The spin magnetic order of Co⁺ (n ≤ 5) clusters

The magnetism of transition metal clusters has been for decades a complicated puzzle, with experimental results disagreeing with calculations performed within the density functional theory formalism. In this work, we provide a key to this puzzle by investigating the lowest-energy spin states of cobalt cluster, Co⁺ (n ≤ 5), using CASSCF/NEVPT2 calculations with very large active spaces. The geometries as well as the spin configurations adopted by the clusters in their ground-state are known from experiments, making Co⁺ clusters an ideal model system for theoretical investigation. Here, using the experimentally known geometries determined by far-infrared spectroscopy as inputs, we calculated the lowest-energy spin configurations of the clusters, revealing that the CASSCF/NEVPT2 formalism correctly predicts the preferred electronic configuration of the clusters known experimentally. This is in contrast to the widely used density functional theory, with results that depend on the selected exchange-correlation functional. The reasons for the failure of density functional theory, in opposition to CASSCF/NEVPT2, are discussed, providing a solid framework for investigating other transition metal and transition metal oxide clusters.