The microcanonical rates are therefore accessible through an inverse Laplace transform of the thermal instanton rates. Because of the well-known difficulty of performing inverse Laplace transforms numerically, we employ a stationary-phase approximation to the transform, as successfully used in Refs. 92 and 93, which is stable and consistent with the semiclassical approximations taken to obtain Eq. ( ) from the exact quantum-mechanical rate. The density of states of the reactant is obtained from its partition function in an analogous manner.