The oxygen atom transfer reaction from the Mimoun-type complex MoO(eta(2)-O-2)(2)OPH3 to ethylene C2H4 affording oxirane C2H4O has been investigated within the framework of the Bonding Evolution Theory in which the corresponding molecular mechanism is characterized by the topological analysis of the electron localization function (ELF) and Thom's catastrophe theory (CT). Topological analysis of ELF and electron density analysis reveals that all Mo-O bonds in MoO(eta(2)-O-2)(2)OPH3 and MoO2(eta(2)-O-2)OPH3 belong to closed-shell type interactions though negative values of total energy densities E-e(r(BCP)) imply some covalent contribution. The peroxo O-i-O-j bonds are characterized as charge-shift or protocovalent species in which pairs of monosynaptic basins V-3(O-i), V-3(O-j) with a small electron population of similar to 0.25e each, are localized between core basins C(O-i), C(O-j). The oxygen transfer reaction from molybdenum diperoxo complex MoO(eta(2)-O-2)(2)PH3 to C2H4 system can be described by the following consecutive chemical events: (a) protocovalent peroxo O-2-O-1 bond breaking, (b) reduction of the double C-1=C-2 bond to single C-1-C-2 bond in ethylene, (c) displacement of oxygen O-1 with two nonbonding basins, V-i=1,V-2(O-1), (d) increase of a number of the nonbonding basins to three (V-i=1,V-2,V-4(O-1)); (e) reorganization and reduction in the number of nonbonding basis to two basins (V-i=1,V-4(O-1)) resembling the ELF-topology of the nonbonding electron density in oxirane, (e) formation of the first O-1-C-2 bond in oxirane, (f) C-2-O-1-C-2 ring closure, (g) formation of singular nonbonding basin V(O-2) in new Mo=O-2 bond. The oxygen atom is transferred as an anionic moiety carrying a rather small electronic charge ranging from 0.5 to 0.7e.