Dipartimento di Chimica, dell'Università degli Studi di Modena , via Campi 183, 41100 Modena, Italy.
J Phys Chem A. 2013 Sep 19;117(37):9083-92. doi: 10.1021/jp406348j. Epub 2013 Sep 6.
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, ∼d(2); hence, the shielding σ∥(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(-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 nanoampère per tesla, where Aeff 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.
为了解释电子离域对平面环状分子磁响应的特殊影响，我们开发了一个基本模型，该模型通过整合微分毕奥-萨伐尔定律来考虑其实际的几何结构。该模型基于具有理想特征的单个多边形电路，适用于电中性或带电的单环化合物以及线性多环稠合碳氢化合物。两个理论量，通过量子化学代码很容易计算（在垂直于分子平面的对称轴上的点 P 的矢磁率的离面分量 ξ∥和磁屏蔽 σ∥(h)，与质心的距离为 h），例如对于单环结构，通过关系 σ∥(h) = ±(μ0/2π)ξ∥D(h) 线性连接，其中 D(h) 是几何参数的简单函数。这种类型的方程有助于合理化磁屏蔽和核独立化学位移沿最高对称轴的扫描轮廓。对于正多边形，D(h) 近似取决于顶点与质心的距离 d 的立方倒数，而 ξ∥与多边形的面积成正比，即 ∼d(2)；因此，屏蔽 σ∥(0) 和相关的核独立化学位移 NICS∥(0) 是磁各向异性的不安全量度；它们被与 d(-1) 的虚假几何依赖性所偏置，在尺寸较小的环状系统中错误地将其排除在外。在垂直于分子平面的外磁场 Bext 的存在下，对于环状化合物，定义了一个更可靠的磁各向异性度量，该度量由多边形电流模型中的电流磁化率或电流强度 ∂I/∂Bext = -ξ∥/Aeff 定义，单位为纳安每特斯拉，其中 Aeff 是用多边形电路适当定义的面积。对广泛的单环和多环化合物系列进行的扩展数值测试以及与相应从头算电流磁化率的比较证明，该指标在磁标准上优于其他常用的芳香性/反芳香性基准。
