Open-site paddle wheels, comprised of two transition metals bridged with four carboxylate ions, have been widely used for constructing metal-organic frameworks with large surface area and high binding energy sites. Using first-principles density functional theory calculations, we have investigated atomic and electronic structures of various 3d transition metal paddle wheels before and after metal exposure and their hydrogen adsorption properties at open metal sites. Notably, the hydrogen adsorption is impeded by covalent metal-metal bonds in early transition metal paddle wheels from Sc to Cr and by the strong ferromagnetic coupling of diatomic Mn and Fe in the paddle wheel configurations. A significantly enhanced H-2 adsorption is predicted in the nonmagnetic Co-2 and Zn-2 paddle wheel with the binding energy of similar to 0.2 eV per H-2. We also propose the use of two-dimensional Co-2 and Zn-2 paddle wheel frameworks that could have strongly adsorbed dihydrogen up to 1.35 wt % for noncryogenic hydrogen storage applications.