pathways in Aromatic Molecular Chameleons

This study comprehensively analyzes the magnetically induced current density of polycyclic compounds labeled as "aromatic chameleons" since they can arrange their π-electrons to exhibit aromaticity in both the ground and the lowest triplet state. These compounds comprise benzenoid moieties fused to a central skeleton with 4n π-electrons and traditional magnetic descriptors are biased due to the superposition of local magnetic responses. In the S0 state, our analysis reveals that the molecular constituent fragments preserve their (anti)aromatic features in agreement with two types of resonant structures: one associated with aromatic benzenoids and the other with a central antiaromatic ring. Regarding the T1 state, a global and diatropic ring current is revealed. Our aromaticity study is complemented with advanced electronic and geometric descriptors to consider different aspects of aromaticity, particularly important in the evaluation of excited state aromaticity. Remarkably, these descriptors consistently align with the general features on the main delocalization pathways in polycyclic hydrocarbons consisting of fused 4n π-electron rings. Moreover, our study demonstrates an inverse correlation between the singlet-triplet energy difference and the antiaromatic character of the central ring in S0.

Generalized kekulenes and clarenes as novel families of cycloarenes: structures, stability, and spectroscopic properties

Cycloarenes constitute a captivating class of polycyclic aromatic hydrocarbons with unique structures and properties, but their synthesis represents a challenging task in organic chemistry. Kekulenes and edge-extended kekulenes as classic types of cycloarenes play an important role in the comprehension of π electron distribution, but their sparse molecular diversity considerably limits their further development and application. In this work, we propose two novel classes of cycloarenes, the generalized kekulenes and the clarenes. Using density functional theory, we carry out a comprehensive study of all possible isomers of the generalized kekulenes and clarenes with different sizes. By applying a simple Hückel model, we show that π delocalization plays a crucial role in determining the relative stability of isomers. We also discover that π-π stacking is commonly present in certain larger clarenes and provides a considerable additional stabilization effect, making the corresponding isomers the lowest-energy ones. Among all considered typical looped polyarenes, generalized kekulenes and/or clarenes are revealed to be the energetically most stable forms, suggesting that these novel cycloarenes proposed here would be viable targets for future synthetic work. The simulated 1H NMR spectra and UV-vis absorption spectra provide valuable information about the electronic and optoelectronic properties for the most stable generalized kekulene and clarene species and may support their identification in future synthesis and experimental characterization.

The curious case of the crystalline tri-thorium cluster: cyclic delocalization without aromatic stabilization?

Actinides have been known to form extremely weak homonuclear bonds with their d-type orbitals, and one should therefore expect the superposition of cyclic resonance forms containing such bonds to bring rather marginal aromatic stabilization to the system, if any. It is for this very reason that the discovery of the cyclically delocalized Th3 σ-bonding in the crystalline cluster isolated by Liddle and co-workers has sparked such vigorous discussion on the actual role of molecular aromaticity on the periphery of the periodic table. It has recently been argued that the tri-thorium ring at the heart of the cluster features considerable aromatic stabilization energy comparable to the heterocyclic π-aromatic rings such as thiophene. However, previous investigations involved highly ionized model clusters like Th3Cl64+ or Th310+ in which aromatic stabilization associated with the cyclic delocalization of charge is dramatically exaggerated. In this work we investigate the model tri-thorium clusters at different geometries and ionization states to show that cyclic delocalization of electrons in the isolated crystalline cluster may be associated with rather marginal σ-aromatic stabilization energy thus strongly suggesting its non-aromatic character.

The application of aromaticity and antiaromaticity to reaction mechanisms

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.

Infinitenes as the Most Stable Form of Cycloarenes: The Interplay among π Delocalization, Strain, and π-π Stacking

The recent successful preparation of infinitene has sparked widespread attention due to its aesthetic appeal and synthetic challenge. Spectroscopic measurements and follow-up computational investigations suggest that infinitene holds fundamental significance and potential applications in chiroptics, optoelectronics, asymmetric synthesis, and supramolecular chemistry. However, unlike other looped polyarenes enriched with sizes and shapes, the infinitene molecule seems, so far, the only known example of this fascinating new form of nanocarbons, whose further exploitation would be considerably limited because of the lack of molecular diversity. Here, we introduce a whole new family of generalized infinitenes with different sizes and topologies. Three types of infinitene structures are rationally designed by joining two units of coronene, kekulene, or their extended analogs. The constructed molecules of varying sizes, each with a large number of possible topoisomers, are systematically studied by DFT calculations. Comprehensive analysis using a simple energy decomposition model uncovers that the stability of infinitenes is governed by the interplay among π delocalization, steric strain, and π-π stacking. While the first two factors are crucial to the stability of smaller infinitenes, the latter is the primary stabilizing interaction for larger infinitenes. Most importantly, we show that larger-sized infinitenes are actually the energetically most favorable form among all known looped polyarenes; their substantial thermodynamic stability surpassing that of circulenes, various carbon nanobelts, and kekulene-like macrocycles renders them promising targets for synthesis. The simulated ¹H NMR, UV-vis, and circular dichroism spectra along with optical rotations for the most stable infinitene species may help their identification in future synthetic efforts.

On the JAP Method for the Indirect Determination of Delocalized Currents from Experimental Chemical Shifts

The JAP model (after Jirásek, Anderson, and Peeks) to retrieve global current strengths from experimental ¹ H chemical shifts has been tested with DFT computations. Both global and local tropicities are correctly predicted in most cases and the quantitative agreement is overall fair. An extension of the model is found to give improvement in an exemplary critical case, where the global delocalized current is negligible and the current density map is dominated by local currents.

Magnetic response properties of carbon nano-onions

The magnetic response of a number of double- and triple-layer carbon nano-onions (CNOs) is analyzed by calculating the magnetically induced current density and the induced magnetic field using the pseudo-π model. Qualitatively the same magnetic response was obtained in calculations at the all-electron level. The calculations show that the CNOs exhibit strong net diatropic (paratropic) ring currents when the external magnetic field points perpendicularly to one of the six-membered (five-membered) rings. They are deshielded inside and shielded outside the CNO; the latter dominates for larger CNOs. The magnetic response originates from a combination of spherical paratropic current densities on the inside of each carbon layer and diatropic current densities on the outside of them. The quantitative differences in the aromaticity of the CNOs as compared to single fullerenes are discussed in terms of ring-current strengths. The magnetic response of some of the CNOs is approximately the sum of the magnetic response of the individual layers, whereas deviations are significant for CNOs containing C₈₀. For the largest CNOs, the deviation from the sum of the fullerene contributions is larger, especially when the external magnetic field is perpendicular to a six-membered ring.

Three-Dimensional Fully π-Conjugated Macrocycles: When 3D-Aromatic and When 2D-Aromatic-in-3D?

Several fully π-conjugated macrocycles with puckered or cage-type structures were recently found to exhibit aromatic character according to both experiments and computations. We examine their electronic structures and put them in relation to 3D-aromatic molecules (e.g., closo-boranes) and to 2D-aromatic polycyclic aromatic hydrocarbons. Using qualitative theory combined with quantum chemical calculations, we find that the macrocycles explored hitherto should be described as 2D-aromatic with three-dimensional molecular structures (abbr. 2D-aromatic-in-3D) and not as truly 3D-aromatic. 3D-aromatic molecules have highly symmetric structures (or nearly so), leading to (at least) triply degenerate molecular orbitals, and for tetrahedral or octahedral molecules, an aromatic closed-shell electronic structure with 6n + 2 electrons. Conversely, 2D-aromatic-in-3D structures exhibit aromaticity that results from the fulfillment of Hückel’s 4n + 2 rule for each macrocyclic path, yet their π-electron counts are coincidentally 6n + 2 numbers for macrocycles with three tethers of equal lengths. It is notable that 2D-aromatic-in-3D macrocyclic cages can be aromatic with tethers of different lengths, i.e., with π-electron counts different from 6n + 2, and they are related to naphthalene. Finally, we identify tetrahedral and cubic π-conjugated molecules that fulfill the 6n + 2 rule and exhibit significant electron delocalization. Yet, their properties resemble those of analogous compounds with electron counts that differ from 6n + 2. Thus, despite the fact that these molecules show substantial π-electron delocalization, they cannot be classified as true 3D-aromatics.

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.

A straightforward method to quantify the electron-delocalizing ability of pi-conjugated molecules

Electronic delocalization is essential to the properties of pi-conjugated molecules. We introduce the inter-fragment delocalization index (IFDI) as an easy-to-use computational method for quantifying the electronic delocalization in pi-conjugated oligomers...

Structure, bonding and adaptive aromaticity in rhenium-oxo complexes: a DFT study

The concept of adaptive aromaticity has been extended to a rhenium-oxo complex, introducing a new member into this novel family.

Revival of Hückel Aromatic (Poly)benzenoid Subunits in Triplet State Polycyclic Aromatic Hydrocarbons by Silicon Substitution

By employing density functional theory (DFT) calculations we show that mono- and disilicon substitution in polycyclic aromatic hydrocarbons, having two to four benzene units, quenches their triplet state antiaromaticity by creating Hückel aromatic (poly)benzenoid subunit(s) and weakly antiaromatic, or almost nonaromatic silacycle. Therefore, such systems are predicted to be globally aromatic in both the ground state and the first excited triplet state. Putting the silicon atom(s) into various positions of a hydrocarbon provides an opportunity to tune the singlet-triplet energy gaps. They depend on the global aromaticity degree which, in turn, depends on the type of aromatic carbocyclic subunit(s) and the extent of their aromaticity. On the basis of the set of studied compounds, some preliminary rules on how to regulate the extent of global, semiglobal and local aromaticity are proposed. The results of this work extend the importance of Hückel aromaticity concept to excited triplet states which are usually characterized by the Baird type of (anti)aromaticity.

The Density Functional Theory Account of Interplaying Long-Range Exchange and Dispersion Effects in Supramolecular Assemblies of Aromatic Hydrocarbons with Spin

Aromatic hydrocarbons with fused benzene rings and regular triangular shapes, called n-triangulenes according to the number of rings on one edge, form groundstates with n-1 unpaired spins because of topological reasons. Here, we focus on methodological aspects emerging from the density functional theory (DFT) treatments of dimer models of the n = 2 triangulene (called also phenalenyl), observing that it poses interesting new problems to the issue of long-range corrections. Namely, the interaction comprises simultaneous spincoupling and van der Waals effects, i.e., a technical conjuncture not considered explicitly in the benchmarks calibrating long-range corrections for the DFT account of supramolecular systems. The academic side of considering dimer models for calculations and related analysis is well mirrored in experimental aspects, and synthetic literature revealed many compounds consisting of stacked phenalenyl cores, with intriguing properties, assignable to their long-range spin coupling. Thus, one may speculate that a thorough study assessing the performance of state-of-the-art DFT procedures has relevance for potential applications in spintronics based on organic compounds.

Fine-Tuning of Nonlinear Optical Contrasts of Hexaphyrin-Based Molecular Switches Using Inverse Design

In the search for new nonlinear optical (NLO) switching devices, expanded porphyrins have emerged as ideal candidates thanks to their tunable chemical and photophysical properties. Introducing meso-substituents to these macrocycles is a successful strategy to enhance the NLO contrasts. Despite its potential, the influence of meso-substitution on their structural and geometrical properties has been scarcely investigated. In this work, we pursue to grasp the underlying pivotal concepts for the fine-tuning of the NLO contrasts of hexaphyrin-based molecular switches, with a particular focus on the first hyperpolarizability related to the hyper-Rayleigh scattering (β_HRS). Building further on these concepts, we also aim to develop a rational design protocol. Starting from the (un)substituted hexaphyrins with various π-conjugation topologies and redox states, structure-property relationships are established linking aromaticity, photophysical properties and β_HRS responses. Ultimately, inverse molecular design using the best-first search algorithm is applied on the most favorable switches with the aim to further explore the combinatorial chemical compound space of meso-substituted hexaphyrins in search of high-contrast NLO switches. Two definitions of the figure-of-merit of the switch performance were used as target objectives in the optimization problem. Several meso-substitution patterns and their underlying characteristics are identified, uncovering molecular symmetry and the electronic nature of the substituents as the key players for fine-tuning the β_HRS values and NLO contrasts of hexaphyrin-based switches.

Bonding Character, Electron Delocalization, and Aromaticity of Cyclo[18]Carbon (C18 ) Precursors, C18 -(CO)n (n=6, 4, and 2): Focusing on the Effect of Carbonyl (-CO) Groups

The bonding character, electron delocalization, and aromaticity of the cyclo[18]carbon (C₁₈ ) precursors, C₁₈ -(CO)_n (n=6, 4, and 2), have been studied by combining quantum chemical calculations and various electronic wavefunction analyses with different physical bases. It was found that C₁₈ -(CO)_n (n=6, 4, and 2) molecules exhibit alternating long and short C-C bonds, and have out-of-plane and in-plane dual π systems (π^out and πⁱⁿ ) perpendicular to each other, which are consistent with the relevant characteristics of C₁₈ . However, the presence of carbonyl (-CO) groups significantly reduced the global electron conjugation of C₁₈ -(CO)_n (n=6, 4, and 2) compared to C₁₈ . Specifically, the -CO group largely breaks the extensive delocalization of πⁱⁿ system, and the π^out system is also affected by it but to a much lesser extent; as a consequence, C₁₈ -(CO)_n (n=6, 4, and 2) with larger n shows weaker overall aromaticity. Mostly because of the decreased but still apparent π^out electron delocalization in the C₁₈ -(CO)_n (n=6, 4, and 2), a notable diatropic induced ring current under the action of external magnetic field is observed, demonstrating the clear aromatic characteristic in the molecules. The correlation between C₁₈ -(CO)_n (n=6, 4, and 2) and C₁₈ in terms of the gradual elimination of -CO from the precursors showed that the direct elimination of two CO molecules in C₁₈ -(CO)_n (n=6, 4, and 2) has a synergistic mechanism, but it is kinetically infeasible under normal conditions due to the high energy barrier.

Adaptive aromaticity in 16-valence-electron metallazapentalenes

According to Hückel's and Baird's rules, cyclic species are generally aromatic only either in the lowest singlet state (S₀) or in the lowest-lying triplet ππ* excited state (T₁). Thus, species with aromaticity both in S₀ and T₁ states (termed as adaptive aromaticity) are particularly rare. Herein, we carry out density functional theory (DFT) calculations to examine the aromaticity of 16e metallapentalenes containing heteroatoms (N, O). Interestingly, metallazapentalenes show adaptive aromaticity whereas metalloxapentalenes display nonaromaticity in the S₀ and T₁ states, which is supported by structural, magnetic, and electronic indices. In addition, a series of metallazapentalenes containing strong σ- or π-donor ligands are predicted to achieve adaptive aromaticity. Our findings expand the family of adaptive aromatics significantly, inviting experimental chemists to realize more hetero-metallapentalenes with adaptive aromaticity.

Valence non-Lewis density as an approach to describe and measure aromaticity of organic and inorganic molecules

Based on the linear combination of atomic orbital-molecular orbital by the natural bond orbitals (NBO) theory, the attractive donor-acceptor superposition interaction between filled (Lewis-type) and vacant (non-Lewis-type) orbitals provide a general mechanism for quantal energy lowering. This interaction has a direct impact on the quantity of the second-order stabilization energy. Therefore, the valence non-Lewis density (VNLD) index, the electron density of unoccupied valence nonbonding and antibonding orbitals, is introduced as an approach to describe and measure aromaticity. This index is based on the frontier orbital concept. To investigate the validity of the proposed aromaticity index, we selected several test sets of organic and inorganic molecules such as different ring sizes in cyclic and heterocyclic hydrocarbons, and all-metal and semimetal clusters, and compared our findings with previous aromaticity analysis. According to the results, VNLD values are well correlated and anticipated the order of aromaticity with the formerly introduced criteria. Furthermore, VNLD reveals that the rings with π-sextet electrons localized in a ring are more aromatic than the other rings, thus, it is in line with Clar's rule. Our proposed aromaticity index has advantages such as, easy to obtain from NBO analysis, and does not require reference molecules which made it more applicable for realizing the aromaticity order in many organic and inorganic compounds.

How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring*

Large conjugated rings with persistent currents are novel promising structures in molecular-scale electronics. A six-porphyrin nanoring structure that allegedly sustained an aromatic ring current involving 78π electrons was recently synthesized. We provide here compelling evidence that this molecule is not aromatic, contrary to what was inferred from the analysis of 1 H-NMR data and computational calculations that suffer from large delocalization errors. The main reason behind the absence of an aromatic ring current in these nanorings is the low delocalization in the transition from the porphyrins to the bridging butadiyne linkers, which disrupts the overall conjugated circuit. These results highlight the importance of choosing a suitable computational method to study large conjugated molecules and the appropriate aromaticity descriptors to identify the part of the molecule responsible for the loss of aromaticity.

Magnetic Aromaticity of Cycloporphyrin Nanorings

The ascertainment of magnetic aromaticity is not necessarily straightforward, especially for large and bent systems, such as the cycloporphyrin nanorings recently synthesized by the group of Anderson. Six of these cycloporphyrin nanorings were studied here computationally. Indirect methods, based on nuclear shielding and magnetizabilities, and direct methods, based on standard quantum mechanics, were both used effectively to determine their magnetically induced current strength, which mostly confirmed Anderson’s classification. However, in the case of hexanions, and in particular for cyclohexaporphyrin hexacations, a significant cancellation of delocalized diatropic and paratropic flow occurred, showing that the resultant faint aromatic character was a result of competing aromatic and antiaromatic contributions, as also evidenced by the ipsocentric method. A warning is renewed on the use of isotropic shielding to determine the tropicity of the magnetically induced current.

Nickel(II)-Based Building Blocks with Schiff Base Derivatives: Experimental Insights and DFT Calculations

We have recently reported a series of neutral square planar tridentate Schiff base (L) complexes of the general formula [(L)M(py)], showing relatively high first-order hyperpolarizabilities and NLO redox switching behavior. In the present study, new members of this family of compounds have been prepared with the objective to investigate their potential as building blocks in the on-demand construction of D-π-A push–pull systems. Namely, ternary nickel(II) building blocks of general formula [(L^A/D)Ni(4-pyX)] (4–7), where L^A/D stands for an electron accepting or donating dianionic O,N,O-tridentate Schiff base ligand resulting from the monocondensation of 2-aminophenol or its 4-substituted nitro derivative and β-diketones R-C(=O)CH₂C(=O)CH₃ (R = methyl, anisyl, ferrocenyl), and 4-pyX is 4-iodopyridine or 4-ethynylpyridine, were synthesized and isolated in 60–78% yields. Unexpectedly, the Sonogashira cross-coupling reaction between the 4-iodopyridine derivative 6 and 4-ethynylpyridine led to the formation of the bis(4-pyridyl) acetylene bridged centrosymmetric dimer [{(L^D)Ni}₂(µ²-py-C≡C-py)] (8). Complexes 4–8 were characterized by elemental analysis, FT-IR and NMR spectroscopy, single crystal X-ray diffraction and computational methods. In each compound, the four-coordinate Ni(II) metal ion adopts a square planar geometry with two nitrogen and two oxygen atoms as donors occupying trans positions. In 8, the Ni…Ni separation is of 13.62(14) Å. Experimental results were proved and explained theoretically exploiting Density Functional Theory calculations.

Singlet/Triplet State Anti/Aromaticity of CyclopentadienylCation: Sensitivity to Substituent Effect

It is well known that singlet state aromaticity is quite insensitive to substituent effects, in the case of monosubstitution. In this work, we use density functional theory (DFT) calculations to examine the sensitivity of triplet state aromaticity to substituent effects. For this purpose, we chose the singlet state antiaromatic cyclopentadienyl cation, antiaromaticity of which reverses to triplet state aromaticity, conforming to Baird’s rule. The extent of (anti)aromaticity was evaluated by using structural (HOMA), magnetic (NICS), energetic (ISE), and electronic (EDDBp) criteria. We find that the extent of triplet state aromaticity of monosubstituted cyclopentadienyl cations is weaker than the singlet state aromaticity of benzene and is, thus, slightly more sensitive to substituent effects. As an addition to the existing literature data, we also discuss substituent effects on singlet state antiaromaticity of cyclopentadienyl cation.

Magnetically Induced Ring-Current Strengths of Planar and Nonplanar Molecules: New Insights from the Pseudo-π Model

The pseudo-π model yields current densities and induced magnetic fields that mimic the π-component, allowing investigations of large molecular structures, whether they are planar or not, at a low computational cost but with high accuracy. Herein the π-contribution to the magnetically induced current densities and induced magnetic fields of large planar molecules and nonplanar molecules (such as [10]cyclophenacene and chiral toroidal nanotubes C₂₀₁₆ and C₂₁₉₆) were computed using the pseudo-π model with the gauge-including magnetically induced currents method. Additionally, we provide a way to determine the π-component of the ring-current strengths, which can be used for assessing the aromatic character of large carbon molecules.

Aromaticity of ortho and meta 8-Cycloparaphenylene and Their Dications: Induced Magnetic Field Analysis with Localized and Delocalized Orbitals in Strained Nanohoops

Dications of cycloparaphenyles ([n]CPPs) are known to exhibit in-plane global aromaticity, contained in a nanobelt structure. Recently synthesized ortho and meta isomers of [n]CPPs break the radial symmetry of π structure incorporating perpendicular oriented π orbitals. Herein we set to explore the aromaticity of neutral and dicationic ortho and meta isomers of [8]CPP by dissecting the induced magnetic field to contributions of the twofold radial/perpendicular π system using delocalized canonical molecular orbitals (CMO), and introducing the natural localized molecular orbitals (NLMO) analysis with DFT methods. The dications sustain a reduced global aromatic character of the radial π system under a perpendicular orientation of the external field which declines from ortho to meta isomer and reinforces local aromaticity of ortho ring while it destroys aromaticity of meta ring. Aromaticity variations are determined by symmetry governed rotational excitations of frontier π orbitals. The parallel orientation reveals a substantial reduction of local aromaticity verified with NICS_π analysis and electron delocalization indices.

Antiaromaticity-aromaticity transition of cyclo[16]carbon upon metal encapsulation

In contrast to aromatic compounds with particular stability, antiaromatic compounds are usually less stable due to their high reactivity and unfavorable formation energies. Cyclo[16]carbon (C₁₆) is a carbon ring molecule with a dual antiaromatic character. In this study, we demonstrate that C₁₆ can be transformed into highly aromatic molecules upon metal encapsulation. The geometrical characteristics, electronic properties and thermodynamic stability of MC₁₆ compounds (M = Ca, Sc, Ti, V, Ce, U) are fully investigated from a theoretical perspective. Based on natural population analysis, atom-in-molecules theory and localized molecular orbital analysis, the nature of the metal-carbon interaction in the MC₁₆ compounds is investigated. It has been proved that the bonding between Ca and C₁₆ corresponds to a typical ionic interaction, while other metal atoms form polar covalent bonds with C₁₆. By analyzing the frontier molecular orbitals and magnetic response of MC₁₆, we have found that all the encapsulated metal atoms donate two electrons to the in-plane π orbitals via either electron transfer or orbital hybridization, which makes the in-plane π orbitals completely satisfy the 4n + 2 (n = 4) Hückel aromaticity rule. The U atom formally transfers four electrons to the carbon ring in total, two to the in-plane π orbitals and two to the out-of-plane π orbitals, which results in the remarkable dual aromaticity feature of UC₁₆. The transformation of aromaticity can be utilized to develop new strategies for the synthesis of novel carbon ring molecules.

Triplet State Baird Aromaticity in Macrocycles: Scope, Limitations, and Complications

The aromaticity of cyclic 4nπ-electron molecules in their first ππ* triplet state (T1), labeled Baird aromaticity, has gained growing attention in the past decade. Here we explore computationally the limitations of T1 state Baird aromaticity in macrocyclic compounds, [n]CM's, which are cyclic oligomers of four different monocycles (M = p-phenylene (PP), 2,5-linked furan (FU), 1,4-linked cyclohexa-1,3-diene (CHD), and 1,4-linked cyclopentadiene (CPD)). We strive for conclusions that are general for various DFT functionals, although for macrocycles with up to 20 π-electrons in their main conjugation paths we find that for their T1 states single-point energies at both canonical UCCSD(T) and approximative DLPNO-UCCSD(T) levels are lowest when based on UB3LYP over UM06-2X and UCAM-B3LYP geometries. This finding is in contrast to what has earlier been observed for the electronic ground state of expanded porphyrins. Yet, irrespective of functional, macrocycles with 2,5-linked furans ([n]CFU's) retain Baird aromaticity until larger n than those composed of the other three monocycles. Also, when based on geometric, electronic and energetic aspects of aromaticity, a 3[n]CFU with a specific n is more strongly Baird-aromatic than the analogous 3[n]CPP while the magnetic indices tell the opposite. To construct large T1 state Baird-aromatic [n]CM's, the design should be such that the T1 state Baird aromaticity of the macrocyclic perimeter dominates over a situation with local closed-shell Hückel aromaticity of one or a few monocycles and semilocalized triplet diradical character. Monomers with lower Hückel aromaticity in S0 than benzene (e.g., furan) that do not impose steric congestion are preferred. Structural confinement imposed by, e.g., methylene bridges is also an approach to larger Baird-aromatic macrocycles. Finally, by using the Zilberg-Haas description of T1 state aromaticity, we reveal the analogy to the Hückel aromaticity of the corresponding closed-shell dications yet observe stronger Hückel aromaticity in the macrocyclic dications than Baird aromaticity in the T1 states of the neutral macrocycles.

Aromaticity Survival in Hydrofullerenes: The Case of C66 H4 with Its π-Aromatic Circuits

The isolated-pentagon rule (IPR) is a determining structural feature that accounts for hollow fullerene stabilization and properties related to C_n (n≥60) cages. The recent characterization of an unprecedented non-IPR hydrofullerene, C_2v C₆₆ H₄ , bearing two heptagons with adjacent fused-pentagon motifs, largely dismisses this feature. Herein, employing DFT calculations, the ¹³ C NMR spectroscopy and aromatic behavior of C_2v C₆₆ H₄ are explored. The results show the presence of three π-aromatic circuits at the bottom boat section of C₆₆ H₄ , indicating the unique features of this hydrofullerene in comparison to those of pristine C₆₀ . In addition, under specific orientations of the external field, certain π-aromatic circuits are enabled, resulting in a more aromatic fullerene than that of C₆₀ , but lower than that of the spherical aromatic C₆₀ ^6- fulleride. Notably, under a field aligned with the saturated carbon atoms, nonaromatic characteristics are exposed. This reveals that spherical-like cages can involve a complex magnetic response that heavily depends on the orientation of the applied field.

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.

Achieving Adaptive Aromaticity in Cyclo[10]carbon by Screening Cyclo[n]carbon (n=8-24)

Discovery of species with adaptive aromaticity (being aromatic in both the lowest singlet and triplet states) is particularly challenging as cyclic species are generally aromatic either in the ground state or in the excited state only, according to Hückel's and Baird's rules. Inspired by the recent realization of cyclo[18]carbon, here we demonstrate that cyclo[10]carbon possesses adaptive aromaticity by screening cyclo[n]carbon (n=8-24), which is supported by nucleus-independent chemical shift (NICS), anisotropy of the current-induced density (ACID), π contribution of electron localization function (ELF_π ) and electron density of delocalized bonds (EDDB) analyses. Further study reveals that the lowest triplet state of cyclo[10]carbon is formed by in-plane ππ* excitation. Thus, the major contribution to the aromaticity from out-of-plane π molecular orbitals does not change significantly in the lowest singlet state. Our findings highlight a crucial role of out-of-plane π orbitals in maintaining aromaticity for both the lowest singlet and triplet states as well as the aromaticity dependence on the number of the carbon in cyclo[n]carbon.

Reversal of Clar's Aromatic-Sextet Rule in Ultrashort Single-End-Capped [5,5] Carbon Nanotubes

The three-fold HOMO-LUMO gap oscillation, typical of finite length armchair carbon nanotubes (CNT), has a major effect on the magnetic response of ultrashort, single-end-capped [5,5] carbon nanotubes to a perturbing magnetic field parallel to the main symmetry axis. For the CNT's containing 40, 70, and 100 carbon atoms, for which 100 % of the C=C double bonds can be grouped into aromatic-sextets, i. e., fully or complete Clar networks, large paratropic (antiaromatic) global circulations around the cylindrical axis are predicted at the DFT level of calculation. Local and semi-global diatropic (aromatic) currents of strengths not larger than that of the benzene molecule are determined for a perpendicular perturbing magnetic field. CNTs of intermediate lengths do not display this enhanced antiaromatic response. The paratropic current flow clearly shows that these complete Clar networks can be viewed as stacked cycloparaphenylene belts, each providing a double 4 n annulene circuit as a consequence of the quinoidal resonance structure that results from their closure. Paradoxically, the fully aromatic Clar structure itself is responsible for the enhanced global antiaromaticity.

Are Hetero-metallapentalenes Aromatic or Not? A DFT Investigation

Aromaticity is one of the most basic concepts in organic chemistry. The planar Möbius aromatic metallapentalynes and metallapentalenes have attracted considerable attention in the past few years. However, the aromaticity of metallapentalenes containing heteroatoms (such as B, N, and O), termed as hetero-metallapentalenes, is rarely studied. Herein, the stability and aromaticity of a series of hetero-metallapentalenes are theoretically investigated. The results reveal lower aromaticity in metallaborapentalene, comparable aromaticity in metallazapentalene, and nonaromaticity in metalloxapentalene relative to that of metallapentalene. Moreover, the effect of Lewis bases on the aromaticity and stability of metallaborapentalene is discussed. These results provide useful information for experimental chemists to realize more hetero-metallapentalenes.

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.

Induced magnetic field in sp-hybridized carbon rings: analysis of double aromaticity and antiaromaticity in cyclo[2N]carbon allotropes

The induced magnetic field of C2N (N = 3-14) carbon rings was dissected to contributions from out-of-plane and in-plane π orbitals revealing two concurrent long range shielding or deshielding cones as a manifestation of the dual aromatic and antiaromatic character of C4n+2 and of C4n rings respectively. Aromaticity based on the magnetic criterion was evaluated with regard to the bonding pattern and geometrical characteristics that elucidate the influence of bond length and bond angle alteration on out-of-plane and in-plane magnetic responses. Ground state polyynic geometries of C4n+2 rings exhibit comparable shielding cones to annulenes, decreasing the magnetic response with regard to the ring size and similar πout and πin diatropicity. Transition state cumulenic rings display increased aromaticity expressed by a very strong constant magnetic response and augmented πout diatropicity with regard to πin. The variations of the induced magnetic field are explained on the basis of frontier orbital interactions through rotational excitations, which enable further rationalization of the aromatic/antiaromatic behavior.

Can Density Functional Theory Be Trusted for High-Order Electric Properties? The Case of Hydrogen-Bonded Complexes

This work reports on an extensive assessment of the performance of a wide palette of density functional approximations in predicting the (high-order) electric properties of hydrogen-bonded complexes. To this end, we compute the electronic and vibrational contributions to the electric polarizability and the first and second hyperpolarizabilities, using the CCSD(T)/aug-cc-pVTZ level of theory as reference. For all the studied properties, the average absolute errors below 20% can only be obtained using the CAM-B3LYP functional, while LC-BLYP and MN15 are shown to be only slightly less accurate (average absolute errors not exceeding 30%). Among Minnesota density functionals, i.e., M06, M06-2X, and MN15, we only recommend the latter one, which quite accurately predicts the electronic and vibrational (hyper)polarizabilities. We also analyze the optimal tuning of the range-separation parameter μ for the LC-BLYP functional, finding that this approach does not bring any systematic improvement in the predictions of electronic and vibrational (hyper)polarizabilities and the accuracy of computed properties is largely system-dependent. Finally, we report huge errors in predicting the vibrational second hyperpolarizability by ωB97X, M06, and M06-2X functionals. Based on the explicit evaluation of anharmonic terms contributing to the second hyperpolarizability, this failure is traced down to a poor determination of third- and fourth-order energy derivatives with respect to normal modes. These results reveal serious flaws of some density functional approximations and suggest caution in selecting the appropriate functional to calculate not only electronic and vibrational (hyper)polarizabilities but also other molecular properties that contain vibrational anharmonic contributions.

Electron Delocalization in Planar Metallacycles: Hückel or Möbius Aromatic?

In this work the relationship between the formal number of π-electrons, d-orbital conjugation topology, π-electron delocalization and aromaticity in d-block metallacycles is investigated in the context of recent findings concerning the correlation of π-HOMO topology and the magnetic aromaticity indices in these species. It is demonstrated that for π-electron rich d-metallacycles the direct link between aromaticity, the number of π-electrons and the frontier π-orbital topology does not strictly hold and for such systems it is very difficult to unambiguously associate their aromaticity with the "4n+2" (Hückel) and "4n" (Möbius) rules. It is also shown that the recently proposed electron density of delocalized bonds (EDDB) method can successfully be used not only to quantify and visualize aromaticity in such difficult cases, but also - in contrast to magnetic aromaticity descriptors - to provide a great deal of information on the real role of d-orbitals in metallacycles without the ambiguity of bookkeeping of electrons in the π-subsystem of the molecular ring. Interestingly, some of the metallacycles studied cannot be classified exclusively as Hückel or Möbius because they have a hybrid Hückel-Möbius or even quasi-aromatic nature.

Second-order nonlinear optical properties of Stenhouse photoswitches: insights from density functional theory

We report the first investigation of the second-order nonlinear optical (NLO) properties of donor-acceptor Stenhouse adducts (DASAs), an emerging class of colored photochromes that undergo photoswitching with visible light to a colorless form. By using time-dependent density functional theory, we provide insights into the relationships linking the nature of the chemical substituents to the amplitude and contrasts of the NLO response. Solvent and frequency dispersion effects are also analyzed. The calculations predict that DASAs behave as high contrast NLO switches, a finding that extends their potential applications to photo-responsive NLO materials and devices.

Aromaticity of acenes: the model of migrating π-circuits

In this work we extend the concept of migrating Clar's sextets to explain local aromaticity trends in linear acenes predicted by theoretical calculations and experimental data. To assess the link between resonance and reactivity and to rationalize the constant-height AFM image of pentacene we used the electron density of delocalized bonds and other functions of the one-electron density from conceptual density functional theory. The presented results provide evidence for migration of Clar's π-sextets and larger circuits in these systems, and clearly show that the link between the theoretical concept of aromaticity and the real electronic structure entails the separation of intra- and inter-ring resonance effects, which in the case of [n]acenes (n = 3, 4, 5) comes down to solving a system of simple linear equations.