The reaction modes of the three isomers, carbonyl oxide (A), dioxirane (B), and methylenebis(oxy) (C), with ethylene (E) were investigated by using CASPT2, CCSD(T), and B3LYP with a 6-311 +G(2d,2p) basis set. Contrary to general expectations, A prefers to react with E via a [4+2] cycloaddition reaction (activation enthalpy DeltaH(#)(298) = 1.0 kcal/mol) to yield 1,2-dioxolane (MA2) (reaction enthalpy, -65.0 kcal/mol) rather than via an epoxidation reaction (DeltaH(#)(298) = 11.3 kcal/mol) leading to oxirane and formaldehyde. Epoxidation by B is slower in view of an activation enthalpy of 13.7 kcal/mol; however, it should proceed stereochemically similar as in the case of A. Biradicals C and E can undergo a pseudo-[4+2] cycloaddition reaction (DeltaH(#)(298) = 1.8 kcal/mol), which leads to 1,3-dioxolane (MC2) in a strongly exothermic reaction (DeltaH(R)(298) = -84.5 kcal/mol). The results obtained lead to a mechanistic reconsideration of epoxidation reactions observed in the course of the ozonolysis. They also provide a general basis for comparing reactions of 1,3-dipolar compounds and 1,3-biradicals with unsaturated compounds.