SPIN COUPLING MODEL FOR TETRAMERIC IRON CLUSTERS IN FERREDOXINS .3. DOUBLE EXCHANGE IN DISTORTED CLUSTER

A spin model for the [4Fe-4S]+ cluster of ferredoxin is considered taking into account the Heisenberg exchange and double exchange interactions in a distorted cluster. Analytical expressions for the exchange-resonance splittings of all S=1/2 states are obtained. The double exchange and delta1 ''deformation'' form together the effective splitting parameter. The double exchange contribution undergoes spin reduction B/(2S12+1 ) relatively to the deformation term; maximal reduction takes place for the ground \S12=4, S=1/2> state with maximal S12 value. Heisenberg, ''deformation.'' terms delta(i) influence essentially the energy spectrum and hyperfine characteristics. It is shown that in the tetrameric [Fe3(II)Fe(III)] cluster of ferredoxin with antiferromagnetic Heisenberg exchange, strong double exchange between two Fe3+-Fe2+ ions leads to the S= 1/2 ground state even in the case when the Heisenberg exchange DELTA term forms the localized high-spin (S=3/2, 5/2, or 7/2) ground state. This exchange-resonance effect is opposite to the result of double exchange theory for mixed-valence dimeric clusters, in which double exchange leads to a ferromagnetic ground state (S(gr)=S(max)) and reduces the Heisenberg antiferromagnetic intra-pair splittings. Due to different directions of the local crystal fields in the [4Fe-4S] cluster, strong double exchange, together with the anisotropy of the overlap of the d-functions, leads to the mixing of the ground and excited exchange-resonance states.