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

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• 作者：Stefano Pelloni ; Paolo Lazzeretti
• 刊名：Journal of Physical Chemistry A
• 出版年：2013
• 出版时间：September 19, 2013
• 年：2013
• 卷：117
• 期：37
• 页码：9083-9092
• 全文大小：580K
• 年卷期：v.117,no.37(September 19, 2013)
• ISSN：1520-5215

文摘

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鈥揝avart 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, 尉, and the magnetic shielding 蟽(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 蟽(h) = 卤(渭₀/2蟺)尉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 尉 is proportional to the area of the polygon, that is, d²; hence, the shielding 蟽(0) and the related nucleus-independent chemical shift NICS(0) are unsafe quantifiers of magnetotropicity; they are biased by a spurious geometrical dependence on d^鈥?, 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 B_ext applied at right angles to the molecular plane, is defined within the polygonal current model by the current susceptibility or current strength, 鈭?i>I/鈭?i>B_ext = 鈭捨?sub>/A_eff, expressed in nanoamp猫re per tesla, where A_eff is a properly defined area enclosed with the polygonal circuit. An extended numerical test on a wide series of mono- and 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.