Diffuse reflectance infrared spectroscopy is used to measure the quantum dynamics of molecular hydrogen adsorbed in the microporous material MOF-5. Low-temperature spectra reveal at least three distinct binding sites. The induced redshifts in the vibrational mode frequencies allow the estimation of site-specific binding energies ranging from 2.5 to 4 kJ/mol. Splittings in the rovibrational sidebands are consistent with the existing theories and indicate that H 2 is relatively freely rotating even at temperatures as low as 10 K. Ortho to para conversion of the adsorbed H 2 is observed to occur over the course of several hours. A translational sideband of 84 cm −1 arises from the center-of-mass motion of H 2 at the primary adsorption site and indicates that the zero-point energy is a substantial fraction of the binding energy of this site.