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Hydrogen molecular ions play an important role for accurate quantum electrodynamics calculations of rovibrational energy levels [1] and the comparison with laser spectroscopy results [2] allowed probing fundamental physics constants and laws. Advances are driven by an accurate control of the external and internal molecular degrees of freedom with a wide range of techniques [3]. Experimental setups with HD+ ions are based on ions in a linear Paul trap and sympathetically cooled to the Lamb-Dick confinement regime by a laser-cooled atomic ion (Be+). Optical transitions allowed rotational cooling [4] and state-resolved detection by resonant-enhanced-multiphoton dissociation (REMPD) [5]. This contribution reports numerical results on the use of a two-photon rotational transition in the terahertz frequency range for preparation of trapped HD+ ions in the rovibrational ground state and for high-resolution spectroscopy.