The identification of membrane materials with high selectivity for CO(2)/CH(4) mixtures could revolutionize this industrially important separation. We predict using computational methods that a metal organic framework (MOF), Cu(hfipbb)(H(2)hfipbb)(0.5), has unprecedented selectivity for membrane-based separation of CO(2)/CH(4) mixtures. Our calculations combine molecular dynamics, transition state theory, and plane wave DFT calculations to assess the importance of framework flexibility in the MOF during molecular diffusion. This combination of methods should also make it possible to identify other MOFs with attractive properties for kinetic separations.