Recrossings and transition-state theory.

When classical trajectory calculations are run on the two isomerization reactions NCCN <==> NCNC and CH3CN right harpoon over left harpoon CH3NC over a long period of time, up to ca. 0.2 micros each, one finds many more recrossings than actual reactive events. In these calculations a "recrossing" is defined as passage over the potential barrier separating the two species followed by return to the original side within 0.2 ps. For the C2N2 case there are about twice as many crossings of the barrier as there are genuine reactive events, and for CH3CN, there are about 10 times as many. Long-term mean residence times, tau(infinity)CN and tau(infinity)NC, in reactant and product wells are compared with the corresponding mean first passage times, tau1(CN) and tau1(NC), the latter found by terminating the trajectories at the first crossing of the barrier. For the NCCN <==> NCNC reaction, except at the lowest energies, the mean residence times are exactly twice the mean first passage times, implying that the transition-state theory transmission coefficient, as traditionally defined, should be kappa = 0.5.