Hybrid DFT calculations are used to study the structures and chemistry of the diiron complex of MMO and RNR. The chemical model used is larger than the ones used previously and contains the full first ligand sphere. New types of structures are suggested for the intermediates observed in the reactions of these enzymes. To obtain the very short Fe-Fe distances recently measured by EXAFS, it is suggested that both compound Q of MMO and compound X of RNR have two bridging carboxylates like the reduced diferrous complex but unlike the diferric complex. Antiferromagnetic coupling is shown to have significant effects on the electronic structure of the complexes and is also important for achieving the short Fe-Fe distance. The new model is also used to study the activation of methane, and a pure hydrogen abstraction transition state is located where a hydrogen of methane is abstracted by a bridging mu-oxo ligand. The combination of the methyl radical with the bridging mu-OH ligand formed occurs without a barrier and is extremely exothermic. This reaction should therefore be very fast. A symmetric transition state for the activation of O-2 is also proposed leading from a suggested compound P to compound Q. In this process, one of the carboxylate bridges of the reduced complex has to move away from O-2 toward one of the irons. These results are discussed in relation to recent experiments.