Ab initio and semiempirical calculations have been performed on the reaction mechanism of the Baeyer-Villiger reaction of acetone and performic acid. They focus, at the rate-limiting step (RLS), on the structures, energies, Mulliken charges, and what we refer to as evolution of the bond orders. The geometries of the Criegee intermediate, the methyl group migration transition state structure (TSs), and the product were found and optimized with the HF/4-21G, the HF/4-31G, and the HF/6-31G** basis sets of double-zeta quality in the ab initio methodology. AM 1, PM3, and MNDO were used in the semiempirical calculations. The correlation energies were also evaluated at the MP2/6-31G//HF/4-31G and MP2/6-31G** level of theory. A discussion dealing with the nature of the transition state structure (TSs) and its determination is presented, observing that irrespective of the method of calculation, the topology of the TSs and the general orientation of the transition vectors are invariant. From the calculations in vacuo, by using novel methodology, we find two reactive cycles : a central one, where the oxygen bonds break in close synchronicity with the methyl group migration, and a secondary one, where a proton is transferred. This proton seems to have protected the carbonyl oxygen from the attack of the methyl group. Scanning the movement of the proton, we can observe the effect that it produces on the atoms belonging to the reactive cycles and, interestingly, the lack of effect on those that do not belong to it. Finally, by using elliptic coordinates, we see that the atoms constituting both of the reactive cycles are found on ellipsoidal surfaces where the reactive centers are the foci.