Modeling cage-to-cage dynamics of adsorbates at arbitrary loadings with dynamically corrected transition-state theory

Transition state theory (TST) formalisms have allowed researchers to extent the time and length scales accessible to the modeling of diffusion in microporous materials. In a previous paper (Tunca, C.; Ford, D. M. J. Chem. Phys. 1999, 111, 2751), we used multidimensional TST to obtain the escape rate of adsorbate molecules from an α cage in zeolite ZK4 as a function of loading. A physically reasonable approximation was applied to make the TST partition functions tractable, and they were evaluated with a nested Widom insertion scheme. However, that study was limited to the case of empty neighboring cages and nondynamically corrected rate constants. This paper extends the work in several ways. First, we consider the effects of adsorbate occupancy in the neighboring cages. Our results show that the TST escape rates increase with loading in the original cage but show nonmonotonic behavior with respect to loading in the destination cage. Furthermore, we employ an expanded ensemble method (EEM) to obtain the partition functions, thus avoiding the limitations associated with the Widom insertions used previously. Even at high cage loadings, the results have small statistical errors due to the use of the EEM. Finally, we calculate and present dynamical corrections to the rate constants. The dynamical corrections are rather modest in magnitude for this model system, typically representing changes of about 10% relative to the TST values.