Trajectory calculations run on global potential energy surfaces have shown that the topology of the entrance channel has strong implications on the dynamics of the title reactions. This may explain why huge differences are observed between the rate constants calculated from global dynamical methods and those obtained from local methods that employ the same potential energy surfaces but ignore such topological details. Local dynamics approaches such as transition state-based theories should then be used with caution for fine-tuning potential energy surfaces, especially for fast reactions with polyatomic species since the key statistical assumptions of the theory may not be valid for all degrees of freedom.