Physisorption is an effective route to meet hydrogen gas (H) storage and delivery requirements for transportation because it is fast and fully reversible under mild conditions. However, most current candidates have too small binding enthalpies to H which leads to volumetric capacity less than 10 g/L compared to that of the system target of 40 g/L at 298 K. Accurate quantum mechanical (QM) methods were used to determine the H binding enthalpy of 5 linkers which were chelated with 11 different transition metals (Tm), including abundant first-row Tm (Sc through Cu), totaling 60 molecular compounds with more than 4 configurations related to the different number of H that interact with the molecular compound. It was found that first-row Tm gave similar and sometimes superior van der Waals interactions with H than precious Tm. Based on these linkers, 30 new covalent organic frameworks (COFs) were constructed. The H uptakes of these new COFs were determined using quantum mechanics (QM)-based force fields and grand canonical Monte Carlo (GCMC) simulations. For the first time, the range for the adsorption pressure was explored for 0-700 bar and 298 K. It was determined that Co-, Ni-, and Fe-based COFs can give high H uptake and delivery when compared to bulk H on this unexplored range of pressure.