Excitation functions from quasiclassical trajectory calculations on the H + H2O → OH + H2, H + HF → F + H2 and H + H’F → H’ + HF reactions indicate a different behavior at low and high low and high vibrational excitation of the breaking bond. All these reactions are activated when the reactant tri- or diatomic molecule is in vibrational ground state or in low vibrationally excited states. i.e. there is a nonzero threshold energy below which there is no reaction. In contrast, at high stretch excited states capture-type behavior is observed, i.e. at low translational energies the reactive cross section diverges. The latter induces extreme vibrational enhancement of the thermal rate consistent with the experiments. The results indicate that the speed-up observed at high vibrational excitation is beyond the applicability of Polanyi’s rules; instead, it can be interpreted in terms of an attractive potential acting on the attacking H atom when it approaches t he reactant with a stretched X-H bond.