Spin–orbit coupling in the double exchange model 2. Comparison of the antisymmetric double exchange with the Dzialoshinsky–Moriya antisymmetric exchange, spin canting and ZFS

Variation of average g values and effective exchange coupling constants among [2Fe-2S] clusters: a density functional theory study of the impact of localization (trapping forces) versus delocalization (double-exchange) as competing factors

A phenomenological model aimed at rationalizing variations in both average g-tensor values (gav identical with 1/3Sigmaigi ) and effective exchange coupling constants Jeff (defined as two-thirds of the energy difference between the S = 3/2 and S = 1/2 spin states) has been derived in order to describe the great variety of magnetic properties exhibited by reduced [2Fe-2S] clusters in proteins. The key quantity in the present analysis is the ratio Delta E/B computed from two competing terms. Delta Ecomprises various effects that result in trapping-site asymmetries: vibronic coupling and the chemical nature (S/N/O) and conformations of the ligands on the one hand and solvation terms, the hydrogen bonding network, etc., on the other. All of these additive terms (in a "bottom-up" approach) favor valence localization of the reducing electron onto one of the two iron sites. In contrast, the B term is the double-exchange term, which favors electronic delocalization. Both gav and Jeff can be expressed as functions of Delta E/ B. We have also shown that electronic localization generally favors small gav and large Jeff values (while the opposite is true for electronic delocalization) in a comparative study of the spectroscopic features of plant-type ferredoxins (Fd's) and Rieske centers (and related mutants). Two other types of problems were particularly challenging. The first of these involved deprotonated Rieske centers and the xanthine oxidase clusters II, which are characterized by very small Jeff values (40-45 cm (-1) with a J S A. S B model) correlated with unusually large gav values (in the range 1.97-2.01) as a result of an antisymmetric exchange coupling mechanism. The second concerned the analogous Fd's from Clostridium pasteurianum (Cp) and Aquifex aeolicus (Aa). Detailed Mössbauer studies of the C56S mutant of the Cp system revealed a mixture of clusters with valence-localized S = 1/2 and valence-delocalized S = 9/2 ground states. We relied on crystallographic structures of wild-type and mutant Aa Fd's in order to explain such a distribution of spin states.

Isotropic and Antisymmetric Double-Exchange, Zero-Field, Zeeman, and Hyperfine Splittings in Trinuclear Valence-Delocalized [Cu37+] Clusters

Valence delocalization in the [Cu3(7+)] trimer is considered in the model of the double-exchange coupling, in which full delocalization corresponds to the migration of the single d(x2-y2) hole and relatively strong isotropic double-exchange coupling. Strong double exchange results in the pairing of the individual spins in the delocalized trimer even at room temperature. The model explains the delocalized singlet 1A1 ground state in the planar Cu3(mu3-O) core by strong double exchange with positive double-exchange parameter t(0), whereas the delocalized triplet ground state of the [Cu3(7+)] trimer, which was observed in the Cu3(mu3-S)2 cluster, may be explained by the double exchange with relatively weak positive t(0): 0 < t(0) < 2J (degenerate 3E ground state) or negative t(0) (triplet 3A2 ground state). An analysis of the splitting of the delocalized degenerate 3E term requires inclusion of the antisymmetric double-exchange interaction, which takes into account the spin-orbit coupling in the double-exchange model. The cluster parameter KZ of the antisymmetric double-exchange coupling is proportional to t(0) and anisotropy of the g factor Deltag(parallel)[Cu(II)], KZ << t(0). Antisymmetric double exchange is relatively large in the [Cu3(7+)] cluster with the d(x2-y2) magnetic orbitals lying in the Cu3 plane [Cu3(mu3-O) core], whereas for the d(x2-y2) magnetic orbitals lying in the plane perpendicular to Cu3, antisymmetric double-exchange coupling is weak [Cu3(mu3-S)2 cluster]. The antisymmetric double-exchange coupling results in the linear zero-field splitting DeltaK = 2[equation: see text]KZ (approximately t(0)) of the delocalized degenerate 3E term that leads to strong anisotropy of the Zeeman splittings in the external magnetic field and a complex electron paramagnetic resonance (EPR) spectrum. The delocalized model of hyperfine interaction explains the hyperfine structure [10 hyperfine lines with the relative intensities 1:3:6:10:12:12:10:6:3:1 and the interval a/3] of the EPR transitions in the triplet states that was observed in the EPR spectra of the Cu3(mu3-S)2 cluster.