EXCHANGE COUPLING AND RESONANCE DELOCALIZATION IN REDUCED [FE4S4]+ AND [FE4SE4]+ CLUSTERS .2. A GENERALIZED NONLINEAR MODEL FOR SPIN-STATE ENERGIES AND EPR AND HYPERFINE PROPERTIES

I develop a generalized nonlinear model for the spin states of reduced [Fe4S4]+ and [Fe4Se4]+ clusters. This model is an extension of that described in the previous paper and allows the internal electron transfer within the mixed-valence pair to couple together a larger set of basis states. The consequences of this model for the energies and properties of various states with spin S = 1/2, 3/2, and 7/2 are explored. For a range of parameters similar to that used previously, we find that the lowest S = 3/2 state appears in much closer proximity to the lowest S = 1/2 state over an extended range of the alpha = J2/J1 parameter compared with the preceding linear model. Such a near proximity of S = 1/2 and 3/2 is consistent with the statistical mixtures of these states often found in reduced [Fe4S4]+ and [Fe4Se4]+ clusters. The observed crossing points among S = 1/2, 3/2, and 7/2 are consistent with the observed coexistence of these three states in [Fe4Se4]+ at low temperatures. In addition to providing reasonable predictions for average g and A values for S = 1/2 states in typical reduced 4Fe ferredoxins, the model shows how the large variation in average g values, 1.97 and 2.05, for the two different rhombic states observed in Desulfovibrio vulgaris hydrogenase can arise from a modest variation in 0.2 less-than-or-equal-to alpha-less-than-or-equal-to 0.5 at low B/J, 3 less-than-or-equal-to B/J 2.5. The predicted variability in average g values is a consequence of the nonlinear model; the linear model cannot give a satisfactory account of this variability. We obtain a good theoretical prediction of the small negative hyperfine constants observed by Mossbauer spectroscopy on all Fe sites in the lowest S = 3/2 state for various clusters. The nonlinear theory gives a far better prediction of hyperfine constants for S = 3/2 than the linear theory. The predicted theoretical A(av) values for the Fe2+ and Fe3+ sites of the S = 7/2 state in Se-substituted Cp ferredoxin are well represented by the nonlinear model; at least partial localization of the mixed-valence pair by extrinsic forces is indicated. The Zeeman parameter g0' determined by EPR spectroscopy is also calculated with reasonable accuracy by the model.