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

The valence intermediate effective Hamiltonian (VIEH) approach has become a powerful tool for dissecting the fundamental components of spin-state energetics in magnetically coupled system. Combined with differently sized complete active space approaches (CASSCF), this method enables a decomposition of the magnetic coupling constant J into its underlying physical contributions. Herein, we extend the VIEH framework to complexes with multiple magnetic coupling pathways. This approach is showcased with a homologous series of [M2(μ−O)(NH3)n]2+ complexes including Cu(II), Ni(II), and Fe(II). Typically, antiferromagnetic coupling progressively weakens from copper to nickel and iron. We demonstrate that this weakening arises primarily from an increase in the ferromagnetic coupling contribution across this series.