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.