On the Accuracy of Mean-Field Spin–Orbit Operators for 3d Transition-Metal Systems
Résumé
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.