Transition State Theory Methods To Measure Diffusion in Flexible Nanoporous Materials: Application to a Porous Organic Cage Crystal

Transition state theory (TST) methods are useful for predicting adsorbate diffusivities in nanoporous materials at time scales inaccessible to molecular dynamics (MD). Most TST applications treat the nanoporous framework as rigid, which is inaccurate in highly flexible materials or where adsorbate dimensions are comparable to the size of pore apertures. In this study, we demonstrate two computationally efficient TST methods for simulating adsorbate diffusion in nanoporous materials where framework flexibility has a significant influence on diffusion. These methods are applied to light gas diffusion in porous organic cage crystal 3 (CC3), a highly flexible molecular crystal that has shown promise in gas separation applications. Diffusion in CC3 is modeled as a series of uncorrelated adsorbate hops between cage molecules and the voids between adjacent cages. The first method we applied to compute adsorbate hopping rates in CC3 is implicit ligand sampling (ILS). In ILS TST, hopping rates are calculated in an ensemble of rigid framework snapshots captured from a fully flexible MD trajectory of the empty CC3 structure. The second TST method we applied is umbrella sampling (US), where hopping rates are computed from a series of biased MD simulations. Our ILS and US TST calculations are shown to agree well with direct MD simulation of adsorbate diffusion in CC3. We anticipate that the efficient TST methods detailed here will be broadly applicable to other classes of flexible nanoporous materials such as metal-organic frameworks.