First-principles density functional and quantum Monte Carlo calculations of light-element doped fullerenes reveal significantly enhanced molecular ${\mathrm{H}}_{2}$ binding for substitutional B and Be. A nonclassical three-center binding mechanism between the dopant and ${\mathrm{H}}_{2}$ is identified, which is maximized when the empty ${p}_{z}$ orbital of the dopant is highly localized. The calculated binding energies of $0.2--0.6\text{ }\text{ }\mathrm{eV}/{\mathrm{H}}_{2}$ is suited for reversible hydrogen storage at near standard conditions. The calculated ${\mathrm{H}}_{2}$ sorption process is barrierless, which could also significantly simplify the kinetics for the storage.
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