The umbrella sampling method is used to evaluate the potential of mean force (PMF) profiles for gas permeation through the oxygen-functionalized graphene pores at different temperatures. Force constants of 500-1000 kJ mol -1 nm -2 are used in the harmonic umbrella potential, and the zcoordinate of the probe gas molecule is varied from 2.0 to -2.0 nm in decrements of 0.05 nm, with the porous graphene located at z = 0. The probe gas molecule is free to move in the x-y plane bounded by the cylindrical region across the nanopore. This cylindrical region extends up to 2.0 nm into both the feed and permeate side of the nanoporous graphene and exhibits a diameter equal to the effective diameter of the nanopore (as determined in Figure ). This resulted in 81 windows along the z direction, and each window is sampled for at least 15 ns, where the first 1.0 ns is treated as the equilibration stage. The collected data is analyzed using a weighted histogram analysis method.