Storing molecular hydrogen in porous media is one of the promising avenues for mobile hydrogen storage. In order to achieve technologically relevant levels of gravimetric density, the density of adsorbed H2 must be increased beyond levels attained for typical high surface area carbons. Here, we demonstrate a strong correlation between exposed and coordinatively unsaturated metal centers and enhanced hydrogen surface density in many framework structures. We show that the MOF-74 framework structure with open Zn2+ sites displays the highest surface density for physisorbed hydrogen in framework structures. Isotherm and neutron scattering methods are used to elucidate the strength of the guest−host interactions and atomic-scale bonding of hydrogen in this material. As a metric with which to compare adsorption density with other materials, we define a surface packing density and model the strength of the H2-surface interaction required to decrease the H2−H2 distance and to estimate the largest possible surface packing density based on surface physisorption methods.