Assessment of Ring Current Models for Monocycles

Aromaticity of six-membered nitro energetic compounds through molecular electrostatic potential, magnetic, electronic delocalization and reactivity-based indices

The electron density depletion associated with π-hole at the ring center typical of energetic compounds was clearly revealed by the molecular electrostatic potential (ESP). In addition, the spatial arrangement of NO2 groups appears to affect the ESP value in the ring center, and therefore sensitivity to detonation. Indeed, for monocyclic nitrobenzene compounds with the same number of NO2 groups, the ESP value in the ring center decreases as the NO2 groups are more closely spaced. As expected, the central rings become less aromatic as NO2 groups are added. The MCI, PDI, PLR, NICSzz(1), FLU indices are all strongly correlated with the ESP values observed in the ring center of the set of nitrobenzenes. Aromaticity indices based on electron delocalization criteria appear to be very sensitive to small variations in aromaticity. Among magnetic-based indices, only NICSzz(1) is capable to predict small changes in aromaticity. The PLR index derived from conceptual DFT is quite relevant for predicting small variations in aromaticity. According to our results, the most suitable aromaticity index is not based on a single criterion, and that selecting it is more subtle. Therefore, it is important to combine information from several criteria to obtain a more complete description of the aromaticity of the studied compounds.

Disentangling global and local ring currents

Magnetic field-induced ring currents in aromatic and antiaromatic molecules cause characteristic shielding and deshielding effects in the molecules' NMR spectra. However, it is difficult to analyze (anti)aromaticity directly from experimental NMR data if a molecule has multiple ring current pathways. Here we present a method for using the Biot-Savart law to deconvolute the contributions of different ring currents to the experimental NMR spectra of polycyclic compounds. This method accurately quantifies local and global ring current susceptibilities in porphyrin nanorings, as well as in a bicyclic dithienothiophene-bridged [34]octaphyrin. There is excellent agreement between ring current susceptibilities derived from both experimental and computationally-predicted chemical shifts, and with ring currents calculated by the GIMIC method. Our method can be applied to any polycyclic system, with any number of ring currents, provided that appropriate NMR data are available.

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.

Correspondence on "How Aromatic Are Molecular Nanorings? The Case of a Six-Porphyrin Nanoring"

A recent Research Article in this journal by Matito and co-workers claimed that none of the oxidation states of a butadiyne-linked six-porphyrin nanoring exhibit global aromaticity or antiaromaticity. Here we show that this conclusion is incorrect. Experimental data from NMR spectroscopy for a whole family of nanorings provide strong evidence for global ring currents. The NMR data reveal these ring currents directly, without needing analysis by density functional theory (DFT). Furthermore, DFT calculations reproduce the experimental results when a suitable functional is used.

Integration of global ring currents using the Ampère-Maxwell law

Magnetically induced ring currents are calculated from the magnetic shielding tensor by employing the Ampère-Maxwell law. The feasibility of the method is demonstrated by integrating the zz component of the shielding tensor along the symmetry axis of highly symmetric ring-shaped aromatic, antiaromatic and nonaromatic molecules. The calculated ring-current strengths agree perfectly with the ones obtained by integrating the current-density flux passing through a plane cutting half the molecular ring. The method can be used in combination with all electronic structure codes capable of calculating nuclear magnetic resonance (NMR) shielding tensors in general points in space. We also show that nucleus independent chemical shifts (NICS) along the symmetry axis are related to the spatial derivative of the strength of the global ring-current along the z axis.

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.

From Macrocycles to Quantum Rings: Does Aromaticity Have a Size Limit?

ConspectusThe ring currents of aromatic and antiaromatic molecules are remarkable emergent phenomena. A ring current is a quantum-mechanical feature of the whole system, and its existence cannot be inferred from the properties of the individual components of the ring. Hückel's rule states that when an aromatic molecule with a circuit of [4n + 2] π electrons is placed in a magnetic field, the field induces a ring current that creates a magnetic field opposing the external field inside the ring. In contrast, antiaromatic rings with 4n π electrons exhibit ring currents in the opposite direction. This rule bears the name of Erich Hückel, and it grew from his molecular orbital theory, but modern formulations of Hückel's rule incorporate contributions from others, particularly William Doering and Ronald Breslow. It is often assumed that aromaticity is restricted to small molecular rings with up to about 22 π electrons. This Account outlines the discovery of global ring currents in large macrocycles with circuits of up to 162 π electrons. The largest aromatic rings yet investigated are cyclic porphyrin oligomers, which exhibit global ring currents after oxidation, reduction or optical excitation but not in the neutral ground state. The global aromaticity in these porphyrin nanorings leads to experimentally measurable aromatic stabilization energies in addition to magnetic effects that can be studied by NMR spectroscopy. Wheel-like templates can be bound inside these nanorings, providing excellent control over the molecular geometry and allowing the magnetic shielding to be probed inside the nanoring. The ring currents in these systems are well-reproduced by density functional theory (DFT), although the choice of DFT functional often turns out to be critical. Here we review recent contributions to this field and present a simple method for determining the ring current susceptibility (in nA/T) in any aromatic or antiaromatic ring from experimental NMR data by classical Biot-Savart calculations. We use this method to quantify the ring currents in a variety of aromatic rings. This survey confirms that Hückel's rule reliably predicts the direction of the ring current, and it reveals that the ring current susceptibility is surprisingly insensitive to the size of the ring. The investigation of aromaticity in even larger molecular rings is interesting because ring currents are also observed when mesoscopic metal rings are placed in a magnetic field at low temperatures. The striking similarity between the ring currents in molecules and mesoscopic metal rings arises because the effects have a common origin: a field-dependent phase shift in the electronic wave function. The main difference is that the magnetic flux through mesoscopic rings is much greater because of their larger areas, so their persistent currents are nonlinear and oscillatory with the applied field, whereas the flux through aromatic molecules is so small that their response is approximately linear in the applied field. We discuss how nonlinearity is expected to emerge in large molecular nanorings at high magnetic fields. The insights from this work are fundamentally important for understanding aromaticity and for bridging the gap between chemistry and mesoscopic physics, potentially leading to new functions in molecular electronics.

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.

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.

Exploitation of Baird Aromaticity and Clar’s Rule for Tuning the Triplet Energies of Polycyclic Aromatic Hydrocarbons

Polycyclic aromatic hydrocarbons (PAH) are a prominent substance class with a variety of applications in molecular materials science. Their electronic properties crucially depend on the bond topology in ways that are often highly non-intuitive. Here, we study, using density functional theory, the triplet states of four biphenylene-derived PAHs finding dramatically different triplet excitation energies for closely related isomeric structures. These differences are rationalised using a qualitative description of Clar sextets and Baird quartets, quantified in terms of nucleus independent chemical shifts, and represented graphically through a recently developed method for visualising chemical shielding tensors (VIST). The results are further interpreted in terms of a 2D rigid rotor model of aromaticity and through an analysis of the natural transition orbitals involved in the triplet excited states showing good consistency between the different viewpoints. We believe that this work constitutes an important step in consolidating these varying viewpoints of electronically excited states.

On the NICS limitations to predict local and global current pathways in polycyclic systems

Here, we analyze the possibility of predicting local and global current densities in a series of bicyclic hydrocarbons with 4n and 4n + 2 π-electrons from the nucleus-independent chemical shifts (NICS) computations.

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.

Switching between Hückel and Möbius aromaticity: a density functional theory and information-theoretic approach study

Benziporphyrins are versatile macrocycles exhibiting aromaticity switching behaviors. The existence of both Hückel and Möbius (anti)aromaticity has been reported in these systems, whose validity is respectively governed by the [4n + 2] and [4n] π-electron rule on the macrocyclic pathway. Despite the experimental evidence on the floppiness of benziporphyrins, the switching mechanism between Hückel and Möbius structures is still not clear, as well as the factors influencing the stability of the different π-conjugation topologies. For these reasons, we performed a systematic study on A,D-di-p-benzihexaphyrins(1.1.1.1.1.1) with two redox states corresponding to [28] and [30] π-electron conjugation pathways. Whereas benzi[28]hexaphyrin obeys Möbius aromaticity, benzi[30]hexaphyrin follows Hückel aromaticity. The dynamic interconversion between Möbius and Hückel aromaticity is investigated through the rotation of a phenylene ring, which acts as the topology selector. Further analyses of the energy profiles using energy decomposition and information-theoretic approaches provide new insights into conformational stability, aromaticity and antiaromaticity for these species. Strong and opposite cross correlations between aromaticity indexes and information-theoretic quantities were found for the two macrocyclic systems with opposite global aromaticity and antiaromaticity behaviors. These results indicate that Hückel and Möbius aromaticity and antiaromaticity, though qualitatively different, are closely related and can be interchanged, and information-theoretic quantities provide a novel understanding about their relevance. Our present results should provide in-depth insights to appreciate the nature and origin about Möbius (anti)aromaticity and its close relationship with Hückel (anti)aromaticity.

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.

Magnetically-induced current density investigation in carbohelicenes and azahelicenes

A computational study of the magnetically-induced current (MIC) density has been carried out for a variety of ortho fused polycyclic aromatic molecules at the density functional theory level with the gauge including magnetically induced current (GIMIC) method. With this method, the aromatic character of each ring in a homologous series of carbohelicenes with an increasing number of fused benzene rings is assessed and compared with other aromaticity criteria such as the Nucleus Independent Chemical Shift [NICS(0), NICSzz(0)] and Bond Length Alternation (BLA) parameters. All criteria indicate that the two outer rings are the most aromatic ones [i.e. higher induced current, more negative NICS(0) and NICSzz(0) values, and smaller BLA values]. For the large helicenes (n > 10), the current drops along the following four rings and then rises again. Additionally, we have proven that this behavior is not due to a difference of the local magnetic field coming from a difference of orientation of the ring with respect to the external magnetic field (oriented along the helical axis). Upon fusing additional benzene rings to form hexa-peri-hexabenzo[7]helicene, some rings (B, D, and F) are a lot less aromatic (even non-aromatic) than the others. The NICS(0) and NICSzz(0) values exaggerate this behavior because they are all positive values, which is a signature of antiaromaticity. Then, when substituting one, three, or four benzene rings with pyrrole ones to form mono-aza-[7]-helicene, tri-aza-[7]-helicene, and tetra-aza-[7]-helicene, remarkable changes in the electronic structures of the helicenes are observed. Indeed, the induced currents are always smaller in the pyrrole rings than in the benzene ones. This has been further investigated using the streamline and the color map representations, which indicate that the diatropic current density passing through the plane cutting the C-N bonds in the pyrrole rings is stronger but is more localized than the current density passing through the plane cutting the C-C bonds in the benzene rings. This gives a positive but smaller total induced current for the pyrrole rings than for the benzene ones. For these systems, the NICS(0) and even more the NICSzz(0) values are not fully reliable to probe the local aromaticity, contrary to the induced current. Indeed, the NICSzz(0) values for the tri-aza-[7]-helicene molecule range from -14.23 to 1.14 ppm, which cannot lead to the same conclusion as the induced current values (10.03 to 12.87 nA T-1).

Frequency-dependent current density tensors as density functions of dynamic polarizabilities

Relationships accounting for contributions to the first-order charge density ρ⁽¹⁾ and current density J⁽¹⁾, induced in the electrons of a molecule by a monochromatic plane wave, have been obtained via time-dependent quantum mechanical perturbation theory. Their gauge invariance and invariance in passive translations of the coordinate system have been demonstrated (i) within the (long wavelengths) electric dipole approximation, in which only the electric field contributions to these densities are required, and (ii) within the electric quadrupole approximation, in which nonseparable terms provided by the magnetic field and by the electric field gradient, assumed uniform over the molecular domain, are needed. It is shown that the physical meaning of current density tensors depending on the frequency ω of the monochromatic wave shone on the molecule, and corresponding to derivatives of the current density J⁽¹⁾(r, ω) with respect to components of the perturbing fields, is that of property density. Therefore, frequency-dependent current density tensors can be interpreted as the integrand function in 3d-space integrals defining dynamic molecular response tensors, e.g., electric dipole, mixed electric dipole-magnetic dipole, and electric dipole-quadrupole polarizabilites. Plots of current density tensors are expected to provide important information on the molecular domains giving dominant contributions to these properties.

Reexamination of NICSπ,zz: Height Dependence, Off-Center Values, and Integration

Applying fine grids of nucleus independent chemical shift (NICS) probes (BQs) at different distances from the molecular plane of aromatic and antiaromatic molecules suggests that, at short distances, NICS_π,zz is maximal (absolute values) off the geometrical center of the systems. In nonsymmetric systems, the center of the induced ring current may be a little off the geometrical center, but the difference is negligible at distances ≥2 Å. At these distances, the change of NICS_π,zz with the distance from the ring follows a power relation. It is shown that the order of diatropicity and paratropicity within a group of molecules depends on the distance from the system (namely, the order of NICS( r)_π,zz depends on r). It is thus suggested to use ∫NICS_π,zz as a quantitative measure of aromaticity.

Magnetically induced current density in triple-layered beryllium–boron clusters

Magnetically induced current densities reveal the double aromatic character of the examined Be–B clusters.

Calculations of current densities and aromatic pathways in cyclic porphyrin and isoporphyrin arrays

Magnetically induced current density susceptibilities have been studied for a number of cyclic ethyne- and butadiyne-bridged porphyrin and isoporphyrin arrays. The current density susceptibilities have been calculated using the gauge-including magnetically induced current (GIMIC) method, which is interfaced to the TURBOMOLE quantum chemistry code. Aromatic properties and current pathways have been analyzed and discussed by numerical integration of the current density susceptibilities passing selected chemical bonds yielding current strength susceptibilities. Despite the interrupted π-framework, zinc(ii) isoporphyrin sustains a ring current of ca. 10 nA T^-1. Porphyrin and isoporphyrin dimers sustain a significant current strength at the linker, whereas the larger porphyrinoid arrays sustain mainly local ring currents. Isoporphyrin dimers with saturated meso carbons have strong net diatropic ring-current strengths of 20 nA T^-1 fulfilling Hückels aromaticity rule. Porphyrin trimers and tetramers exhibit almost no current strength at the linker. The porphyrin moieties maintain their strong net diatropic ring current.

Which NICS method is most consistent with ring current analysis? Assessment in simple monocycles

A linear relationship between NICS_zz,π and NICS_π,σ with their current strength counterparts is shown. The comparative analysis was performed in simple and representative monocycles.

Analysis of the Nucleus-Independent Chemical Shifts of [10]Cyclophenacene: Is It an Aromatic or Antiaromatic Molecule?

[10]Cyclophenacene is an important synthetic target that shows a pair of nucleus-independent chemical shift (NICS) values for the center of mass and six-membered rings typical of an aromatic species. This is found in contrast with the global paratropic current density induced by a magnetic field parallel to the main symmetry axis. This apparent contradiction has been analyzed by studying the tensor character of the magnetic response. It turns out that the molecule displays two characters, one paratropic (antiaromatic) and another one diatropic (aromatic), depending on the orientation of the inducing magnetic field. The paratropic response, which cannot be recognized from the NICS values, is associated with a well-defined destabilization of the belt closure, as witnessed by homodesmotic reactions. A scalar measure of magnetic aromaticity, the field-independent current strength, has been introduced, which allows us to reach the conclusion that [10]cyclophenacene is indeed an aromatic molecule, although it is significantly affected by the paratropic response.

The influence of heteroatoms on the aromatic character and the current pathways of B2N2-dibenzo[a,e]pentalenes

Four polycyclic molecules have been investigated at the DFT level of theory using magnetically induced current densities calculated with the GIMIC program as an indicator of their (anti)aromaticity.

Aromaticity introduced by antiferromagnetic ligand mediated metal–metal interactions. Insights from the induced magnetic response in [Cu6(dmPz)6(OH)6]

Ligand-mediated antiferromagnetic coupling induces aromatic-ring behavior.

A DFT study on dihydropyrazine annulated linear polyacenes: aromaticity, stability and HOMO–LUMO energy modulation

Linear polyacene (LPA) mimics containing up to 34 rings have been designed by annulating dihydropyrazine units to LPA cores and they showed enhanced aromatic character than the LPA due to significant mixing of the N-lone pairs with the carbon π-orbitals.

Topological definition of ring currents

A definition of ring currents in a velocity vector field is proposed according to topological criteria: ring currents are axial vortices confined in, or rotating beyond, a separatrix, i.e., the boundary which marks the limits of the vortex.

The making of ring currents

The π-electron diatropic ring current emerging throughout the trimerization of acetylene to benzene.

Analysis of the magnetically induced current density of molecules consisting of annelated aromatic and antiaromatic hydrocarbon rings

The aromatic pathway of molecules with annelated aromatic and antiaromatic rings has been studied by calculating magnetically induced current densities.

New insights into aromatic pathways of carbachlorins and carbaporphyrins based on calculations of magnetically induced current densities

The aromatic pathways of carbaporphyrins and carbachlorins that are based on magnetically induced current density DFT-GIMIC calculations are presented and discussed.

Understanding the molecular switching properties of octaphyrins

Triggering Hückel–Möbius topological and aromaticity switches in octaphyrins by protonation and redox reactions.

Hydrogen-hydrogen bonding: the current density perspective

Current density plots of closed-shell intermolecular H-H interactions characterized by a bond critical point (BCP) show two vortices separated by a saddle, a pattern which allows for a clear definition of a pair current strength. This H-H current strength turns out to be roughly related to the potential energy density at the BCP and then to the dissociation energy. The same pattern is also recognizable, at least for an azimuthal orientation of a field perpendicular to the H-H line, for the intramolecular interactions previously investigated to propose the H-H bonding. In the case of the H atoms of the bay region of polycyclic aromatic hydrocarbons, the current of the H-H delocalized diatropic vortex gives a quantitative indication of stabilization; however, on rotation of the field and the subsequent onset of a bay-delocalized paratropic vortex (a typical signature of antiaromaticity), the diatropic vortex can be reshaped or it can even disappear, consistently with its smallness, and thus showing the effect of other more relevant interactions.

On the diatropic perimeter of iterated altan-molecules

Ab initio calculations confirm that the design of large paratropic circuits through altanisation fails in altan-[10,5]coronene. This molecule is predicted to be an open-shell singlet biradical, like the cycloacene that it contains.