Hyperfine components of all rovibrational quadrupole transitions in the H$_{2}$ and D$_{2}$ molecules

Abstract: 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.