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Spin Coupling in Roussin’s Red and Black Salts
Author(s) -
Hopmann Kathrin H.,
Noodleman Louis,
Ghosh Abhik
Publication year - 2010
Publication title -
chemistry – a european journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.687
H-Index - 242
eISSN - 1521-3765
pISSN - 0947-6539
DOI - 10.1002/chem.200903344
Subject(s) - hamiltonian (control theory) , heisenberg model , coupling constant , density functional theory , physics , spin (aerodynamics) , ion , order (exchange) , chemistry , crystallography , coupling (piping) , mathematical physics , quantum mechanics , condensed matter physics , thermodynamics , ferromagnetism , materials science , mathematics , mathematical optimization , finance , metallurgy , economics
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.