Realistic master equation modeling of relaxation on complete potential energy surfaces: Partition function models and equilibrium results

To elucidate the role that potential surface topography plays in shaping the evolution of a cluster toward equilibrium, entire sets of kinetically accessible bound-state configurations and transition states on the model potential energy surfaces of (KCl)5 and Ar9 are mapped and compared. To describe the stochastic dynamics on these surfaces in terms of transition-state theory, we require adequate approximations of the partition functions of the minima and transition states. In this paper we introduce several partition function models derived from harmonic and anharmonic approximations and compare their predicted equilibrium population distributions with those determined from canonical-ensemble molecular dynamics. We perform this comparison for both (KCl)5 and Ar9 in order to evaluate the relative performance of the models for two different types of potential surfaces. For each system, particular models are found to give results that agree better with simulation than do the results using the simple harmonic approximation. However, no one unparameterized model gives acceptable results for all minima, and the best parameter-free strategies differ for (KCl)5 and Ar9. Nevertheless, a one-parameter version of one of the models is shown to give the best agreement with simulation for both systems. In an accompanying paper, the best partition function models are used to construct a stochastic master equation which makes predictions of relaxation behavior. These predictions are compared with results from molecular dynamics.