Global Ring Current Research Articles

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.

Aromaticity and Magnetic Behavior in Benzenoids: Unraveling Ring Current Combinations.

Nowadays, an active research topic is the connection between Clar's rule, aromaticity, and magnetic properties of polycyclic benzenoid hydrocarbons. In the present work, we employ a meticulous magnetically induced current density analysis to define the net current flowing through any cyclic circuit, connecting it to aromaticity based on the ring current concept. Our investigation reveals that the analyzed polycyclic systems display a prominent global ring current, contrasting with subdued semi-local and local ring currents. These patterns align with Clar's aromatic π-sextets only in cases where migrating π-sextet structures are invoked. The results of this study will enrich our comprehension of aromaticity and magnetic behavior in such systems, offering significant insights into coexisting ring current circuits in these systems.

Alternating behavior in furan-acetylene macrocycles reveals the size-dependency of Hückel’s rule in neutral molecules

Aromaticity can be assigned by Hückel’s rule, which predicts that planar rings with delocalized (4n + 2) π-electrons are aromatic, whereas those with 4n π-electrons are antiaromatic. However, for neutral rings, the maximal value of “n” to which Hückel’s rule applies remains unknown. Large macrocycles exhibiting global ring current can serve as models for addressing this question, but the global ring current are often overshadowed in these molecules by the local ring current of the constituent units. Here, we present a series of furan-acetylene macrocycles, ranging from the pentamer to octamer, whose neutral states display alternating contributions from global aromatic and antiaromatic ring currents. We find that the odd-membered macrocycles display global aromatic characteristics, whereas the even-membered macrocycles display contributions from globally antiaromatic ring current. These factors are expressed electronically (oxidation potentials), optically (emission spectra), and magnetically (chemical shifts), and DFT calculations predict global ring current alternations up to 54 π-electrons.

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.

A Macrocyclic Furan with Accessible Oxidation States: Switching Between Aromatic and Antiaromatic Global Ring Currents.

Macrocyclic furans are predicted to switch between global aromaticity and antiaromaticity, depending on their oxidation states. However, the macrocyclic furans reported to date are stabilized by electron withdrawing groups, which result in inaccessible oxidation states. To circumvent this problem, a post-macrocyclization approach was applied to introduce methylene-substituted macrocyclic furans, which display an extremely low oxidation potential of -0.23 vs. Fc/Fc+ , and are partially oxidized in ambient conditions. Additional oxidation to the dication results in aromaticity switching to a global 30πe- aromatic state, as indicated by the formation of a strong diatropic current observed in the 1 H NMR spectrum. NICS and ACID calculations support this trend and provide evidence for a different pathway for the global current in the neutral and dicationic states. According to these findings, macrocyclic furans can be rendered as promising p-type materials with stable oxidation states.

Correspondence on “How Aromatic Are Molecular Nanorings? The Case of a Six‐Porphyrin Nanoring”**

AbstractA 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.

Diagnosing Ring Current(s) in Figure-Eight Skeletons: A 3D Through-Space Conjugation in the Two-Loops Crossing.

The macrocyclic structures with local conjugation readily undergo a redox-triggered change in the diatropic character, leading to a global current–density pathway of the doubly charged systems. The figure-eight geometry of the neutral dimer does not significantly change upon oxidation according to the spectroscopic and computational data. The oxidation leads to 3D cross-conjugation at the intersection of the two ethylene bridges resulting in a global ring 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.

Functional group introduction and aromatic unit variation in a set of π-conjugated macrocycles: revealing the central role of local and global aromaticity.

π-Conjugated macrocycles are molecules with unique properties that are increasingly exploited for applications and the question of whether they can sustain global aromatic or antiaromatic ring currents is particularly intriguing. However, there are only a small number of experimental studies that investigate how the properties of π-conjugated macrocycles evolve with systematic structural changes. Here, we present such a systematic experimental study of a set of [2.2.2.2]cyclophanetetraenes, all with formally Hückel antiaromatic ground states, and combine it with an in-depth computational analysis. The study reveals the central role of local and global aromaticity for rationalizing the observed optoelectronic properties, ranging from extremely large Stokes shifts of up to 1.6 eV to reversible fourfold reduction, a highly useful feature for charge storage/accumulation applications. A recently developed method for the visualization of chemical shielding tensors (VIST) is applied to provide unique insight into local and global ring currents occurring in different planes along the macrocycle. Conformational changes as a result of the structural variations can further explain some of the observations. The study contributes to the development of structure–property relationships and molecular design guidelines and will help to understand, rationalize, and predict the properties of other π-conjugated macrocycles. It will also assist in the design of macrocycle-based supramolecular elements with defined properties.

NICS-XY-Scan Predictions of Local, Semi-Global, and Global Ring Currents in Annulated Pentalene and s-Indacene Cores Compared to First-Principles Current Density Maps.

The magnetic response of a set of 20 molecules, their dications and their dianions has been studied by the NICS-XY method, and the results have been compared with first principles current density maps. The molecules have been built from pentalene and s-indacene by single and double annulation of cyclobutadiene, benzene and benzocyclobutadiene in an alternate fashion on both sides of the molecules. The prediction of tropicities obtained by the NICS-XY method are overall consistent with the current density maps. A literal code, developed to give a compact description of the tropicities of currents flowing around rings and bonds cut by the scan trajectory shows that, in most cases, the NICS-XY method leads to an exact match with the current density analyses. Mismatches are generally due to small circulations out of the scan trajectory, and they do not correspond to misinterpretations of the overall tropicities. The dataset provides several cases where the prediction of the overall antiaromatic/aromatic response by the 4n/4n+2 count of π electrons fails.

An Additivity Scheme for Aromaticity: The Heteroatom Case.

The nucleus-independent chemical shift (NICS)-XY-Scan is a simple and easy tool for the quantitative measurement of the aromaticity of polycyclic aromatic hydrocarbons and identification of the existence of local and global ring currents. We recently introduced an additivity scheme that uses the NICS-XY-Scans of smaller building blocks to predict the aromatic profiles of larger polycyclic aromatic hydrocarbon systems. We now report on an expansion of the methodology to include systems of varying aromatic natures containing the heteroatoms B, N, O, and S. The additivity approach allows for rapid and resource-efficient generation of NICS-XY-Scans of large, complex systems. Moreover, it reveals that the magnetic criterion of aromaticity behaves in an additive manner, and that the ring currents of multi-ring systems appear to be mostly localized within subunits of up to three rings.

Aromatic Pathways in Porphycene Derivatives Based on Current-Density Calculations.

Magnetically induced current densities have been calculated for porphycenes at the density functional theory level using gauge-including atomic orbitals to ensure gauge-origin independence and a fast basis-set convergence of the current densities. The current densities have been analyzed by using the gauge-including magnetically induced current (GIMIC) method. The porphycenes are aromatic, sustaining strong diatropic ring currents. The ring-current pathways have been determined by integrating the strength of the current density passing selected bonds. The calculations show that the ring current of the porphycenes splits into an outer and inner branch at the pyrrolic rings implying that the ring current involves all 26 π electrons of the porphycenes, which is similar to the ring current of porphyrins. The pyrrolic rings of the aromatic porphycenes do not sustain any significant local ring currents. Dihydroporphycene with four inner hydrogens is antiaromatic with weakly aromatic pyrrolic rings. The annelated benzoic rings in benzoporphycene sustain local paratropic ring currents, whereas the global ring current of dibenzoporphycene splits into an outer and inner branch at the benzoic rings. Comparison of calculated1H NMR shieldings with ring-current strengths shows that interactions between the inner hydrogen and the neighbor nitrogen is more significant for differences in the 1H NMR shieldings than variations in global ring-current strengths. Calculated excitation energies show that the antiaromatic dihydroporphycene has a smaller optical gap than the aromatic porphycene, even though its HOMO-LUMO gap is larger.

Magnetic Diversity in Heteroisocorroles: Aromatic Pathways in 10-Heteroatom-Substituted Isocorroles.

A recent study on magnetically induced currents in 10-isocorrole derivatives indicated that both the free-base and metal-complexed forms of the unsubstituted macrocycle are homoaromatic. Furthermore, depending on the substituents at the 10-position, the aromatic character was found to swing between substantially homoaromatic to substantially antihomoaromatic. Heteroisocorroles, in which the saturated 10-position has been replaced by a heteroatom-containing group X, are predicted to exhibit even more dramatic variations in aromatic character, ranging from strongly aromatic (X = O, NH, PH, and S) to strongly antiaromatic (X = BH and CO). Interestingly, the experimentally studied X = SiMe2 case does not appear to sustain a significant global ring current.

Is (benzene)Cr(CO)3 really more aromatic than benzene?

(benzene)Cr(CO)3 was claimed to be more aromatic than benzene, based on the central 1H Me chemical shifts in dimethyldihydropyrene annulated to it. In this paper, several dihydropyrenes are computationally investigated. NICS-scan methods are used to assess the ring current properties, and NMR calculations are used for obtaining NMR chemical shifts. The parent and four benz-annulated dihydropyrenes show excellent agreement with the experimental results, reported by R. Mitchell in several papers. The effect of annulating the antiaromatic cyclobutadiene was shown to be larger than that of benzene and to change the type of ring currents; while benz-annulated dihydropyrenes maintain local 14-annulene and local benzenic ring currents, the cyclobutadiene-annulated dihydropyrenes show global (and local) ring currents. A NICS-scan study of (benzene)Cr(CO)3 and a NICS-XY-scan study of the (CO)3Cr(C6H4)-annulated to dihydropyrene show that the benzene in the Cr complex is at most aromatic as benzene, probably somewhat less. A detailed study of the 1H chemical shifts suggests that the experimental results were somewhat misinterpreted, and that (benzene)Cr(CO)3 is at most as aromatic as benzene.

Aromatic and antiaromatic ring currents in a molecular nanoring.

Aromatic and antiaromatic molecules-which have delocalized circuits of [4n + 2] or [4n] electrons, respectively-exhibit ring currents around their perimeters. The direction of the ring current in an aromatic molecule is such as to generate a magnetic field that opposes the external field inside the ring (a 'diatropic' current), while the ring current in an antiaromatic molecule flows in the reverse direction ('paratropic'). Similar persistent currents occur in metal or semiconductor rings, when the phase coherence of the electronic wavefunction is preserved around the ring. Persistent currents in non-molecular rings switch direction as a function of the magnetic flux passing through the ring, so that they can be changed from diatropic ('aromatic') to paratropic ('antiaromatic') simply by changing the external magnetic field. As in molecular systems, the direction of the persistent current also depends on the number of electrons. The relationship between ring currents in molecular and non-molecular rings is poorly understood, partly because they are studied in different size regimes: the largest aromatic molecules have diameters of about one nanometre, whereas persistent currents are observed in microfabricated rings with diameters of 20-1,000 nanometres. Understanding the connection between aromaticity and quantum-coherence effects in mesoscopic rings provides a motivation for investigating ring currents in molecules of an intermediate size. Here we show, using nuclear magnetic resonance spectroscopy and density functional theory, that a six-porphyrin nanoring template complex, with a diameter of 2.4 nanometres, is antiaromatic in its 4+ oxidation state (80 π electrons) and aromatic in its 6+ oxidation state (78 π electrons). The antiaromatic state has a huge paramagnetic susceptibility, despite having no unpaired electrons. This work demonstrates that a global ring current can be promoted in a macrocycle by adjusting its oxidation state to suppress the local ring currents of its components.The discovery of ring currents around a molecule with a circumference of 7.5 nanometres, at room temperature, shows that quantum coherence can persist in surprisingly large molecular frameworks.

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

Magnetically induced current susceptibilities and current pathways have been calculated for molecules consisting of two pentalene groups annelated with a benzene (1) or naphthalene (2) moiety. Current strength susceptibilities have been obtained by numerically integrating separately the diatropic and paratropic contributions to the current flow passing planes through chosen bonds of the molecules. The current density calculations provide novel and unambiguous current pathways for the unusual molecules with annelated aromatic and antiaromatic hydrocarbon moieties. The calculations show that the benzene and naphthalene moieties annelated with two pentalene units as in molecules 1 and 2, respectively, are unexpectedly antiaromatic sustaining only a local paratropic ring current around the ring, whereas a weak diatropic current flows around the C-H moiety of the benzene ring. For 1 and 2, the individual five-membered rings of the pentalenes are antiaromatic and a slightly weaker semilocal paratropic current flows around the two pentalene rings. Molecules 1 and 2 do not sustain any net global ring current. The naphthalene moiety of the molecule consisting of a naphthalene annelated with two pentalene units (3) does not sustain any strong ring current that is typical for naphthalene. Instead, half of the diatropic current passing the naphthalene moiety forms a zig-zag pattern along the C-C bonds of the naphthalene moiety that are not shared with the pentalene moieties and one third of the current continues around the whole molecule partially cancelling the very strong paratropic semilocal ring current of the pentalenes. For molecule 3, the pentalene moieties and the individual five-membered rings of the pentalenes are more antiaromatic than for 1 and 2. The calculated current patterns elucidate why the compounds with formally [4n + 2] π-electrons have unusual aromatic properties violating the Hückel π-electron count rule. The current density calculations also provide valuable information for interpreting the measured (1)H NMR spectra.

The NICS‐XY‐Scan: Identification of Local and Global Ring Currents in Multi‐Ring Systems

Nucleus-independent chemical shift (NICS)-based methods are very popular for the determination of the induced magnetic field under an external magnetic field. These methods are used mostly (but not only) for the determination of the aromaticity and antiaromaticity of molecules and ions, both qualitatively and quantitatively. The ghost atom that serves as the NICS probe senses the induced magnetic field and reports it in the form of an NMR chemical shift. However, the source of the field cannot be determined by NICS. Thus, in a multi-ring system that may contain more than one induced current circuit (and therefore more than one source of the induced magnetic field) the NICS value may represent the sum of many induced magnetic fields. This may lead to wrong assignments of the aromaticity (and antiaromaticity) of the systems under study. In this paper, we present a NICS-based method for the determination of local and global ring currents in conjugated multi-ring systems. The method involves placing the NICS probes along the X axis, and if needed, along the Y axis, at a constant height above the system under study. Following the change in the induced field along these axes allows the identification of global and local induced currents. The best NICS type to use for these scans is NICSπZZ , but it is shown that at a height of 1.7 Å above the molecular plane, NICSZZ provides the same qualitative picture. This method, namely the NICS-XY-scan, gives information equivalent to that obtained through current density analysis methods, and in some cases, provides even more details.

Relativistic ring currents in metallabenzenes: an analysis in terms of contributions of localised orbitals

Ring currents calculated in the ipsocentric CTOCD-DZ formalism are presented for four representative metallabenzenes, compounds in which a benzene CH group is formally replaced by a transition metal atom with ligands. Aromaticity is probed using ring currents computed using non-relativistic and relativistic orbitals (derived with relativistic effective core potentials or ZORA). Maps computed at different levels of relativistic theory turn out to be similar, showing that orbital nodal character is the main determinant of ring current. Diatropic/paratropic global ring currents in these compounds, and also circulations localised on the metal centre, are interpreted in terms of contributions of localised π-type orbitals and metal d-orbitals, respectively. All four considered metallabenzenes should be regarded as 6π electron species, despite the fact that three support diatropic ('aromatic') ring currents and one a paratropic ('anti-aromatic') current. The current-density maps determine the correct way to count electrons in these species: differential occupation of d-orbitals of formal π-symmetry contributes to circulation on the metal centre, but not around the benzenoid ring. The overall trend from strongly diatropic to weakly paratropic ring currents along the series 1 to 4 is explained by the increasing strength of interaction between formally non-bonding orbitals on the metal centre and C(5)H(5) moiety, which together make up the six-membered ring.

Calculation of Magnetically Induced Currents in Hydrocarbon Nanorings

Magnetically induced current densities, nuclear magnetic shieldings, and electric polarizabilities of planar ring-shaped hydrocarbons have been studied at the density-functional theory level using the Becke-Perdew (BP86) functional. The current densities were calculated using the Gauge-Including Magnetically Induced Current (GIMIC) method employing gauge-including atomic orbitals. The GIMIC calculations yield rules to estimate the global and local ring-current strengths as well as the current pathways for the hydrocarbon nanorings. For the overall antiaromatic molecules, aromatic groups such as benzene, naphthalene, anthracene, and pyrene moieties localize the ring current making the global ring currents vanish. The ability of the edge groups to localize the currents is related to the aromatic character of the molecule as a whole. The local ring current prefers to follow the edges of the group. Phenalenyl corner moieties are found to introduce strong global ring currents, whereas with fused benzene and pyrene corner groups the global ring current vanishes. Fused benzene rings in the corner or along the edge of overall antiaromatic molecules sustain local ring currents of about the same size as for a free benzene molecule. For the overall aromatic molecules, the global ring current is split along the bonds of the edge moieties, but the detailed division fulfilling Kirchhoff's current law is not easily predictable and must be calculated for each individual bond. At the phenalenyl corner moieties, the global ring current follows the innermost route isolating the rest of the group from the main delocalization pathway. A hydrocarbon nanoring sustaining strong ring currents should be large and formally aromatic with many and large aromatic moieties along the edges. A clear correlation between the strength of the global ring currents and the size of the electric polarizabilities is obtained. The calculated 1H NMR shieldings of a proton in immediate contact to the global ring current vary between 22 ppm and 67 ppm in the studied molecules. The trend correlates well with the global ring-current strengths, which are in the range of 0-88 nA/T. The 13C NMR shieldings are also sensitive to the strength of the global ring current, but they vary less systematically and are not as good an indicator of the current strength as the hydrogen shieldings.

A statistical study of unstable particle populations in the global ringcurrent and their relation to the generation of high <i>m</i> ULF waves

Abstract. The first statistical study of the unstable proton populations which contain "free energy" required to drive small-scale poloidal mode ULF waves in the magnetosphere between L-shell locations of 6 and 9 is presented. The data examined are all in the form of Ion Distribution Functions (IDFs) covering a particle energy range of 0.025keV to 328keV, amassed over 2.5 years from the TIMAS and CAMMICE (MICS) instruments on-board the Polar spacecraft. Any free energy which is available to drive a resonant wave mode manifests itself as a positive gradient region in the IDF. A new analysis technique applied to the data, allows for the first time, the amount of free energy contained in each IDF to be quantified. The results show that IDFs are a common occurrence in the magnetosphere at these L-shells, although they are most common in the dawn/pre-noon sector. Lower energy (10–45keV) protons are the most commonly observed unstable populations and also contain the largest amounts of free energy (>1010J). Positive gradient regions at higher energies (>100keV) are rarely observed and also contain greatly reduced free energies (<109J). Key words. Magnetospheric physics (Energetic particles, trapped; MHD waves and instabilities) – Space plasma physics (wave-particle interactions)