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We present an extensive study of the performance of mean-field approximations to the spin-orbit operators on realistic molecular systems, as widely used in applications like single-molecule magnets, molecular quantum bits, and molecular spintronic devices. The test systems feature a 3d transition-metal center ion (V, Cr, Mn, Fe, Co, and Ni) in various coordinations and a multitude of energetically close-lying open-shell configurations that can couple via the spin-orbit operator. We performed complete active space spin-orbit configuration interaction calculations and compared the full two-electron Breit-Pauli spin-orbit operator to different approximations: the one-center approximation, the spin-orbit mean-field approach with electron densities from different state-averaging procedures, and the atomic mean-field integral approximation. We show that the mean-field approaches can lead to significant errors in the spin-orbital coupling matrix elements, which becomes particularly visible for the computed zero-field splittings. The one-center approximation, keeping all relevant two-electron terms, seems to be a significantly more accurate choice for the examples from our test set.

We present the in-depth determination of the magnetic properties and electronic structure of the luminescent and volatile dysprosium-based single molecule magnet [Dy 2 (bpm)(fod) 6 ] (Hfod = 6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedione, bpm = 2,2'-bipyrimidine). Ab initio calculations were used to obtain a global picture of the electronic structure and to predict possible single molecule magnet behaviour, confirmed by experiments. The orientation of the susceptibility tensor was determined by means of cantilever torque magnetometry. An experimental determination of the electronic structure of the lanthanide ion was obtained combining Luminescence, Far Infrared and Magnetic Circular Dichroism spectroscopies. Fitting these energies to the full single ion plus crystal field Hamiltonian allowed determination of the eigenstates and crystal field parameters of a lanthanide complex without symmetry idealization. We then discuss the impact of a stepwise symmetry idealization on the modelling of the experimental data. This result is particularly important in view of the misleading outcomes that are often obtained when the symmetry of lanthanide complexes is idealized.