Dipartimento di Chimica dell'Università degli Studi di Modena e Reggio Emilia, Via Campi 183, 41124 Modena, Italy.
J Chem Phys. 2012 Aug 21;137(7):074108. doi: 10.1063/1.4745077.
A gauge transformation of the vector potential A(m(I)), associated to the magnetic dipole m(I) of nucleus I in a molecule, has been studied. The conditions for gauge invariance of nuclear magnetic shielding, nuclear spin/electron orbit contribution to spin-spin coupling between two nuclei, I and J, and electronic current density induced by m(I), have been expressed via quantum mechanical sum rules that are identically satisfied for exact and optimal variational wavefunctions. It is shown that separate diamagnetic and paramagnetic contributions to the properties transform into one another in the gauge transformation, whereas their sum is invariant. Therefore, only total response properties have a physical meaning. In particular, the disjoint diamagnetic and paramagnetic components of nuclear spin/electron orbit contributions to coupling constants are not uniquely defined. The diamagnetic contribution to the nuclear spin-spin coupling tensor, evaluated as an expectation value in the Ramsey theory, can alternatively be expressed as a sum-over-states formula, by rewriting the second-order Hamiltonian in commutator form à la Geertsen, as previously reported by Sauer. Other sum-over-states formulae are obtained via a gauge transformation, by a procedure formally allowing for a continuous translation of the origin of the m(I)-induced current density, analogous to those previously proposed for magnetizabilities and nuclear magnetic shielding.
已经研究了与分子中核 I 的磁偶极子 m(I)相关的向量势 A(m(I))的规范变换。核磁共振屏蔽、核自旋/电子轨道对两个核 I 和 J 之间自旋-自旋耦合的贡献以及由 m(I)引起的电子电流密度的规范不变性的条件，已经通过量子力学求和规则表示出来，这些求和规则对于精确和最优变分波函数是完全满足的。结果表明，在规范变换中，各向异性和各向异性对性质的贡献可以相互转化，而它们的和是不变的。因此，只有总响应性质才有物理意义。特别是，耦合常数的核自旋/电子轨道贡献的不相关抗磁性和顺磁性分量不能唯一地定义。在 Ramsey 理论中作为期望值评估的核自旋-自旋耦合张量的抗磁性贡献，可以通过将二阶哈密顿量改写为类似于 Geertsen 的换子形式的求和公式，以替代 Sauer 之前报道的公式来表示。其他求和公式是通过规范变换获得的，通过一种程序，通过类似于以前提出的磁导率和核磁共振屏蔽的程序，可以连续平移 m(I)引起的电流密度的原点，从而允许连续平移 m(I)引起的电流密度的原点。
