The FeMo cofactor (FeMoco) of Mo nitrogenase is responsible for reducing dinitrogen to ammonia, but it requires the addition of 3-4 e-/H+ pairs before N2 even binds. A binding site at the Fe2/Fe3/Fe6/Fe7 face of the cofactor has long been suggested based on mutation studies, with Fe2 or Fe6 nowadays being primarily discussed as possibilities. However, the nature of N2 binding to the cofactor is enigmatic as the metal ions are coordinatively saturated in the resting state with no obvious binding site. Furthermore, the cofactor consists of high-spin Fe(II)/Fe(III) ions (antiferromagnetically coupled but also mixed-valence delocalized), which are not known to bind N2. This suggests that an Fe binding site with a different molecular and electronic structure than the resting state must be responsible for the experimentally known N2 binding in the E4 state of FeMoco. We have systematically studied N2 binding to Fe2 and Fe6 sites of FeMoco at the broken-symmetry QM/MM level as a function of the redox-, spin-, and protonation state of the cofactor. The local and global electronic structure changes to the cofactor taking place during redox events, protonation, Fe-S cleavage, hydride formation, and N2 coordination are systematically analyzed. Localized orbital and quasi-restricted orbital analysis via diamagnetic substitution is used to get insights into the local single Fe ion electronic structure in various states of FeMoco. A few factors emerge as essential to N2 binding in the calculations: spin-pairing of dxz and dyz orbitals of the N2-binding Fe ion, a coordination change at the N2-binding Fe ion aided by a hemilabile protonated sulfur, and finally hydride ligation. The results show that N2 binding to E0, E1, and E2 models is generally unfavorable, likely due to the high-energy cost of stabilizing the necessary spin paired electronic structure of the N2-binding Fe ion in a ligand environment that clearly favors high-spin states. The results for models of E4, however, suggest a feasible model for why N2 binding occurs experimentally in the E4 state. E4 models with two bridging hydrides between Fe2 and Fe6 show much more favorable N2 binding than other models. When two hydrides coordinate to the same Fe ion, an increased ligand-field splitting due to octahedral coordination at either Fe2 or Fe6 is found. This altered ligand field makes it easier for the Fe ion to acquire a spin-paired electronic structure with doubly occupied dxz and dyz orbitals that backbond to a terminal N2 ligand. Within this model for N2 binding, both Fe2 and Fe6 emerge as possible binding site scenarios. Due to steric effects involving the His195 residue, affecting both the N2 ligand and the terminal SH- group, distinguishing between Fe2 and Fe6 is difficult; furthermore, the binding depends on the protonation state of His195.