The electronic structures of mononuclear Fe-S complexes with a Fe IIS4 core and of binuclear Fe-Mo-S complexes containing the FeS2Mo core have been calculated by a semiempirical molecular orbital method (iterative extended Hückel theory), followed by a spin-orbit coupling calculation on the five highest occupied iron-like molecular orbitals. Fine structure and hyperfine structure tensors and parameters (g, D, E, A, and electric field gradient) have been calculated and compared with data from spin-Hamiltonian analysis of Mössbauer measurements. For the mononuclear complex anions [Fe(SPh)4]2- and [Fe(dts)2] 2- it was found that Fẑẑ negative, D positive, and that the magnetic anisotropy places the preferred direction of the hyperfine magnetic field perpendicular to the redirection in agreement with spin-Hamiltonian results. The similarity of parameters of [Fe(SPh) 4]2- and reduced rubredoxin (Rdred) confirms the suggestion that this anion has a ground electronic state practically identical to Rdred. The complex anion [Fe(dts)2] 2- shows smaller anisotropy, and due to the fact that the orbital ground state is energetically not well separated from higher states in this case a strong temperature dependence of the quadrupole splitting is observed. For the binuclear complex anions [(SPh)2FeS2MoS 2]2-, [S5FeS2MoS2] 2-, and [Cl2FeS2MoS2]2- it was found that D is negative and Vẑẑ is positive. A specific feature of these binuclear Fe-Mo-S complexes is that V ẑẑ is directed perpendicular to the Fe-Mo line. (This theoretical result is confirmed by single crystal Mössbauer studies on [Cl2FeS2MoS2]2-; see the following paper in this journal.) The preferred direction of the magnetic hyperfine field is close to the Vẑẑ axis. The correlation of calculated values of ρ(0) and isomer shifts for mononuclear and binuclear compounds confirms the role of MoS4 2- as a charge withdrawing ligand.