  Precision spectroscopy on cold molecules can potentially enable novel tests
of fundamental laws of physics and alternative determination of some
fundamental constants. Realizing this potential requires a thorough
understanding of the systematic effects that shift the energy levels of
molecules. We have performed a complete ab initio calculation of the magnetic
field effects for a particular system, the heteronuclear molecular hydrogen ion
HD+. Different spectroscopic schemes have been considered, and numerous
transitions, all accessible by modern radiation sources and exhibiting well
controllable or negligible Zeeman shift, have been found to exist. Thus, HD+ is
a perspective candidate for determination of the ratio of electron-to-nuclear
reduced mass, and for tests of its time-independence.
