Abstract
Even if the interaction with the phonons does not mix the initial and final state of a reaction, it may help it by supplying an energy reservoir. Phonon couplings are different in the initial and final states. We demonstrate they may give or absorb the reaction energy by ways of multiple interactions. This process is a leading one for catalysis with weak mixing, i.e. a large class of reactions. Moreover the same phonon interaction is also responsible for desorption of the atoms or molecules. When catalysis and desorption are both taken into account, we show a compensation law occurs among a lot of similar catalysts.