Consequences of Curvature on Induced Magnetic Field: The Case of Helicenes

1H and 13C NMR spectra of infinitene and the ring current effect of the aromatic molecule

The spatial magnetic properties (through-space NMR shieldings-TSNMRSs-actually the ring current effect in 1H NMR spectroscopy) of the recently synthesized infinitene (the helically twisted [12]circulene) have been calculated using the GIAO perturbation method employing the nucleus-independent chemical shift (NICS) concept and visualized as iso-chemical-shielding surfaces (ICSS) of various size and direction. Both 1H and 13C chemical shifts of infinitene and the aromaticity of this esthetically very appealing molecule have been studied subject to the ring current effect thus obtained. This spatial magnetic response property of TSNMRSs dominates the different magnitude of 1H and 13C chemical shifts, especially in the cross-over section of infinitene, which is unequivocally classified as an aromatic molecule based on the deshielding belt of its ring current effect. Differences in aromaticity of infinitene compared with isolated benzene can also be qualified and quantified on the magnetic criterion.

Analysis of bonding motifs in unusual molecules II: infinitene

The bonding structures of infinitene, the Chemical and Engineering News 2021 Molecule of the Year, is studied by means of oriented quasi-atomic orbitals (QUAOs) to assess the degree of aromaticity within the molecule. It is found that the angularity introduced into infinitene when it takes on the helical shape of the infinity symbol has a profound effect on bond order, delocalization of bonding interactions, and the aromatic character of the system. In kekulene, a planar isomer of infinitene, the bonding analysis shows fluctuations of pocketed delocalization of bonding interactions in π-sextets associated with Clar's rule. Conversely, much smaller fluctuations are observed between the adjacent rings of infinitene. The observations drawn from the quasi-atomic bonding analysis support the idea that there is aromatic character across the entire infinitene molecule, not just localized around individual rings as in kekulene.

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.

Aromaticity in Semi-Condensed Figure-Eight Molecules

Electron delocalization and aromaticity was comparatively evaluated in recently synthesized figure-eight molecules made of two condensed U-shaped polycyclic aromatic hydrocarbon moieties connected either by two single bonds or by two para-phenylene groups. The selected examples include molecules that incorporate eight-membered and sixteen-membered rings, as well as a doubly [5]helicene-bridged (1,4)cyclophane. We probe whether some electron delocalization could occur through the stereogenic single bonds in these molecules: Is aromaticity purely (semi-)local, or possibly also global in these molecules? It was concluded that the situation can go from a purely (semi-)local character when the dihedral angle at the connecting single bonds is large, such as in biphenyl, to a predominantly (semi-)local character with a minor global contribution when the dihedral angle is small, such as in the para-phenylene connectors of the [5] helicene-bridged cyclophane.

Helicene Aromaticity Deviates from the Clar Rule-On the Electronic Dissimilarity of Large Isomeric Fibonacenes

This combined experimental and theoretical study illustrates the profound consequences of non-planarity on the electronic properties of polycyclic arenes. Three isomeric [10]fibonacene tetraesters were synthesized through a robust and regiocontrolled Perkin/Mallory approach: a nearly planar [10]phenacene derivative, a moderately twisted [10]semicircle derivative, and a 3D non-planar [10]helicene derivative. The photophysical properties of the 3D [10]helicene isomer were found to be dramatically different from the comparable ones of the [10]phenacene and [10]semicircle isomers. The aromatic properties of the [10]phenacene and [10]semicircle isomers conform well with their predictive Kekulé and Clar analyses, but the [10]helicene isomer deviates from these general topological rules, which appears to be a general phenomenon for [n]fibonacenes with n≥9.

Understanding Aromaticity in [5]Helicene-Bridged Cyclophanes: A Comprehensive Study

This study explores the aromaticity of doubly [5]helicene-bridged (1,4)cyclophane and triply [5]helicene-bridged (1,3,5)cyclophane via calculations of the magnetic response and of electronic aromaticity indices. The primary objective is to assess the π-electron delocalization to determine whether they sustain global ring currents associated with π aromaticity. The molecules show local ring currents in the presence of an external magnetic field. The ring currents flow diatropically in the stacked six-membered rings and in the helicene arms. However, these π currents are not interconnected due to the discontinuity of the π delocalization at the C-C single bonds connecting the central six-membered rings to the helicene arms. Electronic indices suggest that the helicene-arm systems have significantly smaller electron delocalization than benzene. The reduction in the delocalization does not compromise their ability to exhibit ring currents in the presence of an external magnetic field. The analysis provides further evidence that the magnetic criteria yield a different degree of aromaticity for the helicene arms than obtained in the calculation of the electronic aromaticity indices. However, both approaches confirm that the studied molecules are not globally aromatic.

Planar pentacoordinate s-block metals

The presence of a delocalized π-bond is often considered an essential criterion for achieving planar hypercoordination. Herein, we show that σ-delocalization could be sufficient to make the planar configuration the most stable isomer in a series of planar pentacoordinate s-block metals. High-level ab initio computations reveal that the global minimum of a series of interalkali and interalkali-alkaline earth clusters (LiNa5, Li5Mg+, Na5Mg+, K5Ca+, CaRb5+, Rb5Sr+, and SrCs5+) adopts a singlet D5h structure with a planar pentacoordinate lithium or alkaline earth metal (AE = Mg, Ca, Sr). These clusters are unusual combinations to stabilize a planar pentacoordinate atom, as all their constituents are electropositive. Despite the absence of π-electrons, Hückel's rule is fulfilled by the six σ-electrons. Furthermore, the systems exhibit a diatropic ring current in response to an external magnetic field and a strong magnetic shielding, so they might be classified as σ-aromatic. Therefore, multicenter σ-bonds and the resulting σ-delocalization stabilize these clusters, even though they lack π-aromaticity.

The Topology of Molecules with Twelve Fused Phenyl Rings ([12]Circulenes): Rings, Infinitenes, and Möbius Infinitenes

Following the recent preparation of infinitene (J. Am. Chem. Soc. 2022, 144, 862-871), a computational (ωB97XD/6-311G(d)) exploration of 42 isomeric compounds with 12 fused phenyl rings identified structures with linking number of zero (ring, saddle, and ribbon shapes), two (infinitene-like shape), and one (Möbius infinitene shape) is reported. An infinitene isomer composed of two [5]helicene fragments connected to two stacked phenyl rings and a Möbius infinitene isomer are identified that are more stable than the known infinitene. The energies of the structures are examined by assessing their macrocyclization (strain) energies, π-stacking, and possible aromaticity. Examples of fused phenyl molecules with linking numbers of 3, 4, 5, and 6 are shown, indicating the potential topological range that these molecules can possess.

On the antiaromatic-aromatic-antiaromatic transition of the stacked cyclobutadiene dimer

We have studied the changes in the aromatic nature of two cyclobutadiene (C₄H₄) molecules on decreasing the intermolecular distance and approaching the cubane structure in a face-to-face fashion. The analysis based on the calculations of the magnetically induced current density and the induced magnetic field shows that the aromaticity of the two C₄H₄ rings changes from a strongly antiaromatic character at long distances to an aromatic transition state of stacked C₄H₄ rings at intermediate internuclear distances when approaching the antiaromatic state of cubane.

Infinitene as two fused helicoidal trails of fused rings: evaluation of the magnetic behavior of [12]infinitene and anionic species displaying global aromaticity and antiaromaticity

The unique formation of an infinity-shaped carbon backbone made exclusively from fused benzene rings has recently been achieved. The structure of [12]infinitene can be viewed as two fused [6]helicene structures with a central crossover section, depicting a global aromatic behavior along with the overall structure, with deshielding regions along both helicoidal axes. In addition, the ¹³C-NMR characteristics are discussed. The formation of a cumulative region involving the shielding regions from the aromatic rings is depicted along with the overall aesthetically pleasant structural backbone, which is enhanced at the crossover section. For the evaluated dianionic counterpart, the structure shows a deshielding region above the fused-ring trail and a helicoidal shielding region, ascribed to a global antiaromatic counterpart. The aromaticity is recovered and enhanced at the tetranionic state. Thus, the neutral and tetranionic states are able to build up a long-ranged shielding region, given by the global aromatic behavior, with an enhanced shielding region at the center of the crossover section displaying π-π stacked rings.

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.

Core-electron contributions to the molecular magnetic response

Orbital contributions to the magnetic response depend on the method used to compute them. Here, we show that dissecting nuclear magnetic shielding tensors using natural localized molecular orbitals (NLMOs) leads to anomalous core contributions. The arbitrariness of the assignment might significantly affect the interpretation of the magnetic response of nonplanar molecules such as C₆₀ or [14]helicene and the assessment of their aromatic character. We solve this problem by computing the core- and σ-components of the induced magnetic field (and NICS) and the magnetically induced current density by removing the valence electrons (RVE). We estimate the core contributions to the magnetic response by performing calculations on the corresponding highly charged molecules, such as C₆H₆³⁰⁺ for benzene, using gauge-including atomic orbitals and canonical molecular orbitals (CMOs). The orbital contributions to nuclear magnetic shielding tensors are usually estimated by employing a natural chemical shielding (NCS) analysis in NLMO or CMO bases. The RVE approach shows that the core contribution to the magnetic response is small and localized at the nuclei, contrary to what NCS calculations suggest. This may lead to a completely incorrect interpretation of the magnetic σ-orbital response of nonplanar structures, which may play a major role in the overall magnetic shielding of the system. The RVE approach is thus a simple and inexpensive way to determine the magnetic response of the core- and σ-electrons.

Non-intersecting ring currents in [12]infinitene

The aromaticity of the newly synthesized [12]infinitene is addressed via analysis of the magnetically induced current density and the induced magnetic field. Our calculations reveal that [12]infinitene responds to an external magnetic field by creating two current-density pathways that flow diatropically along the edges of the molecule. The current-density pathways do not intersect. The entire structure is completely shielded suggesting that the infinitene molecule is aromatic, contrary to what the Möbius rule for twisted annulene structures predicts. We also studied the dication of [12]infinitene, which sustains two paratropic ring currents flowing along the edges. The space between the stacked rings at the crossing point is shorter for the dication as compared to the neutral molecule. Hence, a strong through-space current density appears at the crossing point of π-π stacked rings.

Disclosure of Ground-State Zimmerman-Möbius Aromaticity in the Radical Anion of [6]Helicene and Evidence for 4π Periodic Aromatic Ring Currents in a Molecular "Metallic" Möbius Strip

In 1966, Zimmerman proposed a type of Möbius aromaticity that involves through-space electron delocalization; it has since been widely applied to explain reactivity in pericyclic reactions, but is considered to be limited to transition-state structures. Although the easily accessible hexahelicene radical anion has been known for more than half a century, it was overlooked that it exhibits a ground-state minimum and robust Zimmerman-Möbius aromaticity in its central noose-like opening, becoming, hence, the oldest existing Möbius aromatic system and with smallest Möbius cycle known. Despite its overall aromatic stabilization energy of 13.6 kcal mol-1 (at B3LYP/6-311+G**), the radical also features a strong, globally induced paramagnetic ring current along its outer edge. Exclusive global paramagnetic currents can also be found in other fully delocalized radical anions of 4N+2 π-electron aromatic polycyclic benzenoid hydrocarbons (PAH), thus questioning the established magnetic criterion of antiaromaticity. As an example of a PAH with nontrivial topology, we studied a novel Möbius[16]cyclacene that has a non-orientable surface manifold and a stable closed-shell singlet ground state at several density functional theory levels. Its metallic monoanion radical (0.0095 eV band gap at HSE06/6-31G* level) is also wave-function stable and displays an unusual 4π-periodic, magnetically induced ring current (reminiscent of the transformation behaviour of spinors under spatial rotation), thus indicating the existence of a new, Hückel-rule-evading type of aromaticity.

Visualizing electron delocalization in contorted polycyclic aromatic hydrocarbons

Electron delocalization in contorted polycyclic aromatic hydrocarbon (PAH) molecules was examined through 3D isotropic magnetic shielding (IMS) contour maps built around the molecules using pseudo-van der Waals surfaces. The resulting maps of electron delocalization provided an intuitive, yet detailed and quantitative evaluation of the aromatic, non aromatic, and antiaromatic character of the local and global conjugated cyclic circuits distributed over the molecules. An attractive pictural feature of the 3D IMS contour maps is that they are reminiscent of the Clar π-sextet model of aromaticity. The difference in delocalization patterns between the two faces of the electron circuits in contorted PAHs was clearly visualized. For π-extended contorted PAHs, some splits of the π system resulted in recognizable patterns typical of smaller PAHs. The differences between the delocalization patterns of diastereomeric chiral PAHs could also be visualized. Mapping IMS on pseudo-van der Waals surfaces around contorted PAHs allowed visualization of their superimposed preferred circuits for electron delocalization and hence their local and global aromaticity patterns.

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.

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.

Program Package for the Calculation of Origin-Independent Electron Current Density and Derived Magnetic Properties in Molecular Systems

We present SYSMOIC, a program package for the calculation of the origin-independent current density induced at first order by an external magnetic field in planar and nonplanar molecular systems. Origin independence is obtained adopting the continuous transformation of the origin of the current density method, implemented at both density functional theory (DFT) and Hartree-Fock (HF) levels. Expansion coefficients for perturbed and unperturbed molecular orbitals, over basis sets containing up to m-type Gaussian functions, can be calculated by the package itself or obtained from a Gaussian calculation. A number of different functionalities presented so far in the literature that are connected to the induced current, such as current density maps for any orientation of the inducing magnetic field, net bond current strengths, stagnation graphs, magnetic shielding densities, vorticities, and anisotropies, are now made available all together in a single multiplatform package installation.

Delocalization in Substituted Benzene Dications: A Magnetic Point of View

In this work, the induced magnetic field is analyzed for a series of substituted benzenes dications with formula C6R62+ (R=I, At, SeH, SeCH3, TeH, TeCH3), presumably exhibiting concentric aromaticity. Previous studies concluded that in the carbon skeleton, just π-electrons are delocalized. However, our results support that both the σ- and π-electrons are delocalized in the carbon skeleton, combined with a σ-delocalization in the external ring. The role of the relativistic effects in these dications is discussed in detail.

Calculation of magnetic response properties of tetrazines

Magnetic response properties of 1,2,3,5-tetrazine derivatives including the newly synthesized 4,6-diphenyl-1,2,3,5-tetrazine have been studied computationally at the density functional theory (DFT) level. Calculations of magnetically induced current densities and induced magnetic fields show that the unsubstituted 1,2,3,5-tetrazine is almost as aromatic as benzene. Separating the magnetic shielding functions into molecular orbital components provided additional insights into the magnetic response. The aromatic character estimated from magnetically induced current densities and induced magnetic fields shows that NICS^π_zz(0) values and ring-current strengths yield about the same degree of aromaticity, whereas NICS_zz(0) and NICS_zz(1) values are contaminated by σ electron contributions. The studied 1,2,3,5-tetrazine derivatives are less aromatic than the unsubstituted one. Calculations of magnetic response properties of 4,6-diphenyl-1,2,3,5-tetrazine showed that it is the least aromatic among the studied molecules according to the ring-current criterion, while 4,6-[1,2,3,5]-ditetrazinyl-1,2,3,5-tetrazine is as aromatic as 4,6-dimethyl-1,2,3,5-tetrazine and slightly less aromatic than the unsubstituted 1,2,3,5-tetrazine.

Magnetic response properties of 1,2,3,5-tetrazine derivatives including the newly synthesized 4,6-diphenyl-1,2,3,5-tetrazine have been studied computationally at the density functional theory level.