Decomposition of magnetic coupling in µ-oxo-bridged metal complexes

Magnetic coupling is a fundamental property of multinuclear transition metal complexes with implications for magnetic applications and potentially even catalysis. It has long been established that both ferromagnetic and antiferromagnetic components contribute to the overall magnetic coupling. We herein propose a methodology that can disentangle these contributions even for complexes with multiple magnetic coupling paths. To this end, we employ foundational equations by R. Hoffmann, O. Kahn and B. Briat in a multicomponent fitting procedure applied to CASSCF and CASSCF/NEVPT2 calculations. For a series of [M2(µ-O)(NH3 )n]2+ complexes with iron, nickel and copper, our method reveals that σ paths contribute twice as much antiferromagnetic coupling as π paths, and that δ paths have no quantitative effect on the overall coupling strength. The ferromagnetic contribution varies little within the series. We discuss technical limitations of the CASSCF/NEVPT2 results related to missing excitation, polarisation and dynamical correlation effects and propose that modifications of the underlying fitting equations will lead to quantitative results for realistic complexes.