Mechanism of L 2,3 -edge x-ray magnetic circular dichroism intensity from quantum chemical calculations and experiment-A case study on V (IV) /V (III) complexes.

In this work, we present a combined experimental and theoretical study on the V L _2,3 -edge x-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectra of V ^IV O(acac) ₂ and V ^III (acac) ₃ prototype complexes. The recorded V L _2,3 -edge XAS and XMCD spectra are richly featured in both V L ₃ and L ₂ spectral regions. In an effort to predict and interpret the nature of the experimentally observed spectral features, a first-principles approach for the simultaneous prediction of XAS and XMCD spectra in the framework of wavefunction based ab initio methods is presented. The theory used here has previously been formulated for predicting optical absorption and MCD spectra. In the present context, it is applied to the prediction of the V L _2,3 -edge XAS and XMCD spectra of the V ^IV O(acac) ₂ and V ^III (acac) ₃ complexes. In this approach, the spin-free Hamiltonian is computed on the basis of the complete active space configuration interaction (CASCI) in conjunction with second order N-electron valence state perturbation theory (NEVPT2) as well as the density functional theory (DFT)/restricted open configuration interaction with singles configuration state functions based on a ground state Kohn-Sham determinant (ROCIS/DFT). Quasi-degenerate perturbation theory is then used to treat the spin-orbit coupling (SOC) operator variationally at the many particle level. The XAS and XMCD transitions are computed between the relativistic many particle states, considering their respective Boltzmann populations. These states are obtained from the diagonalization of the SOC operator along with the spin and orbital Zeeman operators. Upon averaging over all possible magnetic field orientations, the XAS and XMCD spectra of randomly oriented samples are obtained. This approach does not rely on the validity of low-order perturbation theory and provides simultaneous access to the calculation of XMCD A, B, and C terms. The ability of the method to predict the XMCD C-term signs and provide access to the XMCD intensity mechanism is demonstrated on the basis of a generalized state coupling mechanism based on the type of the excitations dominating the relativistically corrected states. In the second step, the performance of CASCI, CASCI/NEVPT2, and ROCIS/DFT is evaluated. The very good agreement between theory and experiment has allowed us to unravel the complicated XMCD C-term mechanism on the basis of the SOC interaction between the various multiplets with spin S' = S, S ± 1. In the last step, it is shown that the commonly used spin and orbital sum rules are inadequate in interpreting the intensity mechanism of the XAS and XMCD spectra of the V ^IV O(acac) ₂ and V ^III (acac) ₃ complexes as they breakdown when they are employed to predict their magneto-optical properties. This conclusion is expected to hold more generally.