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Owing to the possibility of generating theoretically unlimited numbers of ionic liquid (IL)-metal-organic framework (MOF) combinations, experimental studies on IL/MOF composites for gas separation applications are mostly conducted on a trial-and-error basis. To address this problem, an integrated computational-experimental hierarchical approach is presented for selecting the best IL-MOF combination for a target gas separation application. For this purpose, UiO-66 and pyrrolidinium-based ILs are chosen as the parent MOF and IL family, respectively, and three powerful computational tools, Conductor-like Screening Model for Realistic Solvents calculations, density functional theory calculations, and grand canonical Monte Carlo simulations, are integrated to identify the most promising IL-UiO-66 combination as 1-n-butyl-1-methylpyrrolidinium dicyanamide/UiO-66, [BMPyrr][DCA]/UiO-66. Then, this composite is synthesized, characterized in deep detail, and tested for CO2/N-2, CO2/CH4, and CH4/N-2 separations. Results demonstrate that [BMPyrr][DCA]/UiO-66 offers an extraordinary gas separation performance, with practically infinite CO2 and CH4 selectivities over N-2 at 15 degrees C and at low pressures. The integrated hierarchical approach proposed in this work paves the way for the rational design and development of novel IL/MOF composites offering exceptional performance for any desired gas separation application., Scientific and Technological Research Council of Turkey (TÜBİTAK); 1001-Scientific and Technological Research Projects Funding Program; European Research Council (ERC); Europian Union (EU); Horizon 2020; ERC-2017-Starting Grant; Research and Innovation Programme; COSMOS; HEC Pakistan Scholarship