Understanding the magnetic anisotropy in a family of N2(3-) radical-bridged lanthanide complexes: density functional theory and ab initio calculations.

Density functional theory (DFT) and ab initio methods were used to investigate the influence of both intramolecular exchange coupling and single-ion anisotropy on the relaxation barriers of a series of N2(3-) radical-bridged lanthanide complexes {[(Me3Si)2N]2(THF)Ln}2(μ-η(2):η(2)-N2) (Ln = Gd(III) (1), Tb(III) (2), Dy(III) (3), Ho(III) (4), and Er(III) (5)) reported by Long and co-workers. DFT calculations show that the exchange coupling between the lanthanide ions is very weak, but the Ln-N2(3-) coupling is strong for each complex. Moreover, the exchange couplings of Ln-N2(3-) are antiferromagnetic for Ln = Gd(III), Tb(III), Dy(III), and Ho(III) but ferromagnetic for Er(III) for the nearly orthogonal magnetic orbitals on Er(III) and N2(3-). Ab initio calculations show that both of the large magnetic anisotropy of single Tb fragment and the strong Tb-N2(3-) antiferromagnetic couplings lead to the largest energy barrier of complex 2. Although the energy barrier of a single Er fragment is the second largest, the relaxation barrier of complex 5 is only 36.0 cm(-1) due to the weak Er(III)-N2(3-) coupling. This study suggests that both intramolecular exchange coupling and single-ion anisotropy contribute greatly to the full relaxation barrier of lanthanide-based single-molecule magnets (SMMs), which expands the understanding of SMMs using only the giant-spin model.