  The identification of trajectories that contribute to the reaction rate is
the crucial dynamical ingredient in any classical chemical reactivity
calculation. This problem often requires a full scale numerical simulation of
the dynamics, in particular if the reactive system is exposed to the influence
of a heat bath. As an efficient alternative, we propose here to compute
invariant surfaces in the phase space of the reactive system that separate
reactive from nonreactive trajectories. The location of these invariant
manifolds depends both on time and on the realization of the driving force
exerted by the bath. These manifolds allow the identification of reactive
trajectories simply from their initial conditions, without the need of any
further simulation. In this paper, we show how these invariant manifolds can be
calculated, and used in a formally exact reaction rate calculation based on
perturbation theory for any multidimensional potential coupled to a noisy
environment.
