2. SIMULATIONS METHODS
In this work, the MXene models were from the Computational 2D Materials Database (C2DB),41 which have been calculated and optimized except Ti2C model from the Material Project database.42 The simulation system box used for modeling various MXenes had approximate dimensions of 3.2×3.1×30 nm in three directions. The MXene nanopores with different diameters were constructed (Figure 1a ) by gradually removing the atoms closest to the MXene center (Figure 1b ), and their diameters were calculated using the Proeblazer 4.0 software (Figure 1c, the pore limiting diameter (PLD) value), with He as the probe atom. In the xy plane, periodic bounary conditions were applied, and reflective walls were placed along z direction at both ends of the box, as illustrated inFigure 1d . The MXene was placed at z = 15 nm to devide the box into two parts, the feed side and the permeate side. Non-equilibrium MD (NEMD) simulations were performed to simulate the relaxation process of gas molecules permeating from feed side to permeate side. For single gas simulations, 100 gas molecules were initially placed on the feed side randomly, and for mixed gases, 200 gas molecules (CH4 : He = 1:1) were placed on the feed side randomly. In the simulation, the atoms of MXene were fixed, while the gas molecules were allowed to diffuse from the feed side to the permeate side freely. To calculate the flow rate, each simulation was repeated for 5 times (with different initial positions for gas molecules), and the averaged result was reported. Furthermore, equilibrium MD (EMD) simulations were also performed to calculate the potential of mean force (PMF) when gas molecules permeating through the MXene nanopore, where both feed and permeate sides contain 50 gas molecules initially.
The LJ parameters of MXene atoms were taken from the UFF force field,43 with charges calculated by the Qeq method (Table S1) . The force field (FF) parameters of CH4 and He were from the transferable potentials for phase equilibria (TraPPE) force field and the work of Skoulidas et al .44, respectively. The LJ non-bonding parameters for different type of atoms were calculated by the Lorentz-Berthelot combination rule. These FF parameters have been proven to yield accurate results for a wide range of simulation studies.45-47In a typical simulation, energy minimization was performed using the conjugate gradient method, then followed by a 50 ns (if not otherwise specified) NVT MD simulation (T = 298.15 K, Velocity-rescale thermostat48). The cut-off distance of Lennard-Jones (LJ) and short-range coulomb interaction were set as 1.2 nm, with long-range coulomb interaction calculated using the reaction-field method.45 All simulations were performed with GROMACS version 5.1.549 and visualized with VMD 1.9.3.50 The simulation data and trajectory were analyzed with the MDanalysis package.51