Investigation of exchange couplings in [Fe₃S₄]⁺ clusters by electron spin-lattice relaxation

We have studied four proteins containing oxidized 3Fe clusters ([Fe₃S₄]⁺, S = 1/2, composed of three, antiferromagnetically coupled high- spin ferric ions) by continuous wave (CW) and pulsed EPR techniques: Azotobacter vinelandii ferredoxin I, Desulfovibrio gigas ferredoxin II, and the 3Fe forms of Pyrococcus furiosus ferredoxin and aconitase. The 35 GHz (Q- band) CW EPR signals are simulated to yield experimental g tensors, which either had not been reported, or had been reported only at X-band microwave frequency. Pulsed X- and Q-band EPR techniques are used to determine electron spin-lattice (T₁, longitudinal) relaxation times at several positions on the samples' EPR envelope over the temperature range 2-4.2 K. The T₁ values vary sharply across the EPR envelope, a reflection of the fact that the envelope results from a distribution in cluster properties, as seen earlier as a distribution in g₃ values and in ⁵⁷ Fe hyperfine interactions, as detected by electron nuclear double resonance spectroscopy. The temperature dependence of 1/T₁ is analyzed in terms of the Orbach mechanism, with relaxation dominated by resonant two-phonon transitions to a doublet excited state at 20 cm^-1 above the doublet ground state for all four of these 3Fe proteins. The experimental EPR data are combined with previously reported ⁵⁷ Fe hyperfine data to determine electronic spin exchange-coupling within the clusters, following the model of Kent et al. Their model defines the coupling parameters as follows: J₁₃ = J, J₁₂ = J(1 + ε'), J₂₃ = J(1 + ε), where J(ij) is the isotropic exchange coupling between ferric ions i and j, and ε and ε' are measures of coupling inequivalence. We have extended their theory to include the effects of ε' ≠ 0 and thus derived an exact expression for the energy of the doublet excited state for any ε, ε'. This excited state energy corresponds roughly to εJ and is in the range 5-10 cm^{- 1} for each of these four 3Fe proteins. This magnitude of the product εJ, determined by our time-domain relaxation studies in the temperature range 2-4 K, is the same as that obtained from three other distinct types of study: CW EPR studies of spin relaxation in the range 5.5-50 K, NMR studies in the range 293-303 K, and static susceptibility measurements in the range 1.8-200 K. We suggest that an apparent disagreement as to the individual values of J and ε be resolved in favor of the values obtained by susceptibility and NMR (J > 200 cm^-1 and ε > 0.02 cm^-1), as opposed to a smaller J and larger as suggested in CW EPR studies. However, we note that this resolution casts doubt on the accepted theoretical model for describing the distribution in magnetic properties of 3Fe clusters.