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Hyperfine structure in the HD molecule

We investigate interactions between the proton spin, the deuteron spin, and the orbital angular momentum in the electronic ground state of the HD molecule. These interactions lead to hyperfine splittings of molecular energy levels. Our numerical results for the first rotational level agree well with the currently most accurate measurement performed by Ramsey {\em et al.} in the 1950s. Knowledge of the hyperfine structure of other levels is necessary for the accurate determination of rovibrational transition energies in spectroscopic measurements. We present theoretical predictions and share the numerical code used to perform numerical calculations. This work sets the ground for high precision spectroscopic tests of hyperfine interactions in molecular systems. In particular we determine the value of the deuteron quadrupole moment $Q = 0.2856(2)$ fm$^2$ and give outlook for improving its accuracy by three orders of magnitude.