The three pathways postulated for 1,3-migration of the peroxyl group in the allylperoxyl radical (11 a), a key reaction involved in the spontaneous autoxidation of unsaturated lipids of biological importance, have been investigated by means of quantum mechanical electronic structure calculations. According to the barrier heights calculated from RCCSD(T)/6-311+G(3df,2p) energies with optimized molecular geometries and harmonic vibrational frequencies determined at the UMP2/6-311+G(3df,2p) level, the allylperoxyl rearrangement proceeds by fragmentation of la through a transition structure (TS1) with a calculated DeltaH(double dagger)(298 K) of 21.7 kcal/mol to give an allyl radical-triplet dioxygen loosely bound complex (CX). In a subsequent step, the triplet dioxygen moiety of CX recombines at either end of the allyl radical moiety to convert the complex to the rearranged peroxyl radical (1a') or to revert to the starting peroxyl radical la. CX shows an electron charge transfer of 0.026 e in the direction allyl --> O-2. The dominant attractive interactions holding in association the allyl radical-riplet dioxygen pair in CX are due chiefly to dispersion forces. The DeltaH(298 K) for dissociation of CX in its isolated partners, allyl radical and triplet dioxygen, is predicted to be at least 1 kcal/mol. The formation of CX prevents the diffusion of its partners and maintains the stereocontrol along the fragmentation-recombination processes. The concerted 1,3migration in allylperoxyl radical is predicted to take place through a five-membered ring peroxide transition structure (TS2) showing two long C-O bonds. The DeltaH(double dagger)(298 K) calculated for this pathway is less favorable than the fragmentation-recombination pathway by 1.9 kcal/mol. The cyclization of la to give a dioxolanyl radical intermediate (2a) is found to proceed through a five-membered ring transition structure (TS3) with a calculated DeltaH(double dagger)(298 K) of 33.9 kcal/mol. Thus, the sequence of ring closure 1a --> 2a and ring opening 2a --> 1a' is unlikely to play any significant role in allylperoxyl rearrangement 1a --> 1a'. In the three pathways investigated, the energy of the transition structure is predicted to be somewhat lower in either heptane or aqueous solution than in the gas phase. Although the energy lowering calculated for TS1 is smaller than the calculated for TS2 and TS3, it is very unlikely that the solvent effects may reverse the predicted preference of the fragmentation - recombination pathway over the concerted and stepwise ring closure-ring opening mechanisms.