Ferromagnetic Coupling in Hexanuclear Gadolinium Clusters

The magnetic susceptibilities of hexanuclear gadolinium clusters in the compounds Gd(Gd6ZI12) (Z = Co, Fe, or Mn) and CsGd(Gd6CoI12)2 are reported and subjected to theoretical analysis with the help of density functional theory (DFT) computations. The single-crystal structure of Gd(Gd6CoI12) is reported here as well. We find that the compound with a closed shell of cluster bonding electrons, Gd(Gd6CoI12), exhibits the effects of antiferromagnetic coupling over the entire range of temperatures measured (4−300 K). Clusters with unpaired, delocalized cluster bonding electrons (CBEs) exhibit enhanced susceptibilities consistent with strong ferromagnetic coupling, except at lower temperatures (less than 30 K) where intercluster antiferromagnetic coupling suppresses the susceptibilities. The presence of two unpaired CBEs, as in [Gd6MnI12]3-, yields stronger coupling than when just one unpaired CBE is present, as in [Gd6FeI12]3- or [Gd6CoI12]2-. DFT calculations on model molecular systems, [Gd6CoI12](OPH3)6 and [Gd6CoI12]2(OPH3)10, indicate that the delocalized cluster bonding electrons are highly effective at mediating intracluster ferromagnetic exchange coupling between the Gd atom 4f7 moments and that intercluster coupling is expected to be antiferromagnetic. The DFT calculations were used to calculate the relative energies of various 4f7 spin patterns and form the basis for construction of a simple spin Hamiltonian describing the coupling within the [Gd6CoI12] cluster.本文报道了化合物Gd(Gd₆ZI₁₂)（Z=Co、Fe或Mn）与CsGd(Gd₆CoI₁₂)₂中六核钆团簇（hexanuclear gadolinium clusters）的磁化率（magnetic susceptibilities），并借助密度泛函理论（density functional theory, DFT）计算对其开展理论分析。同时，本文还报道了Gd(Gd₆CoI₁₂)的单晶结构（single-crystal structure）。 研究发现，具备团簇成键电子闭壳层的化合物Gd(Gd₆CoI₁₂)在测试的全部温度区间（4~300 K）内均表现出反铁磁耦合（antiferromagnetic coupling）效应。对于带有未配对离域团簇成键电子（cluster bonding electrons, CBEs）的团簇，其磁化率会出现增强，这与强铁磁耦合（ferromagnetic coupling）的特征相符；但在低于30 K的低温区间，团簇间反铁磁耦合（intercluster antiferromagnetic coupling）会抑制磁化率。当存在两个未配对CBEs时（如[Gd₆MnI₁₂]³⁻），其耦合强度高于仅含一个未配对CBEs的体系（如[Gd₆FeI₁₂]³⁻或[Gd₆CoI₁₂]²⁻）。 针对模型分子体系[Gd₆CoI₁₂](OPH₃)₆与[Gd₆CoI₁₂]₂(OPH₃)₁₀的DFT计算结果表明，离域团簇成键电子可高效介导钆原子4f⁷磁矩之间的团簇内铁磁交换耦合（intracluster ferromagnetic exchange coupling），且团簇间耦合应为反铁磁性。本次DFT计算被用于求解多种4f⁷自旋构型的相对能量，并以此为基础构建了描述[Gd₆CoI₁₂]团簇内耦合作用的简易自旋哈密顿量（spin Hamiltonian）。