Neese Frank, Solomon Edward I.
Department of Chemistry, Stanford University, Stanford, California 94305.
Inorg Chem. 1999 Apr 19;38(8):1847-1865. doi: 10.1021/ic981264d.
The magnetic circular dichroism (MCD) properties of a spin-allowed transition from an orbitally nondegenerate ground state manifold A to an orbitally nondegenerate excited state manifold J in the presence of spin-orbit coupling (SOC) are derived for any S >/= (1)/(2). Three physically distinct mechanisms are identified that lead to MCD intensity and depend on SOC between excited states which leads to a sum rule and SOC between the ground state and other excited states that leads to deviations from the sum rule. The model is valid for any symmetry of the magnetic coupling tensors and arbitrary transition polarizations. The S = (1)/(2) case is analytically solved, and the determination of linear polarizations from MCD saturation magnetization data is discussed. For all mechanisms the MCD intensity is proportional to the spin-expectation values of the ground state sublevels which are conveniently generated from a spin-Hamiltonian (SH). For Kramers systems with large zero-field splittings (ZFSs) this allows the contribution from each Kramers doublet to the total MCD intensity to be related through their effective g-values, therefore significantly reducing the number of parameters required to analyze experimental data. The behavior of high-spin systems is discussed in the limits of weak, intermediate, and strong ZFS relative to the Zeeman energy. The model remains valid in the important case of intermediate ZFS where the ground state sublevels may cross as a function of applied magnetic field and there are significant off-axis contributions to the MCD intensity due to a change of the electron spin quantization axis. The model permits calculation of MCD C-term signs from molecular wave functions, and explicit expressions are derived in terms of MOs for S = (1)/(2) and S = (5)/(2). Two examples from the literature are analyzed to demonstrate how the C-term signs can be evaluated by a graphical method that gives insight into their physical origin.
在自旋轨道耦合（SOC）存在的情况下，对于任意(S \geq \frac{1}{2})，推导了从轨道非简并基态流形(A)到轨道非简并激发态流形(J)的自旋允许跃迁的磁圆二色性（MCD）性质。确定了三种物理上不同的机制，它们导致MCD强度，并且取决于激发态之间的SOC，这导致了一个求和规则，以及基态与其他激发态之间的SOC，这导致了与求和规则的偏差。该模型对于磁耦合张量的任何对称性和任意跃迁极化均有效。解析求解了(S = \frac{1}{2})的情况，并讨论了从MCD饱和磁化强度数据确定线性极化的问题。对于所有机制，MCD强度与基态子能级的自旋期望值成正比，这些期望值可方便地从自旋哈密顿量（SH）生成。对于具有大零场分裂（ZFS）的克莱默斯体系，这使得每个克莱默斯二重态对总MCD强度的贡献可以通过它们的有效(g)值相关联，从而显著减少分析实验数据所需的参数数量。在相对于塞曼能量的弱、中、强ZFS极限下讨论了高自旋体系的行为。该模型在重要的中ZFS情况下仍然有效，在这种情况下，基态子能级可能随外加磁场而交叉，并且由于电子自旋量子化轴的变化，对MCD强度有显著的离轴贡献。该模型允许从分子波函数计算MCD C项符号，并针对(S = \frac{1}{2})和(S = \frac{5}{2})以分子轨道（MO）的形式导出显式表达式。分析了文献中的两个例子，以展示如何通过一种图形方法评估C项符号，该方法能深入了解其物理起源。
