For the following Widom insertion simulation, A grid with a spacing of 0.15 Å was generated to define potential insertion points across the unit cells. Grid points located within 1.5 Å of the central positions of gas molecules, such as the C atom in CO₂ and the O atom in H₂O, were excluded to avoid inserting molecules into blocked regions. In each iteration, a gas molecule was randomly rotated and placed at grid points, and their interaction energies between frameworks and gas molecules were calculated using MLFFs. To enhance statistical reliability, two independent Widom insertion simulations were performed, with each consisting of 10,000 insertions. The results from these simulations were averaged to calculate the final KH and Qst.