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: [Fe(2)(NO)(2)(Et-HPTB)(O(2)CPh)](2+) (1; Et-HPTB=N,N,N',N'-tetrakis-(N-ethyl-2-benzimidazolylmethyl)-2-hydroxy-1,3-diaminopropane), [Fe(NO)(2){Fe(NO)(NS(3))}-S,S'] (2), and Roussin's red salt anion [Fe(2)(NO)(4)(μ-S)(2)](2-) (3). Although the Heisenberg J for 1 is small (≈10(2) cm(-1)), 2 and 3 exhibit J values that are at least an order of magnitude higher (≈10(3) cm(-1)), where the J values refer to the following Heisenberg spin Hamiltonian: ℋ=JS(A)⋅S(B). For Roussin's black salt anion, [Fe(4)(NO)(7)(μ(3)-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 [Fe(4)(NO)(7)(μ(3)-S)(3)](-) was assumed to have the form: ℋ=J(12)(S(A)⋅S(B)+S(A)⋅S(C)+S(A)⋅S(D))+J(22)(S(B)⋅S(C)+S(B)⋅S(D)+S(C)⋅S(D)), in which J(12) corresponds to the interaction between the apical iron and a basal iron, and J(22) refers to that between any two basal iron centers. Although the basal-basal coupling constant J(22) was found to be small (≈10(2) cm(-1)), the apical-basal coupling constant J(12) 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.
