Efficient and Accurate Methods for Characterizing Effects of Framework Flexibility on Molecular Diffusion in Zeolites: CH4 Diffusion in Eight Member Ring Zeolites

Molecular dynamics (MD) and transition state theory (TST) methods are becoming efficient tools for predicting diffusion of molecules in nanoporous materials. The accuracy of predictions, however, often depends upon a major assumption that the framework of the material is rigid. This saves a considerable amount of computational time and is often the only method applicable to materials for which accurate force fields to model framework flexibility are not available. In this study, we systematically characterize the effect of framework flexibility on diffusion in four model zeolites (LTA, CHA, ERI, and BIK) that exhibit different patterns of window flexibility. We show that for molecules with kinetic diameters comparable to (or larger than) the size of the window the rigid framework approximation can produce order(s) of magnitude difference in diffusivities as compared to the simulations performed with a fully flexible framework. We also show that simple recipes to include the effect of framework flexibility are not generally accurate. To account for framework flexibility effects efficiently and reliably, we introduce two new methods in which the flexible structure is approximated as a set of discrete rigid snapshots obtained from simulations of dynamics of an empty framework, using either classical or, in principle, ab initio methods. In the first method, we perform MD simulations of diffusion in a usual manner but replace the rigid structure with a new random snapshot at a certain characteristic frequency corresponding to the breathing motion of the window, while keeping positions of adsorbate molecules constant. In the second method, we directly compute cage to cage hopping rates in each rigid snapshot using TST and average over a distribution of snapshots. Excellent agreement is obtained between diffusivities predicted with these two new methods and direct MD simulations using fully flexible structures. Both methods are orders of magnitude more efficient than the simulations with the fully flexible structure. The new methods are broadly applicable for fast and accurate predictions of both infinite dilution and finite loading diffusivities of simple molecules in zeolites and other nanoporous materials, generally without the need for an accurate flexible force field.