Hydrogen storage in a metal-organic-framework structure from a nonempirical van der Waals density functional approach*

Hydrogen adsorption in the metal-organic-framework structure Zn$_2$(BDC)$_2$(TED) (BDC=benzenedicarboxylate; TED=triethylenediamine) is studied using a van der Waals-density-functional approach.\footnote{M. Dion et al., PRL {\bf 92}, 246401 (2004); T. Thonhauser et al., PRB {\bf 76}, 125112 (2007).} Two types of adsorbtion sites are located in the structure. The binding energies and the number of such sites are in good agreement with the values obtained from the experimental isotherms and isosteric heat of adsorption.\footnote{J.Y. Lee et al., Adv. Func. Mater. {\bf 17}, 1255 (2007).} The stretching mode frequency of the adsorbed H$_2$ is calculated for various H--H bond orientations at the two positions. The frequency changes by approximately $-30$ cm$^{-1}$ for the strongest binding direction at each of the two points, which is consistent with the measured infrared absorption band measured at 4120 cm$^{-1}$ at room temperature and high pressures (300-800 psi).