Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / Section F / 46 / b / i / Solution

Choose a reaction coordinate $s(q)$ that is negative in the reactant region and positive in the product region; $s=0$ defines a dividing surface. With unnormalized canonical phase-space averaging, defineThe signed initial flux $\delta (s)\dot{s}$ counts both directions, while the later side function tests product commitment. The rate is $k=C_{fs}(t_{\mathrm{pl}})/Q_r$ on a plateau after microscopic recrossings have died away but before reactant depletion and global equilibration become important. The $t\to 0^{+}$ limit instead gives the transition-state-theory positive flux and can overcount trajectories that later return. A suitable dividing surface changes that early flux but not a correctly evaluated committed plateau rate. This correlation formulation provides the dynamical correction to a transition-state estimate.^[ref]