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#### MCD C-Term Signs, Saturation Behavior, and Determination of Band Polarizations in Randomly Oriented Systems with Spin S ≥ 1/2. Applications to S = 1/2 and S = 5/2

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Neese, F., & Solomon, E. I. (1999). MCD C-Term Signs, Saturation Behavior, and
Determination of Band Polarizations in Randomly Oriented Systems with Spin S ≥ 1/2. Applications to S = 1/2 and S = 5/2.* Inorganic Chemistry,* *38*(8), 1847-1865. doi:10.1021/ic981264d.

Cite as: http://hdl.handle.net/21.11116/0000-0007-F28F-7

##### Abstract

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.