Excitation functions from quasiclassical trajectory calculations on the H + H2O -> OH + H-2, H + HF -> F + H-2, and H + H'F - H' -> HF reactions indicate a different behavior at low and high vibrational excitation of the breaking bond. When the reactant tri- or diatomic molecule is in vibrational ground state or in a low vibrationally excited state, all these reactions are activated; 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., with decreasing translational energy 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 in their common form; instead, it can be interpreted in terms of an attractive potential acting on the attacking H atom when it approaches the reactant with a stretched X-H bond.