Application of the Hubbard Model to Cp*₂Yb(bipy), a Model System for Strong Exchange Coupling in Lanthanide Systems

Abstract

Exchange coupling is quantified in lanthanide (Ln) single molecule magnets (SMMs) containing a bridging N 2 3-radical ligand and between [Cp* 2 Yb] + and bipy -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 the rational design of future lanthanide SMMs.

Radical ligand-containing single-molecule magnets

“…This bonding model encloses the electron correlation and represents an extension of Hückel theory by adding a parameter that considers electron pairing energy [326]. By extending the spin-only Heisenberg, Dirac, van Vleck (HDVV) Hamiltonian to metal ions with unquenched orbital angular momentum, an extraordinarily large exchange coupling of Cp* 2 Yb(bipy) was quantified as J = −460 cm −1 , in agreement with the predicted value from computations [325]. Remarkably, this coupling is about three orders of magnitude larger than typical coupling constants found for lanthanide ions [316,317].…”

“…The third computational approach yielded values of 2J = 21, 83 and 102 cm −1 for the Dy, Ho and Er species, similar to their experimentally determined relaxation barriers of U eff = 36, 73 and 123 cm −1 [325]. The Hubbard Molecule Model employed to elucidate the strong exchange interaction suggested two strategies to enhance the coupling.…”

“…One way to determine the strength of this coupling involves the temperature-independent paramagnetism (TIP) of the open-shell singlet ground state through employing Griffith's methodology for metal ions with unquenched orbital angular momentum [321]. Another method to quantify the strong exchange coupling in 28 is through employing the Hubbard molecule model (HMM) [322,323], which is essentially the Hubbard model [324] adapted to a single molecule [325]. This bonding model encloses the electron correlation and represents an extension of Hückel theory by adding a parameter that considers electron pairing energy [326].…”

Reversible Sigma C–C Bond Formation Between Phenanthroline Ligands Activated by (C5Me5)2Yb

“…11 When an f-electron is transferred to the LUMO, only one of the four possible *-orbitals, the b 1 -orbital, is of sufficiently low energy to be populated and the unpaired spin density is distributed among the p-orbitals on the C and N atoms of the bipyridine ligand. In this case, the half-occupied ligand orbital and the half-occupied Yb 4f…”

Exchange interaction betweenJmultiplets

“…Nevertheless, this form is often used for the description of interaction between lanthanides or actinides (or a similar form, ∝Ĵ 1 ·Ŝ 2 , in the case of their interaction with an isotropic spin), especially, in the last years [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. One of the reasons that the simple bilinear form has been often used is that the large numbers of the phenomenological exchange parameters cannot be easily determined.…”