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First, the simulation system consisted of a single monolayer ZIF-8 nanosheet and a gas molecule. ZIF-8 was modeled by force field parameters developed by Economou and co-workers (13, 31), while gas molecules were modeled by the united atom Trappe force field (32, 33). The crystal structures of ZIF-8 were taken from the recent publication (17). The periodic boundary condition (PBC) was applied to the xy direction of the system (the membrane plane), and the wall condition was applied to the z direction (vertical to the membrane plane). In the beginning, a gas molecule was put near the ZIF-8 nanosheet. The system was subjected to a 500-step steepest-descent energy minimization, and then an NVT (constant particle number, volume, and temperature) simulation was performed (leapfrog algorithm with a time step of 1 fs). The ZIF-8 nanosheet was flexible during the NVT simulation. The Nose-Hoover thermostat (34) was used to maintain a constant simulation temperature of 298.2 K. The short-range interactions were evaluated using a neighbor list of 10 Å that was updated every 10 steps, and the Lennard-Jones interactions were switched off smoothly between 8 and 9 Å. A long-range analytical dispersion correction was applied to the energy to account for the truncation of these interactions (35). The electrostatic interactions were evaluated using the reaction field method (36). In a normal NVT simulation where no pulling force was applied to the gas molecule, it could not pass the membrane even though the simulation time was extended to 500 ns. This is quite expected, since the size of gas molecules (propane, ~0.42 nm; propene, ~0.40 nm) was considerably larger than the window size of ZIF-8 (0.34 nm, with the flexibility of ZIF-8 taken into account). Thus, we applied a constant force of 50 kJ/(mol nm) to the gas molecule during the following NVT simulations, where the gas molecule passed through the membrane during a time course ranging from 0.1 to 50 ns, which depends on the specific gas molecule and the ZIF-8 phase. As for each specific gas molecule (propane or propene) + ZIF-8 phase (IEmbedded Image or Cm) membrane system, the simulation was repeated five times, and the average time it took the gas molecule to pass through the membrane was reported (table S4). The permeability was defined as the reciprocal of the time course, and the selectivity was defined as the ratio of permeability between propane and propene.Embedded Image

To better mimic the experiments, the other set of simulations were also performed, where a propane/propene molecule moved in bulk ZIF-8 membrane (IEmbedded Image or Cm phase) (PBC was applied to all xyz directions). A constant force of 100 kJ/(mol nm) was exerted to the gas molecule, and the time course it took to move 200 nm along the membrane thickness direction (z) was recorded (table S5).

The bulk modulus of the single monolayer and 200-nm-thick membrane was calculated from the fluctuation of the membrane volumeEmbedded Imagewhere Kbulk is the bulk modulus, V is the volume of the membrane, kB is Boltzmann’s constant, T is the temperature, and Embedded Image is the variance of the volume.

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