We present the in-depth determination of the magnetic properties and electronic structure of the luminescent and volatile dysprosium-based single molecule magnet [Dy2(bpm)(fod)6] (Hfod = 6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedione, bpm = 2,2-bipyrimidine).

We propose a machine learning method to model molecular tensorial quantities, namely, the magnetic anisotropy tensor, based on the Gaussian moment neural network approach. We demonstrate that the proposed methodology can achieve an accuracy of 0.3−0.4 cm −1 and has excellent generalization capability for out-of-sample configurations. Moreover, in combination with machine-learned interatomic potential energies based on Gaussian moments, our approach can be applied to study the dynamic behavior of magnetic anisotropy tensors and provide a unique insight into spin−phonon relaxation.

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 closelying 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.

Correction for ‘Determination of the electronic structure of a dinuclear dysprosium single molecule magnet without symmetry idealization’ by Mauro Perfetti et al., Chem. Sci., 2019, 10, 2101–2110.