It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

中文翻译：

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电流密度张量

结果表明，与磁场和核磁偶极矩所感应的电流密度有关的非对称二阶电流密度张量是分子的基本特性。连同可磁化性，核磁屏蔽和核自旋自旋耦合一起，它们完全表征了其对磁扰动的响应。讨论了量规不变性，分解为各向同性，偏斜和反对称的零件，以及电流密度张量对磁性能的影响。通过将它们明确地与感应电流密度矢量的方向以及电流密度张量的分量相关联的关系，可以合理化第二阶张量特性的分量。偏斜部分对磁化率，核屏蔽，由电流密度张量的反对称部分唯一确定的核自旋-自旋耦合将完全消失。研究了电流密度张量的各向同性和各向异性不变量的物理含义，并讨论了各向异性大小与电子离域的关系。