  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.
