Theoretical Studies on Hexanuclear [M₃(μ₃-O/OH)]₂ (M = Fe(III), Mn(III), and Ni(II)) Clusters: Magnetic Exchange,...

Controlling spin Hamiltonian parameters such as magnetic exchange and magnetic anisotropy of polynuclear clusters is of great interest in the area of single molecule magnets (SMMs). Among large polynuclear clusters, hexanuclear clusters offer the best compromise in terms of size as they are often rigid, solution stable, and chemically amenable. The {M₆O₂} core is one of the common architectures known for many hexanuclear clusters and generally reported to possess a diamagnetic S_T = 0 spin ground state, barring a few exceptions. In these clusters, there are several open questions that are poorly understood: (a) What controls the nature of magnetic exchange, which in turn dictates the ground state spin values? (b) For clusters possessing a nonzero spin ground state, what dictates the magnetic anisotropy? Here, using density functional methods, we have attempted to shed light on these two question by evaluating the exchange coupling constants in [Fe₆^IIIO₂(OH)₂{(C₄N₂H₂SMe)₂C(OH)O}₂( ^tBuCO₂)₁₀] (1), [Fe₆^III(O)₂(O₂CH₂)(O₂CCH₂ ^tBu)₁₂(py)₂] (2), [Fe₆^III(O₂)(O)₂(O₂CCMe₃)₁₂(py)₂] (3), [Fe^III₆O₃(O₂CMe)₉(OEt)₂(bpy)₂]ClO₄ (4), [Mn^III₆O₂(O₂CH₂)(O₂CPe ^t)₁₁(HO₂CPe ^t)₂(O₂CMe)] (5), and [Ni^II₆(OH)₄(O₂C ^tBu)₈( ^tBuCO₂H)₄] (6) complexes. We have estimated all the eight near-neighbor exchange coupling constants in these clusters. Our calculations not only agree with the experimental results but also offer insight on the origin of the spin ground state. Extensive magneto-structural correlations developed by varying M-O-M angles and M-O distances reveal that J values are extremely sensitive to small structural distortions. Correlations developed indicate that both the parameters are important for Fe(III), but for Mn(III) and Ni(II), the angles were found to play a dominant role. Quite interestingly, the computed zero-field splitting parameter D _S=5 of complex 1 reveals that the exchange contribution to the anisotropy controls the sign of the ground state D value-an observation which differs from the general perception that the ground state D is controlled by the single-ion zero-field splitting parameter.