Comparative analysis of the calculated gas-phase activation barriers (DeltaE++) for the epoxidation of ethylene with dimethyldioxirane (DMDO) and peroxyformic acid (PFA) [15.2 and 16.4 kcal/mol at QCISD(T)// QCISD/6-31+G(d,p)] and E-2-butene [14.3 and 13.2 kcal/mol at QCISD(T)/6-31G(d)//B3LYP/6-311+G(3df,2p)] suggests similar oxygen atom donor capacities for both oxidants. Competition experiments in CH(2)Cl(2) solvent reveal that DMDO reacts with cyclohexene much faster than peracetic acid/acetic acid under scrupulously dried conditions. The rate of DMDO epoxidation is catalyzed by acetic acid with a reduction in the classical activation barrier of 8 kcal/mol. In many cases, the observed increase in the rate for DMDO epoxidation in solution may be attributed to well-established solvent and hydrogen-bonding effects. This predicted epoxidative reactivity for DMDO is not consistent with what has generally been presumed for a highly strained cyclic peroxide. The strain energy (SE) of DMDO has been reassessed and its moderated value (about 11 kcal/mol) is now more consistent with its inherent gas-phase reactivity toward alkenes in the epoxidation reaction. The unusual thermodynamic stability of DMDO is largely a consequence of the combined geminal dimethyl- and dioxa-substitution effects and unusually strong C-H and C-CH(3) bonds. Methyl(trifluoromethyl)dioxirane (TFDO) exhibits much lower calculated activation barriers than DMDO in the epoxidation reaction (the average DeltaDeltaE++ values are about 7.5 kcal/mol). The rate increase relative to DMDO of approximately 10(5), while consistent with the higher strain energy for TFDO (SE approximately 19 kcal/mol) is attributed largely to the inductive effect of the CF(3) group. We have also examined the effect of alkene strain on the rate of epoxidation with PFA. The epoxidation barriers are only slightly higher for the strained alkenes cyclopropene (DeltaE++ = 14.5 kcal/mol) and cyclobutene (DeltaE++ = 13.7 kcal/mol) than for cyclopentene (DeltaE++ = 12.1 kcal/mol), reflecting the fact there is little relief of strain in the transition state. Alkenes strained by twist or pi-bond torsion do exhibit much lower activation barriers.