The oxidized state of the active site of E. coli sulfite reductase (SiR(0)) consists of two covalently linked chromophores, a siroheme and an [Fe4S4](2+) cluster. This work is motivated by the observation of paramagnetic hyperfine structure at the Fe-57 sites of the [Fe4S4](2+) moiety, a species which is diamagnetic if it were an isolated cluster. The first part of the paper presents the results for the ubiquitous [Fe4S4](2+) core that is found in enzymes, proteins, and synthetic analogs. The core is analyzed in the framework of an effective-Hamiltonian model, including terms for itinerant electron transfer and antiferromagnetic exchange. Spin-dependent electron delocalization (double exchange) in clusters with T-d symmetry gives rise to degenerate ground states for both positive and of the transfer parameters, beta(0). A vibronic coupling mechanism is introduced that is based on the structure dependence of the transfer parameters, beta(ij) = beta(0) + Delta Delta r(ij).