By a density functional theory (DFT) based quantum chemical calculation at the B3LYP/6-311G(d,p) level, we found that the mechanism of epoxidation of alkenes by peracids is a protonation-promoted pathway. The protonation site is the oxygen atom of carbonyl group in peracids. Orbital energy E-UMO sigma* of the UMO in which the sigma* orbital of peroxo bond of protonated peracids lies is much lower than that of neutral peracids. The E-UMO sigma* are in the range of -6.21 to -7.96 eV, which is 5-7 eV lower than that of neutral peracids. The E-UMO sigma* is in the same as or even lower level than the HOMO energy of alkenes. The study first exhibits the images of sigma* orbital of the peroxo bonds in neutral or protonated peroxy acids. A reaction path calculation (IRC) revealed that the microscopic process of the epoxidation by peracids is a nucleophilic transfer of pi-electrons of alkene toward the sigma* orbital of peroxo bond. The calculation has given the transition structures (TS) and activation barriers to the attack of epoxidation of performic acid, peracetic acid, trifluoroperacetic acid and their protonated counterparts on ethylene. Their activation barriers are 17.51, 19.18, 13.93, 3.18, 4.25, and 2.77 kcal/mol, respectively, showing that the protonation greatly dropped the activation barriers of epoxidation by peracids, i.e. the neutral peracids were strongly activated by the protonation. According to this mechanism, some important and puzzling kinetic facts of epoxidation by peracids are easily elucidated. (c) 2005 Elsevier B.V. All rights reserved.