  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.
