Realistic master equation modeling of relaxation on complete potential energy surfaces: Kinetic results

Using the potential surface information for (KCl)5 and Ar9 and partition function models introduced in the preceding paper [Ball and Berry, J. Chem. Phys. 109, 8541 (1998)] we construct a stochastic master equation for each system using Rice–Ramsperger–Kassel–Marcus (RRKM) theory for transition rates between adjacent minima. We test several model approximations to reactant and transition-state partition functions by comparing their master equation predictions of isothermal relaxation for (KCl)5 and Ar9 with the results of molecular dynamics simulations of relaxations performed in the canonical ensemble. Accurate modeling of the transition-state partition functions is more important for (KCl)5 than for Ar9 in reproducing the relaxation observed in simulation. For both systems, several models yield qualitative agreement with simulation over a large temperature range. This full treatment of small systems using realistic partition function models is a necessary first step in the application of the master equation method to larger systems, for which one can only expect to have statistical samples of the potential energy surfaces.