CYLINDRICAL MANIFOLDS IN PHASE-SPACE AS MEDIATORS OF CHEMICAL-REACTION DYNAMICS AND KINETICS .2. NUMERICAL CONSIDERATIONS AND APPLICATIONS TO MODELS WITH 2-DEGREES OF FREEDOM

In Paper I we discussed the existence of cylindrical manifolds embedded in phase space which mediate the dynamics of chemical reactions. A kinetic theory of population decays and decay rate constants was developed which we called "reactive island" (RI) theory. In this paper we discuss the details of the numerical implementation of the theory and then apply it to several molecular models (with two coupled degrees of freedom) representing isomerization between two and three states. Numerical simulations of population decays and asymptotic decay rate constants are compared to the RI theoretical predictions as well as the predictions from the purely random theory (PRT) and transition state theory (TST) of reactions. Of the ten systems studied we find that RI theory is generally in good to excellent agreement with the numerical simulations. Only one system exhibits significant deviation between the RI and numerical results. This deviation is seen to be a result of a strong intraconformer dynamical bottleneck. Finally, we compare the theoretical prediction and the numerical simulation for the average n-map mapping time T(rxn) and find that the agreement, within numerical error, is exact irrespective of the character of the dynamics (i.e., chaotic or regular).