Two possible mechanisms for dioxygen cleavage on non-heme diiron enzyme models are studied with an approximate molecular orbital method, the extended Huckel method. Diiron peroxo model complexes with different mu-eta(1):eta(1)-O-2 and mu-eta(2):eta(2)-O-2 binding modes are distorted to corresponding dioxo complexes along an assumed O-O bond cleavage reaction coordinate. Fragment molecular orbital (FMO) and Walsh diagram analyses clarify the bonding and orbital interactions. While the pi(g)* orbitals of O-2 are initially occupied by two electrons, in the first dioxygen binding step two other electrons are effectively transferred from the "t(2g)" block to O-2 to form O-2(2-). To cleave the dioxygen O-O bond, it is necessary further to fill the sigma(u)* orbital (high lying and unoccupied in the peroxide). The computations suggest that the mu-eta(1):eta(1)-O-2 mode is more effective for electron transfer from the d-block orbitals to the sigma(u)*. Our calculations indicate that a C-3v- or D-2d-distorted methane can be activated if a coordinatively unsaturated iron, which has been proposed to exist in the diamond Fe-2(u-O)(2) core of intermediate Q of methane monooxygenase, is generated. The complex is suggested to include a five-coordinate carbon species with an Fe-CH4 bond. We propose possible concerted reaction pathways for the conversion of methane to methanol on the supposed diiron active site of methane monooxygenase. Inversion at a five-coordinate carbon, species is suggested to reasonably occur in an initially formed complex of methane and a model of intermediate Q, leading to inversion of stereochemistry at a labelled carbon center.