Metal-organic frameworks (MOFs) with open metal sites (OMS) are known to have selectivity in olefin/paraffin separations because of π-π interactions between olefin double bonds and OMS. One challenge associated with these separations is that other species that potentially bind to OMS may also be present in feed streams, causing competition for these sites. We used density functional theory (DFT) to assess the binding energy of ethylene, water, and carbon monoxide on a set of more than 60 MOFs with open Cu sites in the form of Cu dimers. One useful observation from our results is that the relative binding energies of pairs of molecules (e.g., ethylene and water) can be calculated accurately from calculations that hold the MOF structure rigid and only relax the positions of the adsorbing molecules. These kinds of calculations are far more numerically efficient than calculations that relax all degrees of freedom in the system, so this observation will be useful in future efforts to screen larger collections of materials. A second observation is that the binding energies of each molecule in the 60 MOFs are quite similar to the binding energies in CuBTC, an exemplar MOF with open Cu sites in the form of Cu dimers. Analysis of the variations that do exist in the binding energies among materials points to possible avenues for controlling either the absolute binding energies or the relative binding energies of species associated with OMS in these materials. The third observation is that two unusual MOFs can bind ethylene more strongly than water because of a dual-site binding mechanism in which an ethylene molecule can interact simultaneously with both dimers while the smaller water molecule interacts primarily with a single OMS. This observation suggests a possible avenue for developing other MOFs in which the binding energy of ethylene is higher than that of water.