  We report results of a theoretical investigation of hyperfine interactions in
two homonuclear isotopologues of the hydrogen molecule: H$_{2}$ and D$_{2}$. We
present a set of hyperfine coupling constants: spin-rotation, spin-spin dipole
and, in the case of the D$_{2}$ molecule, electric quadrupole coupling
constants for all bound states of the two isotopologues in their ground
electronic $X^{1}\Sigma^{+}_{g}$ state. We provide a list of positions and
intensities of 220 997 hyperfine components of 16 079 rovibrational quadrupole
transitions of the O, Q and S branches. The positions and intensities of the
hyperfine components are necessary for a reliable interpretation of accurate
measurements of rovibrational transition frequencies in H$_{2}$ and D$_{2}$,
which are used for tests of the quantum electrodynamics of molecules and
searches for new physics beyond the Standard Model.
