Analysis of spin frustration in an Fe^III₇ cluster using a combination of computational, experimental, and magnetostructural correlation methods

The synthesis, structure, and magnetic properties are reported for [Fe₇O₃(O₂C^tBu)₉(mda)₃(H₂O)₃] (1), where mdaH₂ is N-methyldiethanolamine. 1 was prepared from the reaction of [Fe₃O(O₂C^tBu)₆(H₂O)₃](NO₃) with mdaH₂ in a 1:∼3 ratio in MeCN. The core of 1 consists of a central octahedral Fe^III ion held within a non-planar Fe₆ loop by three μ₃-O^2- and three μ₂-RO^- arms from the three mda^2- chelates. Variable-temperature dc and ac magnetic susceptibility studies revealed dominant antiferromagnetic coupling, leading to a ground state spin of S = ⁵/₂. The ground state was confirmed by a fit of magnetization data collected in the 0.1–7.0 T and 1.8–10.0 K ranges. The four Fe₂ pairwise exchange parameters (J₁-J₄) were estimated by independent methods: theoretical calculations using either broken symmetry energy differences (−46.3, −16.2, −3.9, and − 28.1 cm⁻¹, respectively) or Green's function approximation methods (−41.4, −14.8, −13.2, and − 24.7 cm⁻¹), and a magnetostructural correlation (MSC) previously developed for high nuclearity Fe^III/O complexes (−39.5, −13.8, −6.7, and − 23.5 cm⁻¹). Additionally, the J₁-J₄ obtained from the MSC and theoretical methods were used with the program PHI to both simulate χ_MT vs T as well as to serve as reasonable input values to fit the experimental data (−41.0, −11.4, −5.0, and − 27.3 cm⁻¹). Analysis of the J_ij led to identification of the spin frustration effects operative and the resultant spin vector alignments at each Fe^III ion, thus allowing for the rationalization of the experimental ground state.