Spin Coupling in Roussin's Red and Black Salts

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)(O2CPh)](2+) (1; Et-HPTB = N,N,N',N'-tetrakis-(N-ethyl-2-benzimi-dazolylmethyl)-2-hydroxy-1,3-diamino-propane), [Fe(NO)2{Fe(NO)(NS3))S,S' (2), and Roussin's red salt anion [Fe-2(NO)(4)(mu-S)(2)](2-) (3). Although the Heisenberg J for 1 is small (approximate to 10(2) cm(-1)), 2 and 3 exhibit J values that are at least an order of magnitude higher (approximate to 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)(mu(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)mu(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 (approximate to 10(2) cm(-1)), the apical-basal coupling constant J(12) is some forty times higher (approximate to 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 ironsulfur 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 I values.