Ab initio-based determination of lanthanoid-radical exchange as visualised by inelastic neutron scattering

Magnetic exchange coupling can modulate the slow magnetic relaxation in single-molecule magnets. Despite this, elucidation of exchange coupling remains a significant challenge for the lanthanoid(III) ions, both experimentally and computationally. In this work, the crystal field splitting and 4f-pi exchange coupling in the erbium-semiquinonate complex [ErTp(2)dbsq] (<bold>Er-dbsq</bold>; Tp(-) = hydro-tris(1-pyrazolyl)borate, dbsqH(2) = 3,5-di-tert-butyl-1,2-semiquinone) have been determined by inelastic neutron scattering (INS), magnetometry, and CASSCF-SO ab initio calculations. A related complex with a diamagnetic ligand, [ErTp(2)trop] (<bold>Er-trop</bold>; tropH = tropolone), has been used as a model for the crystal field splitting in the absence of coupling. Magnetic and INS data indicate antiferromagnetic exchange for <bold>Er-dbsq</bold> with a coupling constant of J(ex) = -0.23 meV (-1.8 cm(-1)) (-2J(ex) formalism) and good agreement is found between theory and experiment, with the low energy magnetic and spectroscopic properties well modelled. Most notable is the ability of the ab initio modelling to reproduce the signature of interference between localised 4f states and delocalised pi-radical states that is evident in the Q-dependence of the exchange excitation. This work highlights the power of combining INS with EPR and magnetometry for determination of ground state properties, as well as the enhanced capability of CASSCF-SO ab initio calculations and purposely developed ab initio-based theoretical models. We deliver an unprecedentedly detailed representation of the entangled character of 4f-pi exchange states, which is obtained via an accurate image of the spin-orbital transition density between the 4f-pi exchange coupled wavefunctions.