Spin coupling model for tetrameric iron clusters in ferredoxins. III. Double exchange in distorted cluster

Abstract

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 δ 1 “deformation” form together the effective splitting parameter. The double exchange contribution undergoes spin reduction B/(2 S 12 + 1) relatively to the deformation term; maximal reduction takes place for the ground | S 12 = 4, S = 1 2 〉 state with maximal S 12 value. Heisenberg “deformation” terms δ i influence essentially the energy spectrum and hyperfine characteristics. It is shown that in the tetrameric [Fe 3(II)Fe(III)] cluster of ferredoxin with antiferromagnetic Heisenberg exchange, strong double exchange between two Fe 3+-Fe 2+ ions leads to the S = 1 2 ground state even in the case when the Heisenberg exchange Δ 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.