Of course the instanton results are not perfect and deviate on average by about 20% from the experimental rates due to small inaccuracies in the electronic-structure theory as well as the semiclassical approximation and the neglect of real-time quantum-dynamical effects. Instanton theory thus predicts a smooth energydependence of the rate due to the statistical approximations, whereas the experiments demonstrate a small but complicated dependence on the initial state. This can probably not be predicted theoretically without explicitly run-ning time-dependent quantum-mechanical simulations, which would be completely impractical with current methods. We are therefore content to describe the underlying smooth part, which is almost constant over this range but is predicted to rise sharply at higher energies as shown in Fig. . Note that it is by no means trivial to recover this behavior of the microcanonical rates, which is not seen in the results of other methods. It is due to the fact that the cumulative reaction probability and the reactant density of states have a similar exponential growth at low energies, as depicted in Fig. SI.6.