Energetics and dynamics of H$_2$ adsorbed in metal-organic frameworks from a van der Waals density functional approach

We performed van der Waals-density-functional calculations of the hydrogen adsorption in metal-orgnic frameworks.\footnote{M. Dion et al. PRL 92,246401(2004); T. Thonhauser et al. PRB 76,125112(2007).} The quantum dynamic behavior of the adsorbed dihydrogen is studied. The low-lying energy levels of the hindered rotational, frustrated translational and vibrational motions are calculated and compared with experimental inelastic neutron scattering and IR measurements. A consistent picture is obtained. Zero point energies due to the rotational and translational motions are estimated to be around 10 meV and 15 meV, respectively. The zero-point corrected binding energies agree with the measured isosteric heat of adsorption.