Unexpected acidic transformation of allylic menthene sulfoxides into saturated sulfones

Prolonged treatment of menth-4-en-3-yl sulfides with H₂O₂ in acidic medium leads to saturated menthan-3-yl sulfones, the same products having been obtained from menth-4-en-3-yl sulfoxides in acidic medium in the absence of H₂O₂. The mechanism was evaluated by quantum chemical calculations.