Marked Influence of the Nature of the Chemical Bond on $CP$-Violating Signature in Molecular Ions ${\mathrm{H}\mathrm{B}\mathrm{r}}^{+}$ and ${\mathrm{H}\mathrm{I}}^{+}$

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 ${\mathrm{H}\mathrm{B}\mathrm{r}}^{+}$ and ${\mathrm{H}\mathrm{I}}^{+}$ 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 15. 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 ${\mathrm{H}\mathrm{B}\mathrm{r}}^{+}$ exhibits predominantly a covalent nature in ${\mathrm{H}\mathrm{I}}^{+}$. We conclude that because of this enhancement the ${\mathrm{H}\mathrm{I}}^{+}$ ion may be a potentially competitive candidate for the EDM search.