Polygonal Current Model: An Effective Quantifier of Aromaticity on the Magnetic Criterion

To explain peculiar effects of electron delocalization
on the magnetic response of planar cyclic molecules, a
basic model that accounts for their actual geometrical structure
has been developed by integrating the differential Biot−Savart
law. Such a model, based on a single polygonal circuit with
ideal features, is shown to be applicable to electrically neutral
or charged monocyclic compounds, as well as linear polycyclic
condensed hydrocarbons. Two theoretical quantities, easily computed via quantum chemistry codes (the out-of-plane
components of the magnetizability, ξ∥, and the magnetic shielding σ∥(h) of points P on the symmetry axis orthogonal to the
molecular plane, at distance h from the center of mass) are shown to be linearly connected, for example, for monocyclic
structures, via the relationship σ∥(h) = ±(μ0/2π)ξ∥D(h), where D(h) is a simple function of geometrical parameters. Equations of
this type are useful to rationalize scan profiles of magnetic shielding and nucleus-independent chemical shift along the highest
symmetry axis. For a regular polygon, D(h) depends approximately on the third inverse power of the distance d of the vertices
from the center, and ξ∥ is proportional to the area of the polygon, that is, ∼d2; hence, the shielding σ∥(0) and the related nucleusindependent
chemical shift NICS∥(0) are unsafe quantifiers of magnetotropicity; they are biased by a spurious geometrical
dependence on d−1, incorrectly exhalting them in cyclic systems with smaller size. A more reliable magnetotropicity measure for a
cyclic compound, in the presence of a magnetic field Bext applied at right angles to the molecular plane, is defined within the
polygonal current model by the current susceptibility or current strength, ∂I/∂Bext = −ξ∥/Aeff, expressed in nanoampe re per tesla,
where Aeff is a properly defined area enclosed with the polygonal circuit. An extended numerical test on a wide series of monoand
polycyclic compounds and a comparison with corresponding ab initio current susceptibilities prove the superior quality of
this indicator over other commonly employed aromaticity/antiaromaticity benchmarks on the magnetic criterion.