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.

Aromaticity Reversal Induced by Vibrations in Cyclo[16]carbon

Aromaticity is typically regarded as an intrinsic property of a molecule, correlated with electron delocalization, stability, and other properties. Small variations in the molecular geometry usually result in small changes in aromaticity, in line with Hammond's postulate. For example, introducing bond-length alternation in benzene and square cyclobutadiene by modulating the geometry along the Kekulé vibration gradually decreases the magnitude of their ring currents, making them less aromatic and less antiaromatic, respectively. A sign change in the ring current, corresponding to a reversal of aromaticity, typically requires a gross perturbation such as electronic excitation, addition or removal of two electrons, or a dramatic change in the molecular geometry. Here, we use multireference calculations to show how movement along the Kekulé vibration, which controls bond-length alternation, induces a sudden reversal in the ring current of cyclo[16]carbon, C16. This reversal occurs when the two orthogonal π systems of C16 sustain opposing currents. These results are rationalized by a Hückel model which includes bond-length alternation, and which is combined with a minimal model accounting for orbital contributions to the ring current. Finally, we successfully describe the electronic structure of C16 with a "divide-and-conquer" approach suitable for execution on a quantum computer.

Current-Density Calculations on Zn-Porphyrin40 Nanorings

Two porphyrinoid nanorings have been studied computationally. They were built by linking 40 Zn-porphyrin units with butadiyne bridges. The molecular structures belonging to the D40h point group were fully optimized with the Turbomole program at the density functional theory (DFT) level using the B3LYP functional and the def2-SVP basis sets. The aromatic character was studied at the DFT level by calculating the magnetically induced current-density (MICD) susceptibility using the GIMIC program. The neutral molecules are globally non-aromatic with aromatic Zn-porphyrin units. Charged nanorings could not be studied because almost degenerate frontier orbitals led to vanishing optical gaps for the cations. Since DFT calculations of the MICD are computationally expensive, we also calculated the MICD using three pseudo-π models. Appropriate pseudo-π models were constructed by removing the outer hydrogen atoms and replacing all carbon and nitrogen atoms with hydrogen atoms. The central Zn atom was either replaced with a beryllium atom or with two inner hydrogen atoms. Calculations with the computationally inexpensive pseudo-π models yielded qualitatively the same magnetic response as obtained in the all-electron calculations.

Aromaticity: Quo Vadis

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

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.

The spin–orbit effects on platinabenzene: a ring current and electron delocalization approach

The aromaticity of platinabenzene was studied using the electronic structure and magnetic descriptors with relativistic corrections. It presents aromatic character following the Hückel's rule, negative NICS values, and diatropic current densities.

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.

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.

Heteroatom effects on aromaticity of five-membered rings in acenaphthylene analogs

The pattern of cyclic conjugation was thoroughly studied in the series of N- and P-acenaphthylene derivatives using several different aromaticity indices: the energy effect (ef), multicenter delocalization index (MCI), harmonic oscillator model of aromaticity (HOMA) index, and nucleus independent chemical shifts (NICS). The Kekulé-structure-based reasoning predicts that there would be no cyclic conjugation in the "empty" five-membered heteroatom-containing rings in the studied molecules. It was found that according to the ef, MCI, and HOMA values, the extent of cyclic conjugation in the pentagonal rings is strongly influenced by the number and mutual arrangement of the hexagonal rings. In addition, it was revealed that in some of the examined molecules, the intensity of cyclic conjugation in the "empty" pentagons is even stronger than that of some hexagonal rings within the same molecule. The obtained results refute what one would expect based on "chemical intuition," which is usually strongly rooted to the Kekulé structures.Graphical abstract.

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.

Chemical Bonding in Transition Metal Nitride Os3N3 + Cluster: 6π Inorganic Benzene and δ2δ*1δ*1 Aromaticity

Inorganic benzene-like clusters with a planar hexagonal ring are of interest in chemistry, as are new types of aromaticity, multifold aromaticity, and in particular δ aromaticity beyond carbon-based organic systems. Here we report on a computational study of chemical bonding in a binary Os₃N₃ ⁺ D _3h (⁷A₂″) cluster. This transition metal nitride cluster assumes a perfectly planar, heteroatomic, hexagonal geometry. An array of quantum chemistry tools is exploited to elucidate the electronic, structural, and bonding properties of D _3h Os₃N₃ ⁺ cluster, which include canonical molecular orbitals, adaptive natural density partitioning, natural bond orbital analysis, orbital composition calculations, and nucleus-independent chemical shifts. The computational data collectively support the bonding picture of 2-fold π/δ aromaticity: 6π electrons delocalized over all Os/N centers versus an Os-based 4δ framework in the unique δ²δ*¹δ*¹ configuration. The π sextet renders this heteroatomic cluster an inorganic analog of benzene. Transition metal-based inorganic benzenes are unknown in the literature, to our knowledge. The triplet 4δ electron-counting is a rare case of d-orbital aromaticity and δ-aromaticity, following the reversed 4n Hückel rule for aromaticity in a triplet system. This bonding picture is concrete, differing fundamentally from a recent study on the relevant system.

D2BIA-flexible, not (explicitly) arbitrary and reference/structurally invariant-a very effective and improved version of the D3BIA aromaticity index

Although there are a multitude of aromaticity indexes, only a few have a widespread usage. All famous aromaticity indexes are limited: HOMA and FLU are reference-dependent; ELF is π-bond-dependent; PDI is structurally dependent and NICS is ring size dependent. These limitations stimulate the continuous search for better (i.e., having no dependency), more flexible (i.e., applied to any aromatic system) and more effective (i.e., with excellent correlations with other indexes) aromaticity indexes. The D3BIA was our first topological aromaticity index. It is flexible, reference-independent and effective for planar and caged aromatic molecules. However, one of its terms, the degree of degeneracy (δ), is arbitrary and difficult to carry out for new users. Thus, in this work, we show that D2BIA-an improved version of D3BIA-is a good candidate to be used widely, since it retains the strong points of D3BIA while avoiding its weak point. In particular cases where all studied systems have δ = 1 (e.g., for acenes), then D2BIA equals D3BIA. For our recent study with acenes, D3BIA (and, as a consequence, D2BIA) has (have) an excellent correlation with FLU according to the MP3 method. In this work, by using DFT calculations for a series involving several six-membered and five-membered heteroaromatic rings, only D2BIA and NICS have very good correlation. All other well known aromaticity indexes used in this work (FLU, HOMA and ELF) gave poor correlations. As to homoaromatic systems, only D2BIA vs NICS and D2BIA vs FLU plots have excellent correlations. HOMA has the worst results in this series. Thus, D2BIA proved to be flexible and effective for the analysis of heteroaromatic rings of different sizes and for caged homoaromatic systems. Moreover, D2BIA has better correlations than D3BIA for planar aromatic systems, and same correlations for caged-homoaromatic systems. Graphical abstract D2BIA-an effective and improved version of the D3BIA aromaticity index.

Aromaticity and antiaromaticity of substituted fulvene derivatives: perspectives from the information-theoretic approach in density functional reactivity theory

Strong correlations among aromaticity descriptors and information-theoretic quantities are unveiled, providing novel insights about aromaticity and antiaromaticity from different perspectives.