The influence of the interstitial atom, X, discovered in a recent crystallographic study of the MoFe protein of nitrogenase, on the electric hyperfine interactions of Fe-57 has been investigated with density functional theory. A semiempirical theory for the isomer shift, delta, is formulated and applied to the cofactor. The values of delta for the relevant redox states of the cofactor are predicted to be higher in the presence of X than in its absence. The analysis strongly suggests a [Mo(4+)4Fe(2+)3Fe(3+)] oxidation state for the S = 3/2 state M-N. Among C4-, N3-, and O2-, oxide is found to be the least likely candidate for X. The analysis suggests that X should be present in the cofactor states M-OX and M-R as well as in the alternative nitrogenases. The calculations of the electric field gradients (EFGs) indicate that the small values for DeltaE(Q) in MN result from an extensive cancellation between valence and ligand contributions. X emerges from the analysis of the hyperfine interactions as an ionically bonded species. Its major effect is on the asymmetry parameters for the EFGs at the six equatorial sites, Fe-Eq. A spin-coupling scheme is proposed for the state [Mo(4+)4Fe(2+)3Fe(3+)] that is consistent with the measured Fe-57 A-tensors and DeltaE(Q) values for M-N and identifies the unique site exhibiting the small A value with the terminal Fe site, Fe-T. The optimized structure of a cofactor model has been calculated for several oxidation states. The study reveals a contraction in the average Fe-Fe distance upon increasing the number of electrons stored in the cluster, in accord with extended X-ray absorption fine structure studies. The reliability of the adopted methodology for predicting redox-structural correlations is tested for cuboidal [4Fe-4S] clusters. The calculations reveal a systematic increase in the S...S sulfide distances, in quantitative agreement with the available data. These trends are rationalized by a simple electrostatic model.