Magnetic Exchange Coupling in Radical-Bridged Lanthanide Complexes

Exchange coupling in radical-bridged lanthanide complexes is a crucial aspect of their magnetic behavior, but it is challenging to model due to the interplay of strong electron correlation, spin-orbit coupling, and the localized nature of 4f orbitals. Here, we present a comprehensive ab initio analysis of isotropic and anisotropic exchange interactions in two families of radical-bridged dilanthanide complexes, [(Cp₂^*Ln)₂(μ - bpym^•)]⁺ and [(Cp₂^*Ln)₂(μ - Co(pdt)₂)], where Ln = Gd³⁺ and Dy³⁺; Cp* = pentamethylcyclopentadienyl; and the radical ligands are bpym = bipyrimidyl and pdt^2- = 1,2-diphenylethylene-dithiolate. The microscopic contributions of direct and kinetic exchange to the isotropic exchange in the radical-bridged gadolinium complexes are disentangled, revealing that antiferromagnetic coupling in the μ-bpym^•-bridged complex is dominated by virtual intersite electron hopping, largely facilitated by the delocalized radical orbitals, while ferromagnetic behavior in the μ-Co(pdt)₂-bridged complex arises from direct exchange where virtual electron hopping is greatly hindered by localized d-orbitals. The finding thus explains the experimentally observed ferromagnetic coupling in a large number of gadolinium-transition metal complexes as well as observed antiferromagnetic coupling in the aromatic radical-bridged lanthanide complexes. Extending to radical-bridged dysprosium complexes, multiconfigurational spin-orbit calculations capture the full anisotropic exchange coupling, enabling the construction of effective exchange and crystal field Hamiltonians. The computed low-energy spectra and magnetic properties show close agreement with the experiment, clarifying the distinct ferro- versus antiferromagnetic ground states. This study provides a unified framework for quantifying and interpreting exchange in radical-bridged lanthanides, thereby advancing predictive design strategies for molecular magnetism.