= 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, define
$$
C_{fs}(t)=\frac1{(2\pi\hbar)^f}\int dq\,dp\,e^{-\beta H(q,p)}\,\delta[s(q)]\dot s(q,p)\Theta[s(q_t)].
$$
The signed initial flux $\delta(s)\dot s$ counts both directions, while the later side function tests product commitment. The rate is \b[$k=C_{fs}(t_{\rm pl})/Q_r$] on a plateau after microscopic recrossings have died away but before reactant depletion and global equilibration become important. The $t\to0^+$ 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.<Statistical mechanics of isomerization dynamics in liquids and the transition state approximation by David Chandler>[Journal of Chemical Physics 68, pp. 2959–2970: rate correlation functions and recrossing]{ref}
Back to article page
