Particulate MMO (pMMO) catalyzes the oxidation of methane to methanol and also ammonia to hydroxylamine. Experimental characterization of the active site has been very difficult partly because the enzyme is membrane-bound. However, recently, there has been major progress mainly through the use of cryogenic electron microscopy (cryoEM). Electron paramagnetic resonance (EPR) and X-ray spectroscopy have also been employed. Surprisingly, the active site has only one copper. There are two histidine ligands and one asparagine ligand, and the active site is surrounded by phenyl alanines but no charged amino acids in the close surrounding. The present study is the first quantum chemical study using a model of that active site (Cu-D). Low barrier mechanisms have been found, where an important part is that there are two initial proton-coupled electron transfer steps to a bound O-2 ligand before the substrate enters. Surprisingly, this leads to large radical character for the oxygens even though they are protonated. That result is very important for the ability to accept a proton from the substrates. Methods have been used which have been thoroughly tested for redox enzyme mechanisms.