Spin coupling model for tetrameric iron clusters in ferredoxins. I. Theory, exchange levels, g-factors

Abstract

A Heisenberg exchange model of the [4Fe4S] + clusters of ferredoxins, enzymes and of synthetic analog compounds is developed. The proposed approach gives the generalized solution of the exchange problem which leads to the results of different Kambe models in particular cases. The exchange mixing of the states with fixed intermediate spins determines the splittings and transformation of levels, the features of EPR spectra of these systems with [Fe 3(II)Fe(III)] clusters. The problem of calculation of all types (diagonal and non-diagonal) matrix elements of one- and two-particle (exchange) spin operators was solved on the base of the technique of the irreducible tensor operators. The analytical expressions for the exchange variations of the factors K i  < S iz >/< S Z >, which form the relationship g mol  Σ 4 i=1 K i g i between molecular and local g-factors, were derived. Exchange variations explain the values and the change of the molecular g-factors. The characteristics “ g av < 2” values g mol = 1.94–1.98 of the [4Fe4S] + clusters of the majority of ferredoxins, enzymes and of synthetic analog compounds with S gr = 1 2 are explained by strong δ 1/Δ “distortion”. The small deformations lead to g av > 2.