Five porous metal-organic frameworks based on linking zinc oxide clusters with benzene-1,4-dicarboxylate, naphthalene-2,6-dicarboxylate, 4,5,9,10-tetrahydropyrene-2,7-dicarboxylate, 2,3,5,6-tetramethylbenzene-1,4-dicarboxylate, or benzene-1,3,5-tris(4-benzoate) were synthesized in gram-scale quantities to measure their hydrogen uptake properties. Hydrogen adsorption isotherms measured at 77 K show a distinct dependence of uptake on the nature of the link. At 1 atm, the materials sorb between 4.2 and 9.3 molecules of H2 per formula unit. The results imply a trend in hydrogen uptake with the number of rings in the organic moiety.