Comparative analysis of the calculated gas-phase activation barriers (DeltaEdouble dagger) 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 QCISID(T)/6-31G(d)HB3LYP/6-311+G(3df,2p)] suggests similar oxygen atom donor capacities for both oxidants. Competition experiments in CH2Cl2 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 epoxiclation 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-CH3 bonds. Methyl(trifluoromethyl)dioxirane (TFDO) exhibits much lower calculated activation barriers than DMDO in the epoxiclation reaction (the average DeltaDeltaE(double dagger) values are about 7.5 kcal/mol). The rate increase relative to DMDO of similar to 10(5), while consistent with the higher strain energy for TFDO (SE similar to 19 kcal/mol) is attributed largely to the inductive effect of the CF3 group. We have also examined the effect of alkene strain on the rate of epoxiclation with PFA. The epoxiclation barriers are only slightly higher for the strained alkenes cyclopropene (DeltaE(double dagger) = 14.5 kcal/mol) and cyclobutene (DeltaE(double dagger) = 13.7 kcal/mol) than for cyclopentene (DeltaE(double dagger) = 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.