Is [Cu3(L2)Cl2]2+ a molecule with geometrically spin frustration? DFT study on magnetic competing interaction in hetero-bridged tricopper(II) complex

The theoretical calculations on magnetic exchange interaction of the hetero-bridged tricopper(II) complex Cu₃(L²)Cl₂]²⁺ and a related binuclear copper(II) model are carried out by using the density functional theory combined with the broken-symmetry approach. Meanwhile, one strategy computationally, so called isolated magnetic pair approach, is suggested to explore the spin frustration from geometry topology in poly-nuclear magnetic systems. It is found that the ferromagnetic coupling (J₂>0) of Cu1–Cu3 pair bridged by double μ–Cl ligands, in nature, is intrinsic, not resulted from geometrically spin frustration in the hetero-bridged tricopper(II) studied. However, in the whole molecule exist two competing contributions of antiferromagnetic and ferromagnetic coupling, and the antiferromagnetic coupling (J₁) from Cu1–(μ–OR)–Cu2 and Cu2–(μ–OR)–Cu3 pairs dominates the magnetic behavior of the whole molecular system. On the other hand, the variation of J₁/J₂ ratio affects significantly on magnetic properties of the system. The calculated effective magnetic moment μ_eff of 2.26μ_B at the OPerdew functional level is compared to experimentally observation of 2.70μ_B in the solution. The briefly analysis of molecular magnetic orbitals demonstrated that the two local magnetic orbitals on Cu1 and Cu3 ions are orthogonal each other, and primarily responsible for the intrinsic ferromagnetic coupling between Cu1–(μ–Cl)₂–Cu3. By comparison of spin population distributions for the Cu-triad and Cu-dimer the validity of the isolated magnetic pair approach is confirmed.