Using broken-symmetry unrestricted Density Functional Theory, the mechanism of enzymatic dioxygen activation by the hydroxylase component of soluble methane monooxygenase (MMOH) is determined to atomic detail. After a thorough examination of mechanistic alternatives, an optimal pathway was identified. The diiron(II) state H-red reacts with dioxygen to give a ferromagnetically coupled diiron(II,III) H-superoxo structure, which undergoes intersystem crossing to the antiferromagnetic surface and affords H-peroxo, a symmetric diiron(III) unit with a nonplanar mu-eta(2):eta(2)-O2- binding mode. Homolytic cleavage of the O-O bond yields the catalytically competent intermediate 0, which has a di (mu-oxo)diiron(IV) core. A carboxylate shift involving Glu243 is essential to the formation of the symmetric Hperoxo and Q structures. Both thermodynamic and kinetic features agree well with experimental data, and computed spin-exchange coupling constants are in accord with spectroscopic values. Evidence is presented for pH-independent decay of H-red and H-peroxo. Key electron-transfer steps that occur in the course of generating Q from H-red are also detailed and interpreted. In contrast to prior theoretical studies, a requisite large model has been employed, electron spins and couplings have been treated in a quantitative manner, potential energy surfaces have been extensively explored, and quantitative total energies have been determined along the reaction pathway.