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Use of the tritopic bridging ligand 1,3,5-benzenetristetrazolate (BTT^3-) enables formation of [Mn(DMF)₆]₃[(Mn₄Cl)₃(BTT)₈(H₂O)₁₂]₂·42DMF·11H₂O·20CH₃OH, featuring a porous metal−organic framework with a previously unknown cubic topology. Crystals of the compound remain intact upon desolvation and show a total H₂ uptake of 6.9 wt % at 77 K and 90 bar, which at 60 g H₂/L provides a storage density 85% of that of liquid hydrogen. The material exhibits a maximum isosteric heat of adsorption of 10.1 kJ/mol, the highest yet observed for a metal−organic framework. Neutron powder diffraction data demonstrate that this is directly related to H₂ binding at coordinatively unsaturated Mn²⁺ centers within the framework.