High-resolution spectroscopy of hydrogen molecular ions (H2+ and its isotopes HD+, D2+...), the simplest molecules in nature, is currently one of the most promising methods to test the Standard Model at low energies and to improve the determination of fundamental constants. As several groups worldwide are developing experimental projects with very ambitious accuracy goals, it becomes increasingly important to improve the theory as well. This involves calculation of higher-order Quantum Electrodynamics (QED) corrections to the energy levels. Two possible topics are offered for the internship, and can be adapted to the applicant's preferences between theoretical and numerical work. The first one is to improve the theoretical hyperfine structure in HD+ by computing the proton-deuteron spin-spin interaction coefficient. The second one is to implement a new method to solve numerically the Dirac equation with high accuracy, which will be useful to calculate the one-loop self-energy correction in a fully relativistic framework.