The all-ferrous, carbene-capped Fe4S4 cluster, synthesized by Deng and Holm (DH complex), has been studied with density functional theory (DFT). The geometry of the complex was optimized for several electronic configurations. The lowest energy was obtained for the broken-symmetry (BS) configuration derived from the ferromagnetic state by reversing the spin projection of one of the high spin (S-i = 2) irons. The optimized geometry of the latter configuration contains one unique and three equivalent iron sites, which are both structurally and electronically clearly distinguishable. For example, a distinctive feature of the unique iron site is the diagonal Fe center dot center dot center dot S distance, which is 0.3 angstrom longer than for the equivalent irons. The calculated Fe-s7 hyperfine parameters show the same 1:3 pattern as observed in the Mossbauer spectra and are in good agreement with experiment. BS analysis of the exchange interactions in the optimized geometry for the 1:3, M-s = 4, BS configuration confirms the prediction of an earlier study that the unique site is coupled to the three equivalent ones by strong antiferromagnetic exchange (J > 0 in J Sigma(j<4) <(S)over cap>(4) . (S) over cap (j) ) and that the latter are mutually coupled by ferromagnetic exchange (J' < 0 in J' Sigma(i(i) . (S) over cap (j)). In combination, these exchange couplings stabilize an S = 4 ground state in which the composite spin of the three equivalent sites (S-123 = 6) is antiparallel to the spin (S-4 = 2) of the unique site. Thus, DFT analysis supports the idea that the unprecedented high value of the spin of the DH complex and, by analogy, of the all-ferrous cluster of the Fe-protein of nitrogenase, results from a remarkably strong dependence of the exchange interactions on cluster core geometry. The structure dependence of the exchange-coupling constants in the Fe-II-(mu(3)-S)(2)-Fe-II moieties of the all-ferrous clusters is compared with the magneto-structural correlations observed in the data for dinuclear copper complexes. Finally, we discuss two all-ferric clusters in the light of the results for the all-ferrous cluster.