  Chemical reactions in multidimensional driven systems are typically described
by a time-dependent rank-1 saddle associated with one reaction and several
orthogonal coordinates (including the solvent bath). To investigate reactions
in such systems, we develop a fast and robust method ---viz., local manifold
analysis (LMA)--- for computing the instantaneous decay rate of reactants.
Specifically, it computes the instantaneous decay rates along saddle-bound
trajectories near the activated complex by exploiting local properties of the
stable and unstable manifold associated with the normally hyperbolic invariant
manifold (NHIM). The LMA method offers substantial reduction of numerical
effort and increased reliability in comparison to direct ensemble integration.
It provides an instantaneous flux that can be assigned to every point on the
NHIM and which is associated with a trajectory ---regardless of whether it is
periodic, quasi-periodic, or chaotic--- that is bound on the NHIM. The time
average of these fluxes in the driven system corresponds to the average rate
through a given local section containing the corresponding point on the NHIM.
We find good agreement between the results of the LMA and direct ensemble
integration obtained using numerically constructed, recrossing-free dividing
surfaces.
