Spin Coupling in Roussin’s Red and Black Salts

摘要

Although DFT calculations have provided a first-order electronic-structural description for Roussin’s red and black salts, a detailed study of spin coupling in these species has yet to be reported. Such an analysis is presented here for the first time, based on broken-symmetry density functional theory (DFT, chiefly OLYP/STO-TZP) calculations. Both the Noodleman and Yamaguchi formulas were used to evaluate the Heisenberg coupling constants (J). Three nitrosylated binuclear clusters were studied: [Fe₂(NO)₂(Et-HPTB)(O₂CPh)]2+ (1; Et-HPTB=N,N,N',N'-tetrakis-(N-ethyl-2-benzimidazolylmethyl)-2-hydroxy-1,3-diaminopropane), [Fe(NO)₂{Fe(NO)(NS₃)}-S,S'] (2), and Roussin’s red salt anion [Fe₂(NO)₄(μ-S)₂]2− (3). Although the Heisenberg J for 1 is small (≈102 cm−1), 2 and 3 exhibit J values that are at least an order of magnitude higher (≈103 cm−1), where the J values refer to the following Heisenberg spin Hamiltonian: =JS_AS_B. For Roussin’s black salt anion, [Fe₄(NO)₇(μ₃-S)₃]− (4), the Heisenberg spin Hamiltonian describing spin coupling between the {FeNO}7 unit (S_A=3/2) and the three {Fe(NO)₂}9 units (S_B=S_C=S_D=1/2) in [Fe₄(NO)₇(μ₃-S)₃]− was assumed to have the form: =J₁₂(S_AS_B+S_AS_C+S_AS_D)+J₂₂(S_BS_C+S_BS_D+S_CS_D), in which J₁₂ corresponds to the interaction between the apical iron and a basal iron, and J₂₂ refers to that between any two basal iron centers. Although the basal–basal coupling constant J₂₂ was found to be small (≈102 cm−1), the apical–basal coupling constant J₁₂ is some forty times higher (≈4000 cm−1). Thus, the nitrosylated iron–sulfur clusters feature some exceptionally high J values relative to the non-nitrosylated {2Fe2S} and {4Fe4S} clusters. An analysis of spin-dependent bonding energies shed light on this curious feature. In essence, the energy difference between the high-spin (i.e., ferromagnetically coupled iron sites) and low-spin (i.e., maximum spin coupling) states of Roussin’s salts are indeed rather similar to those of analogous non-nitrosylated iron–sulfur clusters. However, the individual Fe(NO)_x (x=1, 2) site spins are lower in the nitrosylated systems, resulting in a smaller denominator in both the Noodleman and Yamaguchi formulas for J, which in turn translates into the very high J values.