Understanding the Magnetic Anisotropy in a Family of N23- 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 N-2(3-) radical-bridged lanthanide complexes [{[(Me3Si)(2)N](2)(THF)Ln}(2)(mu-eta(2):eta(2)-N-2)](-) (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-N-2(3-) coupling is strong for each complex. Moreover, the exchange couplings of Ln-N-2(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 N-2(3-). Ab initio calculations show that both of the large magnetic anisotropy of single Tb fragment and the strong Tb-N-2(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-N-2(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.