  Heavy polar molecules offer a great sensitivity to the electron Electric
Dipole Moment(EDM). To guide emerging searches for EDMs with molecular ions, we
estimate the EDM-induced energy corrections for hydrogen halide ions
$\mathrm{HBr}^{+}$ and $\mathrm{HI}^{+}$ in their respective ground $X
^2\Pi_{3/2}$ states. We find that the energy corrections due to EDM for the two
ions differ by an unexpectedly large factor of fifteen. We demonstrate that a
major part of this enhancement is due to a dissimilarity in the nature of the
chemical bond for the two ions: the bond that is nearly of ionic character in
$\mathrm{HBr}^{+}$ exhibits predominantly covalent nature in $\mathrm{HI}^{+}$.
We conclude that because of this enhancement the HI$^+$ ion may be a
potentially competitive candidate for the EDM search.
