The application of the Biot-Savart law to the ring current analysis of proton chemical shifts—I

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.

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.

Topological ring-currents and bond-currents in some nonalternant isomers of coronene

The Hückel-London-Pople-McWeeny (HLPM) (topological) approach for calculating π-electron ring-currents and bond-currents in conjugated systems is applied to coronene and the 17 nonalternant isomers of it for which Balaban, Bean, and Fowler recently published ab initio ipso-centric π-electron current-density maps. In a parallel investigation to that conducted by Balaban et al., the key findings of their quantum-mechanical study are confirmed by this topological one: (a) all seven rings in all of the 18 structures studied are found to bear substantial diamagnetic ring-currents, greater than the benzene value; (b) all 18 conjugated systems have a pronounced, overall London diamagnetic-susceptibility, perpendicular to their respective molecular-planes; (c) a substantial diamagnetic current runs around the periphery of each of these structures; and (d) there is general agreement between the two studies as to which structures, of those treated, respect the annulene-within-an-annulene model for conjugated systems of this sort. The same ideas are also tested against ring-current and bond-current intensities recently calculated by Randić et al. using purely graph-theoretical methods that are based on circuits of conjugation. Considerable qualitative agreement is found, and when there is disagreement, arguments are offered as to why the HLPM topological ring-currents and bond-currents are to be preferred.

The Phenalenyl Motif: A Magnetic Chameleon

The 12pi cation (3) and 14pi anion (4) derived from the phenalenyl radical (2) support diatropic ("aromatic") perimeter ring currents, but isoelectronic replacement of the central atom by either boron (5) or nitrogen (6) leads to paratropic ("antiaromatic") current; the ipsocentric approach to molecular magnetic response accounts for all four patterns in terms of competition between translationally and rotationally allowed virtual pi-pi* excitations.

Ring-Current Models from the Differential Biot-Savart Law

The differential Biot-Savart law provides simple models for the pi ring currents induced in diatropic and paratropic planar conjugated molecules by a perpendicular magnetic field. The model predictions are confirmed by ab initio maps of nuclear magnetic shielding density. The effects on the protons and on the ring carbon atoms from the closest and furthest segments of the current loop are easily interpreted. [structure: see text]

Ring Currents in Icosahedral C60

A new formulation of the current within the London approximation allows the calculation of ring currents in topologically complex molecules. Application of this theory to C(60) demonstrates the existence of remarkable pi electron ring currents. Paramagnetic currents, in size comparable to the ones in benzene, flow within the pentagons, whereas weaker diamagnetic currents flow all around the C.(60) molecule. The overall vanishing ring-current magnetic susceptibility results from a cancellation of diamagnetic and paramagnetic contributions. The presence of ring currents significantly affects chemical shifts as measured in nuclear magnetic resonance experiments. In contrast to the magnetic susceptibility, which is a property of the molecule as a whole, chemical shifts are sensitive to the local magnetic field and the effect of ring currents does not vanish.