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Marked influence of the nature of chemical bond on CP-violating signature in molecular ions $\mathrm{HBr}^{+}$ and $\mathrm{HI}^{+}$

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 $X ^2Π_{3/2}$ 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.