Aromaticity of giant polycyclic aromatic hydrocarbons with hollow sites: super ring currents in super-rings

We present a systematic theoretical study based on semi-empirical, Hartree-Fock (HF), and density functional theory (DFT) models of a series of polycyclic aromatic hydrocarbons (PAHs) that exhibit hollow sites. In this study we focus particularly on the magnetic criteria of aromaticity, namely (1)H NMR and nucleus-independent chemical shifts (NICS), and on their relationships with other electronic properties. The computed shifts and NICS indices indicate that an external magnetic field induces exceptionally strong ring currents in even-layered PAH doughnuts, in particular in the layer directly adjacent to the central hole of double-layered compounds. These exceptionally strong ring currents also correlate with particularly small HOMO-LUMO gaps and electronic excitation energies and to abnormally high polarizabilities, indicating in turn that these compounds have a more pronounced metallic character. Comparison is made with further depictions of aromaticity in these systems and in [18]-[66]annulene rings by employing topological, structural, and energetic criteria.     

Cyclopenta Ring Fused Bisanthene and Its Charged Species with Open‐Shell Singlet Diradical Character and Global Aromaticity/ Anti‐Aromaticity

Cyclopenta ring fused bisanthene and its charged species were synthesized. The neutral compound has an open‐shell singlet ground state and displays global anti‐aromaticity. The dication also exhibits singlet diradical character but has a unique [10]annulene‐within‐[18]annulene global aromatic structure. The dianion is closed‐shell singlet in the ground state and shows global aromaticity with 22 π electrons delocalized on the periphery. These findings prrovide new insight into the design and properties of global aromatic/anti‐aromatic systems based on π‐conjugated polycyclic hydrocarbons.     

Interpreting Aromaticity and Antiaromaticity through Bifurcation Analysis of the Induced Magnetic Field

In all molecules, a current density is induced when the molecule is subjected to an external magnetic field. In turn, this current density creates a particular magnetic field. In this work, the bifurcation value of the induced magnetic field is analyzed in a representative set of aromatic, non-aromatic and antiaromatic monocycles, as well as a set of polycyclic hydrocarbons. The results show that the bifurcation value of the ring-shaped domain adequately classifies the studied molecules according to their aromatic character. For aromatic and nonaromatic molecules, it is possible to analyze two ring-shaped domains, one diatropic (inside the molecular ring) and one paratropic (outside the molecular ring). Meanwhile, for antiaromatic rings, only a diatropic ring-shaped domain (outside the molecular ring) is possible to analyze, since the paratropic domain (inside the molecular ring) is irreducible with the maximum value (attractor) at the center of the molecular ring. In some of the studied cases, i. e., in heteroatomic species, bifurcation values do not follow aromaticity trends and present some inconsistencies in comparison to ring currents strengths, showing that this approximation provides only a qualitative estimation about (anti)aromaticity.     

Ring currents in condensed ring systems

We have studied magnetism and aromaticity of polycyclic ring systems by analyzing ring currents for different circulations in these molecules. The technique employed for calculating ring currents uses correction vectors which implicitly includes all the eigenstates of the Hamiltonian in the space of the chosen configurations. We have employed the Pariser–Parr–Pople Hamiltonian and have carried out full configuration interaction (CI) calculations for small systems and approximate CI calculations for large systems. The systems studied include polyacenes, nonaromatic ring systems including the C₆₀ fragments pyracylene, fluoranthene, and corannulene, and heteroatomic systems with upto two six-membered rings. We find that in polyacenes, the aromaticity of the extreme phenyl rings reduces with increasing number of phenyl rings in the system, and it saturates at ≈⅔ the benzene value. In systems containing nonaromatic rings, we find paramagnetic or diamagnetic behavior for different circulations depending upon the number of atoms in the chosen ring cycle, in agreement with the 4n+2 rule. In corannulene, the largest fragment of C₆₀ we have studied, the five-membered ring is weakly diamagnetic while the six-membered ring is more diamagnetic, although much less than in isolated benzene. The ring structures with heteroatoms studied are pyridine, pyrimidine, and its isomers, s-triazine, quinoline and its isomer, and quinazoline and its isomers. All these have similar ring currents as in their purely carbon counterparts, although ions of these molecules show interesting behavior. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 503–513, 1998     

Aromatic character of polycyclic π systems formed by fusion of two or more rings of the same size

The sequential line plot of topological resonance energy (TRE) against the number of π electrons (N(π)) for any polycyclic aromatic hydrocarbon (PAH) is very similar with the same number of extrema to that for benzene. Thus, global aromaticity of a PAH molecular ion strongly reflects that of a benzene molecular ion. Likewise, the N(π) dependence of TRE for any polycyclic π system formed by fusion of two or more rings of the same size reflects that for a monocyclic species of the same ring size. In general, TREs for such polycyclic π systems and their molecular ions can be interpreted consistently by reference to those for neutral and charged monocyclic species of the same ring size.     

Electron delocalization in the metallabenzenes: a computational analysis of ring currents

Many metallabenzene complexes appear to exhibit an enhanced thermodynamic stability which has been attributed to the concept of aromaticity. Analysis of the ring currents induced by a magnetic field, either by direct visualization or by considering nuclear or nucleus-independent chemical shielding values (NMR or NICS), have become useful theoretical tools to characterize the aromaticity of many molecules involving the main group elements. We have analyzed 21 metallabenzenes using variations of these techniques, which take account of the large core and metal orbital contributions which often lead to transition-metal-containing systems exhibiting anomalous shielding values. Analysis of individual orbital contributions to both the ring currents and chemical shielding values based upon the ipsocentric and CSGT (continuous set of gauge transformations) methods has shown that complexes such as the 18 electron Ir or Rh(C 5H 5)(PH 3) 2Cl 2 molecules should be classed as aromatic, whereas the 16 electron complexes such as Os or Ru(C 5H 5)(PH 3) 2Cl 2 should not, despite having the same occupancy of pi-MOs. The differences can be directly attributed to the HOMO/LUMO b 2 in-plane (d xy ) molecular orbital, which, when unoccupied, is available to disrupt the delocalized currents typical of aromatic systems. A range of Pd and Pt metallabenzenes with cyclopentadienyl and phosphine ligands is also discussed as having aromatic and nonaromatic character, respectively.     

The aromatic character of magnesium porphyrins

The aromaticity of magnesium porphyrins have been studied by calculating the nuclear magnetic shieldings in selected points outside the molecules. The strength of the induced ring currents for a given magnetic field have been obtained by using the aromatic-ring-current-shielding (ARCS) method. Nucleus-independent chemical shift (NICS) calculations provide additional information about the current routes in the multiple-ring systems. The total aromatic pathway of magnesium porphyrins must be considered as a superposition of several (4n + 2) pi-electron Huckel pathways. We found that all beta-unsaturated pyrrolic rings have local ring currents the strength of which is 70-90% of the current strength for the pyrrole molecule. The present study also shows that the 18pi-[16]annulene aromatic pathway does not exist in magnesium porphyrins until all four pyrrolic units are saturated in the beta-position.     

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.     

Circuit resonance energy: a key quantity that links energetic and magnetic criteria of aromaticity

Energetic and magnetic criteria of aromaticity are different in nature and sometimes make different predictions as to the aromaticity of a polycyclic pi-system. Thus, some charged polycyclic pi-systems are aromatic but paratropic. We derived the individual circuit contributions to aromaticity from the magnetic response of a polycyclic pi-system and named them circuit resonance energies (CREs). Each CRE has the same sign and essentially the same magnitude as the corresponding cyclic conjugation energy (CCE) defined by Bosanac and Gutman. Such CREs were found to play a crucial role in associating the energetic criteria for determining the degree of aromaticity with the magnetic ones. We can now interpret both energetic and magnetic criteria of aromaticity consistently in terms of CREs. Ring-current diamagnetism proved to be the tendency of a cyclic pi-system to retain aromatic stabilization energy (ASE) at the level of individual circuits.     

Local aromaticity of the six-membered rings in pyracylene. A difficult case for the NICS indicator of aromaticity

In this work, we have analyzed the local aromaticity of the six-membered rings (6-MRs) of planar and pyramidalized pyracylene species through the structurally based harmonic oscillator model of aromaticity (HOMA), the electronically based para-delocalization index (PDI), and the magnetic-based nucleus independent chemical shift (NICS) measurements, as well as with maps of ring current density. According to ring currents and PDI and HOMA indicators of aromaticity, there is a small reduction of local aromaticity in the 6-MRs of pyracylene with a bending of the molecule. In the case of NICS, the results depend on whether the NICS value is calculated at the center of the ring (NICS(0)) or at 1 A above (NICS(1)(out)) or below (NICS(1)(in)) the ring plane. While NICS(1)(out) values also indicate a slight decrease of aromaticity with bending, NICS(0) and NICS(1)(in) wrongly point out a large increase of aromaticity upon distortion. We have demonstrated that the NICS(0) reduction in the 6-MRs of pyracylene upon bending is due to (a) a strong reduction of the paratropic currents in 5-MRs and (b) the fact that, due to the distortion, the paratropic currents point their effects in other directions.     

The aromatic fluctuation index (FLU): a new aromaticity index based on electron delocalization

In this work, the aromatic fluctuation index (FLU) that describes the fluctuation of electronic charge between adjacent atoms in a given ring is introduced as a new aromaticity measure. This new electronic criterion of aromaticity is based on the fact that aromaticity is related to the cyclic delocalized circulation of pi electrons. It is defined not only considering the amount of electron sharing between contiguous atoms, which should be substantial in aromatic molecules, but also taking into account the similarity of electron sharing between adjacent atoms. For a series of rings in 15 planar polycyclic aromatic hydrocarbons, we have found that, in general, FLU is strongly correlated with other widely used indicators of local aromaticity, such as the harmonic-oscillator model of aromaticity, the nucleus independent chemical shift, and the para-delocalization index (PDI). In contrast to PDI, the FLU index can be applied to study the aromaticity of rings with any number of members and it can be used to analyze both the local and global aromatic character of rings and molecules.     

Multidimensionality of delocalization indices and nucleus independent chemical shifts in polycyclic aromatic hydrocarbons

The aromaticity and local-aromaticity of a large set of polycyclic aromatic hydrocarbons (PAHs) is studied using multicenter delocalization indices from generalized population analysis and the popular nucleus independent chemical shift (NICS) index. A method for the fast computation of the NICS values is introduced, using the so-called pseudo-pi-method. A detailed examination is made of the multidimensional nature of aromaticity. The lack of a good correlation between the NICS and the multicenter delocalization indices is reported and the grounds discussed. It is shown through a thorough statistical analysis that the NICS values arise not only from local aromaticity of the benzenoid rings, but also from other circuits. It is shown that the NICS indices do not reveal the individual aromatic nature of a specific ring, contrary to the delocalization indices.     

Correlation of delocalization indices and current-density maps in polycyclic aromatic hydrocarbons

Using multicentre delocalization indices, the ring current maps of a large set of polycyclic aromatic hydrocarbons (PAH) are reconstructed and compared with ab initio computations of the same maps in the pseudo-pi version of the ipsocentric approach to magnetic response. The quality of the comparison indicates that both delocalization and ring current approaches capture the same information about the aromatic nature of the PAH. Aromaticity as a global property, requires knowledge of more than single circuits, but the present results suggest no need to introduce a "multidimensional character" for aromaticity.     

Does the concept of Clar's aromatic sextet work for dicationic forms of polycyclic aromatic hydrocarbons?--testing the model against charged systems in singlet and triplet states

The concept of Clar's π-electron aromatic sextet was tested against a set of polycyclic aromatic hydrocarbons in neutral and doubly charged forms. Systems containing different types of rings (in the context of Clar's concept) were chosen, including benzene, naphthalene, anthracene, phenanthrene and triphenylene. In the case of dicationic structures both singlet and triplet states were considered. It was found that for singlet state dicationic structures the concept of aromatic sextet could be applied and the local aromaticity could be discussed in the context of that model, whereas in the case of triplet state dicationic structures Clar's model rather failed. Different aromaticity indices based on various properties of molecular systems were applied for the purpose of the studies. The discussion about the interdependence between the values of different aromaticity indices applied to neutral and charged systems in singlet and triplet states is also included.     

Interplay of para- and diatropic ring currents [(anti)aromaticity] of macrocyclic rings subject to conformational influences,further annelation and hydrogenation of aromatic ring moieties

The spatial magnetic properties (Through Space NMR Shieldings—TSNMRS) of a variety of porphyrins, hemiporphyrazines and tetraoxo[8]circulenes have been computed, visualized as Iso-chemical Shielding Surfaces (ICSS) of various size and direction, and were examined subject to the interplay of present (para)-diatropic ring currents [(anti)aromaticity] and influences on the latter property originating from the macrocyclic ring conformation, further annelation and partial to complete hydrogenation of aromatic ring moieties. Caution seems to be indicated when concluding from a single NICS parameter to present (para)diatropic ring currents [(anti)aromaticity].     

A unified orbital model of delocalised and localised currents in monocycles, from annulenes to azabora-heterocycles

Why are some (4n+2)π systems aromatic, and some not? The ipsocentric approach to the calculation of the current density induced in a molecule by an external magnetic field predicts a four‐electron diatropic (aromatic) ring current for (4n+2)π carbocycles and a two‐electron paratropic (antiaromatic) current for (4n)π carbocycles. With the inclusion of an electronegativity parameter, an ipsocentric frontier‐orbital model also predicts the transition from delocalised currents in carbocycles to nitrogen‐localised currents in alternating azabora‐heterocycles, which rationalises the differences in (magnetic) aromaticity between these isoelectronic π‐conjugated systems. Ab initio valence‐bond calculations confirm the localisation predicted by the naïve model, and coupled‐Hartree–Fock calculations give current‐density maps that exhibit the predicted delocalised‐to‐localised/carbocycle–heterocycle transition.     

Interplay among aromaticity, magnetism, and nonlinear optical response in all-metal aromatic systems

All-metal aromatic molecules are the latest inclusion in the family of aromatic systems. Two different classes of all-metal aromatic clusters are primarily identified: one is aromatic only in the low spin state, and the other shows aromaticity even in high-spin situations. This observation prompts us to investigate the effect of spin multiplicity on aromaticity, taking Al(4)(2-), Te(2)As(2)(2-), and their copper complexes as reference systems. Among these clusters, it has been found that the molecules that are aromatic only in their singlet state manifest antiaromaticity in their triplet state. The aromaticity in the singlet state is characterized by the diatropic ring current circulated through the bonds, which are cleaved to generate excess spin density on the atoms in the antiaromatic triplet state. Hence, in such systems, an antagonistic relationship between aromaticity and high-spin situations emerges. On the other hand, in the case of triplet aromatic molecules, the magnetic orbitals and the orbitals maintaining aromaticity are different; hence, aromaticity is not depleted in the high-spin state. The nonlinear optical (NLO) behavior of the same set of clusters in different spin states has also been addressed. We correlate the second hyperpolarizability and spin density in order to judge the effect of spin multiplicity on third-order NLO response. This correlation reveals a high degree of NLO behavior in systems with excess spin density. The variance of aromaticity and NLO response with spin multiplicity is found to stem from a single aspect, the energy gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), and eventually the interplay among aromaticity, magnetism, and NLO response in such materials is established. Hence, the HOMO-LUMO energy gap becomes the cornerstone for tuning the interplay. This correlation among the said properties is not system-specific and thus can be envisaged even beyond the periphery of all-metal aromatic clusters. Such interplay is of crucial importance in tailoring novel paradigm of multifunctional materials.     

Nucleus-independent chemical shifts (NICS): distance dependence and revised criteria for aromaticity and antiaromaticity

Nucleus-independent chemical shifts (NICS) have been used extensively for the identification of aromaticity properties of molecules, ions, intermediates, and transition states since their introduction in 1996 by Schleyer et al. Initially, probes (bq's) were placed at the centers of systems (NICS(0)) and later, 1A above the molecular planes (NICS(1)). However, contradicting assignments of aromaticity by NICS and other methods were found for some systems. In this article, an alternative NICS-based method is introduced. The method is based on scanning NICS values over a distance and separating them into in-plane and out-of plane contributions. The shapes of the plots of the chemical shifts and their components as a function of the distance of the NICS probe (bq) from the molecular plane give a clear indication of diamagnetic and paramagnetic ring currents. This method is applied to several (4n + 2)- and 4n pi-electron systems (molecules and ions) in the singlet and triplet electronic states, including some of the problematic systems mentioned above. It is also shown that relative aromaticities of rings in polycyclic systems (local aromaticities) cannot be estimated by comparing NICS or NICS-scan values.