where N is the number of gas molecules and 𝑟 𝑡 is the position of molecule 𝑖 at time 𝑡. MSD is calculated from the ensemble average ⟨ ⋯ ⟩ of the trajectory, and we use the multiple-origin method to improve the statistical accuracy. In addition, to account for molecular adsorption to the polymer membrane at the saturation state, we consider the diffusivity of different numbers of gas molecules: 5, 10, 20, 30, 40, 50, and 100. We find that using 20, 30, or 40 gas molecules result in similar diffusivities, which are averaged to give the calculated diffusivity. Finally, based on the solution-diffusion mechanism, gas permeability (𝑃 ) in a polymer membrane can be expressed as the product of the diffusivity (𝐷 ) and the solubility constant (𝑆 ). As summarized in Table of Supporting Information, our benchmark study on the solubility, diffusivity, and permeability of five pertinent gases (H2, N2, O2, CO2, and CH4) in a PIM-1 membrane agrees well with available experimental data and simulation results , which suggests that our MD model and method are physically reasonable.