Is the Beckmann rearrangement a concerted or stepwise reaction? A computational study

[reaction: see text] RB3LYP calculations were performed on the Beckman rearrangement by the use of three substrates, acetone oxime (1), acetophenone oxime (2), and cyclohexanone oxime (3). Acidic solvents were modeled by H+ (CH3COOH)3 and H3O+ (H2O)6, and reaction paths were determined precisely. For 1, a two-step process involving a sigma-type cationic complex was obtained. For 2, a three-step process with pi- and sigma-type complexes was found in H+ (CH3COOH)3 and a two-step process involving a sigma-type cationic complex was obtained in H3O+ (H2O)6. However, for 3, a concerted process without pi and sigma complexes was calculated, which leads to the product, epsilon-caprolactam. Three different mechanisms were explained in terms of FMO theory.