The static and dynamic polarisability, and the Stark and black-body radiation frequency shifts of the molecular hydrogen ions H2+, HD+, and D2+

We calculate the DC Stark effect for three molecular hydrogen ions in the non-relativistic approximation. The effect is calculated both in dependence on the rovibrational state and in dependence on the hyperfine state. We discuss special cases and approximations. We also calculate the AC polarisabilities for several rovibrational levels, and therefrom evaluate accurately the black-body radiation shift, including the effects of excited electronic states. The results enable the detailed evaluation of certain systematic shifts of the transitions frequencies for the purpose of ultra-high-precision optical, microwave or radio-frequency spectroscopy in ion traps.