Application of the Hubbard Model to Cp2* Yb(bipy), a Model System for Strong Exchange Coupling in Lanthanide Systems

Exchange coupling is quantified in lanthanide (Ln) single-molecule magnets (SMMs) containing a bridging N-2(3-) radical ligand and between [Cp*Yb-2](+) and bipy(center dot-) in Cp-2*Yb(bipy), where Cp* is pentamethylcyclopentadienyl and bipy is 2,2'-bipyridyl. In the case of these lanthanide SMMs, the magnitude of exchange coupling between the Ln ion and the bridging N-2(3-), 2J, is very similar to the barrier to magnetic relaxation, U-eff. A molecular version of the Hubbard model is applied to systems in which unpaired electrons on magnetic metal ions have direct overlap with unpaired electrons residing on ligands. The Hubbard model explicitly addresses electron correlation, which is essential for understanding the magnetic behavior of these complexes. This model is applied quantitatively to Cp-2*Yb(bipy) to explain its very strong exchange coupling, 2J = -0.11 eV (-920 cm(-1)). The model is also used to explain the presence of strong exchange coupling in Ln SMMs in which the lanthanide spins are coupled via bridging N-2(3-) radical ligands. The results suggest that increasing the magnetic coupling in lanthanide clusters could lead to an increase in the blocking temperatures of exchange-coupled lanthanide SMMs, suggesting routes to rational design of future lanthanide SMMs.