The availability of accurate computational tools for modeling and simulation is vital to accelerate the discovery of materials capable of storing hydrogen (H2) under given parameters of pressure swing and temperature. Previously, we compiled the H2Bind275 data set consisting of equilibrium geometries and assessed the performance of 55 density functionals over this data set (Veccham, S. P.; Head-Gordon, M. J. Chem. Theory Comput. 2020, 16, 4963-4982). As it is crucial for computational tools to accurately model the entire potential energy curve (PEC), in addition to the equilibrium geometry, we extended this data set with 389 new data points to include two compressed and three elongated geometries along 78 PECs for H2 binding, forming the H2Bind78 × 7 data set. By assessing the performance of 55 density functionals on this significantly larger and more comprehensive H2Bind78 × 7 data set, we identified the best performing density functionals for H2 binding applications: PBE0-DH, ωB97X-V, ωB97M-V, and DSD-PBEPBE-D3(BJ). The addition of Hartree-Fock exchange improves the performance of density functionals, albeit not uniformly throughout the PEC. We recommend the usage of ωB97X-V and ωB97M-V density functionals as they offer good performance for both geometries and energies. In addition, we also identified B97M-V and B97M-rV as the best semilocal density functionals for predicting H2 binding energy at its equilibrium geometry.