Electron-impact excitation of diatomic hydride cations I: HeH$^+$,
  CH$^+$, ArH$^+$
  {\bf R}-matrix calculations combined with the adiabatic nuclei approximation
are used to compute electron-impact rotiational excitation rates for three
closed-shell diatomic cations, HeH$^+$, CH$^+$, ArH$^+$. Comparisons with
previous studies show that an improved treatment of threshold effects leads to
significant changes in the low temperature rates, furthermore the new
calculations suggest that excitation of CH$^+$ is dominated by $\Delta J =1$
transitions as is expected for cations with a large dipole moment. A model for
ArH$^+$ excitation in the Crab Nebula is presented which gives results
consistent with the observations for electron densities in the range $2-3\times
10^3$~cm$^{-3}$.
