Abstract We propose a reassessment of quadrupole radiative association and dissociation for the formation, destruction, and detection of molecular hydrogen in the early universe and in very cold molecular clouds by taking into account orbiting (shape) resonances. We provide accurate data needed for the modeling of this mechanism—namely, the energies and lifetimes of all the orbiting resonances up to J = 30 in the ground electronic state ( <?CDATA ${X}^{1}{{\rm{\Sigma }}}_{g}^{+}$?> ) and the energies and quadrupole matrix elements for all the associated resonance–resonance and resonance-bound rovibrational transitions.