Statistical properties of quantum probability fluctuations in complex-forming chemical reactions

The energy dependence of quantum complex-forming reaction probabilities is well known to involve sharp fluctuations, but little seems to be known about their amplitudes. We develop here, for triatomic reactions, an analytical approach of their statistical distribution. This approach shows that the fluctuation amplitudes depend essentially on the number of available quantum states in the reagent and product channels. Moreover, the more numerous the product states, the more efficiently the fluctuations of their populations compensate each other when they add up to give the reaction probability. The predictions of our approach appear to be in good quantitative agreement with quantum scattering calculations for the prototypical reaction H⁺ + H₂.