  Molecular hydrogen ions are of metrological relevance due to the possibility
of precise theoretical evaluation of their spectrum and of
external-field-induced shifts. We report the results of the calculations of the
rate of laser-induced electric quadrupole transitions between a large set of
ro-vibrational states of ${\rm H_2^+}$. The hyperfine and Zeeman structure of
the E2 transition spectrum and the effects of the laser polarization are
treated in detail. We also present the nuclear spin-electron spin coupling
constants, computed with a precision 10 times higher than previously.
