Physisorption is an effective route to meet hydrogen gas (H-2) 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-2 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-2 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-2 that interact with the molecular compound. It was found that first-row Tm gave similar and sometimes superior van der Waals interactions with H-2 than precious Tm. Based on these linkers, 30 new covalent organic frameworks (COFs) were constructed. The H-2 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-2 uptake and delivery when compared to bulk H-2 on this unexplored range of pressure.