Metal-organic frameworks (MOFs) with open metal sites (OMS) are known to be selective for ethylene relative to ethane. In practical applications of this separation, the presence of other small molecules such as H2O, CO, and C2H2 may affect the suitability of sorbents. We used density functional theory (DFT) calculations to compute the binding energies of H2O, CO, C2H2, C2H4, and C2H6 in M-BTC (BTC = 1,3,5-benzenetricarboxylic acid) with 12 different metals forming OMS (M = Mg, Ti, V, Cr, Mo, Mn, Fe, Ru, Co, Ni, Cu, and Zn). To probe the generality of these results for MOFs containing other ligands, we performed similar calculations for metal-substituted MOFs based on four more materials with dimeric Cu sites. Our results provide useful insights into the variations in binding energies that are achievable by metal substitution in this broad class of MOFs, as well as pointing toward feasible adsorption-based separation strategies for complex molecular mixtures. Zn OMS MOFs were predicted to have the highest C2H4/C2H6 selectivity, but the strong binding energy of solvents and other small molecules in these materials may create practical challenges. We used DFT calculations to examine whether functionalizing linkers in these materials with electron withdrawing (-fluorine) and donating (-methyl) groups offer a useful way to tune molecular binding energies on OMS in these materials.